THE BOOK--Playing The Percentages In Baseball

Wow, 12 mil!

Francouer last year was -25.1 in everything adjusted batting lwts.  BIS UZR has him at -7.  STATS UZR has -16.  We’ll split the difference to -11.  His arm rating is +2 runs.  His baserunning was +2.

That is a total of (do I really need to add these up?) -34 runs.  With a positional adjustment of 10 runs, that is -44 runs, which is a tad below replacement level.

I don’t really get what JC is saying/doing here.  If you get lots of points for “just showing up” then I don’t see the point of his evaluation system.

If the by far and away worst player in the major leagues (based on actual context-neutral stats, not by talent), a full 25 runs worse than replacement, is worth 12 mil…

Now, obviously there are other ways of measuring actual value - WPA, Runs+RBI-HR, etc.  Context neutral lwts is certainly not THE way - in a sense they are meaningless, except to use to compute an estimate of a player’s true talent and future performance.  Is there some other measure that suggests that Frenchy was a league average player in 1008?

Now I’ll go and read the article/blog entry to see what he (JC) is doing.  Hopefully it will shed some light on what seems to be a ridiculous assertion.

I almost feel like reading his book to see how he designed a system that could get things so incredibly wrong…

JC said:

“He is well below average.  An average player who had played as much as Francoeur would have been worth more.”

He also said:

“Pujols’s 2008 MRP = $26.7 million.”

Ok, so he says that Frenchy is well-below average, and that is worth 12MM.  How much is average worth?  Hard to tell, but if French is well-below average, and Pujols is far above average, then, what, 16MM for average?  That sets Frenchy at 4MM below average and Pujols at 10MM above average?

It’s impossible to accept that the gap between French and Pujols is only $14MM (in 2008), and that the average player would be, say 16MM$.  At least this explains why he had Ibanez so incredibly high earlier.

He also suggested to someone to read his book. I think he means p. 321, footnotes 77-79, if someone wants to go through it.

He also says:
“In my book, I report that position players tend to receive 77 percent less than their estimated marginal revenue product during their fourth through sixth years of service”

I estimate they earn 50% less than they would as free agents. 

Now, the only way to reconcile our two positions is that the player’s MRP is far higher than he actually earns.

So, let’s say that the average player’s MRP is $16MM, but that he is actually paid $12MM as a free agent, and $6MM for years of service 4 through 6.  So, that sort of puts JC’s model and mine much closer.  But, I don’t think JC would accept that a player would earn, as a free agent, 75% of his MRP, as I’m sure I read on his site that he’s going to earn close to 100%.

Anyway…

In about two years of reading Sabernomics (the website, not the book), JC was never wrong about anything, ever.  I’ve long since deleted the bookmark.  I’m starting to think it’s a professor thing, because the only two other folks I’ve read that delved into baseball stats and refused to admit their mistakes were Art De Vany and Steve Levitt.  I can only hope these guys are more open to debate in their classrooms than they are in their blogs’ comments.

There is nothing in the article that indicates what methodology he is using to value players.  All he does is say that a “major league caliber player is worth a lot of money.” Francoeur is likely a major league caliber player who had an awful year last year. If you are to value his true talent estimate or his projection for 2009, it might be 12 mil. But his actual production last year, at least in terms of context neutral lwts, was worth nothing, at least as compared to a replacement player playing for the major league minimum.

Is it just me, or is JC talking about how much revenue a player is responsible for bringing into the team’s coffers and here we’re talking about how much salary he should be paid?

Well, MRP is marginal revenue product.  JC is an economist or econometrician.  He or someone else can explain what MRP means in relation to baseball players.  Salaries in baseball are on the order of 50% of total net revenues (or is it gross), no?  If that is the case, then a win could be worth 10 mil in net or gross revenues, no? (Of course, no matter how you look at it, since Frenchy was so far below replacement level in 2008, he was really worth nothing.) I really don’t know.  Does it really matter?  The only things we care about are one, a player’s marginal runs or wins above some baseline, either actual in any given year, or an estimate of true talent which is the same thing as a projection, and how much money in salary that is worth given what is being paid to other players (depending upon what year of service they are in), and how much extra revenue a win provides to a given team, given their chances of making the post-season, what their expected wins are without the player, etc.  Once we start using words like MRP (or whatever) we confuse the issue - at least if we are not all economists.

I don’t think it is fair to criticize JC without him or someone else explaining what he means.  If I say that Francouer was worth 28 million in FWZ last year, should I be attacked and criticized.  I made up FWZ of course.

Now, if JC says that given what players are currently being paid, that on average, a team should fairly pay a player whose expected stats are similar to Frechy’s 2008 stats, then we can start criticizing and attacking.  I am not at all sure that JC is saying anything like that. In fact, I have no idea what he is saying (what the 12 mil means) and so far no one else has tried to explain it either.  He may be talking about something completely different than we are talking about.  I would simply like to hear an explanation.

MRP is marginal revenue product—in baseball terms, it’s value over replacement. Theoretically, players are paid the revenue that they bring in over a replacement-level player (their MRP), and reality generally matches with that theory (though in baseball I would argue, it does not, for many reasons). Anyway, JC’s estimate is clearly off here. I don’t see the point of arguing about this, however—no one is going to change their mind, so what’s the point?

You don’t pay a player (or person) 100% of the marginal revenue they provide/produce, right?  You pay them some percentage of that, and keep the rest for yourself.

There is no point in arguing, because I don’t see that anyone knows what they are arguing about, especially since the person with whom they are arguing is not even participating in the argument.

Like Matt in #6, I think that the difference between how much revenue a player is estimated to bring in versus how much he is paid needs to be taken seriously. For example, what if a player who is not so good brings in more revenue than a player of better quality? Do you pay him more? As a fan I would say no, because I think that a player should be paid for his performance on the field. Looking at it from the purely business point of view of an owner however, I might say yes, because I am presumably in it to make money. Of course, there are owners in all pro sports who take the fans point of view and would rather win it all than maximize profit. The Braves were like that under Ted Turner during their salad years, as were the Yankees when George Steinbrenner was in charge of the club.

I’ve read JC’s site before so without clicking on today’s link, I think I know where this is going.  He’s got a valuation model, but he’s not going to explain it until he publishes his next book.

Which makes this suggestion “If you would like to point to where the model is making mistakes” pretty meaningless.

When he comes out and says that the worst regular player in baseball was worth 12 million dollars, he’s making an incredible claim, and the burden of proof is on him.

He had Pat Burrell and Raul Ibanez worth much more than we around here think they are worth, and more even than those two got in free agent money (14-16 million I think).  But then he had Derek Lowe right around where I had him, and right around where the Braves signed him. 

It’s possible that as far as marginal revenue gained, a run scored may be worth more than a run saved, so if where looking at it from a standpoint of teams making money it looks a little different than maximizing team wins.  But from what I have seen, his model does NOT do that.  He’s looking at wins added, and somewhere mangles the numbers to the point where before I found his formula a bit curious, but now with Frenchy I can’t even begin to take it seriously.

I ditto Rally/11 word-for-word, and he did it with more brevity and clarity than I could have done it.

JC said this in the comments as well:

“If there was one concept that I could remove from sabermetrics it would be “replacement level.” It is a concept that adds nothing to our understanding of player value, and it causes people to believe that marginal players are worth the league minimum. I have explained why this is incorrect, and I have seen no argument to change my thinking on this.”

I don’t know where to begin.  It’s simple supply and demand.  There are limited major league spots available.  If you have an outfielder hitting at what we measure as replacement level or below, then there are many, many players without big league jobs who could do just as well and would kill for a job.  Why is Brandon Jones worth less than 400K (whatever me made in the minors plus his brief time in the majors) and Frenchy is worth 12 million?  It has nothing to do with the performance of the players and everything to do with the decision by the team.  Just a terrible way to value performance.

I do agree with JC that replacement level is not important.  Indeed, using my “sanity check” illustration in the main thread, I say that a league average player playing full-time would get $6MM.

If we accept that the $ per win is around 2.5MM, then at what “x” point (wins) is the intercept zero (0$ dollars, or if you want 400,000$).  Well, if you set x=-2.25 wins, then y=375,000$.

So, it’s the EXACT SAME THING, to say that a player’s salary is:
salary = (wins above average)*2.5 + 5.6*games/162 + 0.4

As it is to say:
salary = (wins above replacement)*2.5 + 0.4

If you play 162 games at the league average, you get $6MM in either case.

If you play 81 games at the league average, you get $3.2MM in either case.

If you play 162 games at 1 win below average, you get $3.5MM in either case.

So, the exact same thing.

The only issue is where does that $2.5MM per win come from.  That’s the number that ties the two equations together to make them equal.  And, I would argue here that it is because of the replacement level that that 2.5MM is true.  So, on this issue, I disagree with JC that it is not important.  It becomes the centering point.

In any case, the simplicity of explaining replacement level, as well as the simplicity of the equation itself, makes replacement level a good concept to know.

I don’t think this is necessarily what JC is thinking, but it is possible Francoeur made the Braves $12M last year, possibly due to qualities that he has over a “replacement player”.  For example, his previous performance and his local roots may have people paying more money (in merchandise, ticket sales, etc) than his on field performance would merit. 

(A great example of this in the cartoons would be Leela from Futurama as the only woman in baseball, who beans every batter she faces.  She’s totally worthless to the teams performance, but she really boosts the ticket sales).

It’s not at all what JC said:

Even during his awful 2008 season, his marginal revenue product (MRP) contribution for his play in the field was approximately $12 million.

Has anyone actually read The Baseball Economist? JC makes it sounds like his model is explained ("explained"?) in there. Reading through the comments though, whatever JC is doing is making less and less sense.

Yes, I own the book, and I cited the likely pages he is referring to in post 3 above.

# # 27 Sky Says:
January 22nd, 2009 at 5:34 pm

JC, it’s kind of tough to admit you’re right or feel confident I’m right without having any clue about what MRP is.  I’m curious, however.

Have you done any research about the increase in revenue caused by increasing win totals, especially the importance of going from low 80s to low 90s?  (Just out of playoffs to just in playoffs.) That’s an area I think traditional sabermetrics misses the boat.

# # 28 JC Says:
January 22nd, 2009 at 6:22 pm

Sky,

You’re asking me to answer things that I addressed in a book that was published nearly two years ago. The system is too complex to explain fully in a blog post or comment. Read mybook if you want those questions answered.

You guys gave it your best shot, being respectfully inquisitive, but I don’t think we’re going to get any closer to an answer here.

You don’t pay a player (or person) 100% of the marginal revenue they provide/produce, right?  You pay them some percentage of that, and keep the rest for yourself.

---

No, in economic theory, you are paid your full marginal product (because firms will bid up your price until they are indifferent, i.e. there is no profit to be made by bidding further), though like I said, it is a bit more complicated in baseball given that (a) your marginal product is not the same for every team, and (b) teams are not fully rational economic operators (i.e. owners will sometimes overpay because winning is worth more than profit for them).

Again, depends on what he means by “so-and-so is worth”.  Once that is defined, there really is no argument.

If what he means is that if we can anticipate a player (any player) playing full time next year and putting up the numbers that JF put up in 2008, an average team should pay him around 12 mil (because they would make money in doing so), then of course he is dead wrong.  If he means JF in particular, and not some random player, then he might be right if there is something about JF (his charm, his looks, etc.) that puts more than $12mm of fannies into the seats, as well as Jersey’s and beer mugs sold.  If that is his contention, I would sure like to see some evidence to support that.

However, if he means something else, other than that, which it appears that he does, then I am all ears.  Otherwise there is nothing left to discuss.

A player is worth to a team whatever marginal revenue he provides to that team.  All the research that I have seen indicates that that is based upon the marginal number of wins/runs that that player provides as compared to any baseline you want (replacement, average, whatever) plus the positive or negative marquis value of the player.  There is obviously a league-wide average $ value for a marginal win/run.  However, on a case by case basis, we are pretty sure that that number varies tremendously from team to team and from year to year.  And it also obviously varies with the service time of the player. When we talk about the value of a player, we are usually talking about that league-wide average number, adjusted for service time.  The reason we usually talk about it that way is because that is the most important number that determines a player’s salary no matter who pays that salary.  For example, if a marginal win in 2006 is only worth 1mm to the Royals, good luck to them trying to sign someone for 1mm per win.  That ain’t going to happend when many other teams are willing and able to sign the same player for 4 or 5mm per win. At the same time, a marginal win in 2008 to the Yankees before the season started might have been worth 10mm to them.  Do they have to pay that kind of money to the FA that they sign, even though they could and still make money?  Of course not.  They only need to pay a little more than the average team.  So and and so forth.

I’ll repeat what he said:

“Even during his awful 2008 season, his marginal revenue product (MRP) contribution for his play in the field was approximately $12 million.”

That’s pretty clear, isn’t it?

"If what he means is that if we can anticipate a player (any player) playing full time next year and putting up the numbers that JF put up in 2008, an average team should pay him around 12 mil (because they would make money in doing so), then of course he is dead wrong.”

Yes, that is essentially what he is saying.  Or more precisely, he’s saying that JF generated $12M in revenue for the Braves with his 2008 on-field performance (with no “box office” factor considered), and so was worth $12M to the Braves (how much of that he should be paid is a somewhat separate issue). 

And of course, that’s absurd.  If the worst player in baseball generates $12M, then the average position player must generate what, maybe $16M?  But that means all of a team’s revenue (actually, more than 100%) is generated by the players.  Which is clearly not true.  A team of the 25 worst players, all paid league minimum, would still have considerable revenues.  To credit that to the players is silly.  It’s the franchise—the right to perform “major league” baseball games, and play against major league opponents, that generates a lot of the revenue.  Why else would someone pay $900M to own the Cubs?

A commenter at JC’s site asked the $12M question:  “JC, please forgive my basic question, but what does the “marginal” in MRP represent?.... So Frenchy produced $12M more revenue than what? than zero?” This is the question JC can’t/won’t answer.  Maybe the Braves would be $12M worse off if they left RF empty, letting balls roll to the fence, and took an automatic out for his spot in the lineup.  Who knows?  But that’s not the choice the Braves face.  And JF’s on-field performance added virtually no revenue beyond what a league-minimum player would generate.

A commenter at JC’s site asked the $12M question:  “JC, please forgive my basic question, but what does the “marginal” in MRP represent?.... So Frenchy produced $12M more revenue than what? than zero?” This is the question JC can’t/won’t answer.  Maybe the Braves would be $12M worse off if they left RF empty, letting balls roll to the fence, and took an automatic out for his spot in the lineup.

Well, maybe that IS what he means.  As I keep saying, you can’t criticize what he is saying without knowing what the heck he means.  To answer Tango’s (presumably) rhetorical question in #22 above, no, it is NOT clear what he means.

I agree completely with Guy/23.

JC says that Pujols’ MRP was $27M in 2008. Pujols was about +70 batting runs above average, +10 fielding by bUZR, -10 for position, +20 for replacement makes +90 runs, so +9 wins. Let’s be generous to Francoeur and give him -1.5 wins, which is what Dave Cameron has on his Fangraphs page. The difference is 10.5 wins. Meanwhile the difference in MRP is $15M.

So, the MRP for one extra win under JC’s system is about $1.5M. ($1.43M by these numbers.) Of course it will vary depending on market size, place on the win curve, etc.

In 2008, MLB reported $6.5B in revenue (link). That is $217M per team.

Pretend that everything is linear. Then JC’s model dictates that an 81 win team will have $217M in revenue; a 61 win team will have $188M in revenue; and a 101 win team will have $245M in revenue.

In order to reach zero revenue, the team would have to win -71 games and lose 233 games. Of course this is absurd, but bear with me.

This team would be 152 wins below average. Say that the pitchers are 61 wins below average and the position players are 91 wins below average. (60/40 split.) A position player getting one-ninth of the team’s playing time would be 10 wins below average.

Francoeur is sitting near 3.5 wins below average, thus 6.5 wins above this baseline. At $1.43M per win, this is $9.3M. Pujols is 7 wins above average, so 17 wins above baseline, so $24.3M.

If we assume a 70/30 split, Francoeur and Pujols end up at $12M and $27M respectively, which are JC’s MRP values.

Continued in next post…

Given the above, here’s what I think JC did.

1. Use regression to figure out the MRP of an extra win. Of course large market teams will tend to have higher revenue and more wins, and small market teams will have lower revenue and fewer wins. This is exactly the kind of problem that regression is designed to solve.

So, JC computes that the MRP of an extra win is about $1.5M on average. This may be right, or he may underestimate the long-term benefits of being a perennial contender. Whatever.

2. As Guy said, assign 100% of the revenue to the players. Francoeur or Pujols is being compared to a “zero-revenue player,” which is a player so bad that a team at that level would have zero revenue. It sounds good in the abstract: if you have a team of bums, you don’t make any money. Now replace the bums with real major league caliber players like Francoeur, and you are raking in $200M a year.

The problem is that there are two constraints. First, the $1.5M MRP per win. Second, the requirement that an 81 win team have $217M in revenue. Those constraints determine the number of games a team of bums would win per season: about minus seventy. Whoops.

The error is in assigning all the revenue to the players, just like Guy says. It may also be true that $1.5M revenue per extra win is an underestimate, but that’s secondary.

Funny that in his disdain for replacement level, JC has come up with a system having an implied replacement level of around 10 wins below average.

Tom,
You are incorrect to state that I do not fully explain the method in my book. I have had several people replicate my work from the text of the book, and I have presented the method before many knowledgeable economists. The only parts that I have not presented yet are modifications for defense, and I also now use batting runs instead of a regression estimate of run contribution, which shouldn’t be too difficult to understand. The reason for this is that I am writing the long and technical explanation up to be published in a future book. If you want to stay mad at that part of my analysis, you are free to do so. But, I’m not going to walk people through the basics of thetechnique online when there is a perfectly good explanation available if you have a library card. I’m not hiding my work, and it is disingenuous of you to suggest that I am.

Anyone wanting to know the origins of MRP can check out an introductory microeconomics or labor economics textbook, or try Wikipedia.  The method for estimating MRP in baseball was developed by Gerald Scully in his 1974 article in American Economics Review. It was quite a technical article for its time considering that the regression estimates had to be done by hand back then.  Versions of Scully’s model frequently have been employed in arbitration hearings. The article is widely read and cited frequently by economists (and also available for the price of a library card). Again, it is your responsibility to educate yourself on the basics. If you’re having trouble grasping what MRP is, then you should proceed with your examination of the model.

As for the high dollars for Francoeur, I have to say I was somewhat surprised myself. The biggest thing that Francoeur has going for himself in the model is that he plays a lot. In most situations, players as bad as Francoeur don’t get to play that much. MRP estimates can only tell us the contribution to revenue that each input provides.  It doesn’t necessarily imply an optimal use of resources (though in most cases we can expect that they are if the manager is a win-maximizer). Had the Braves used a different bundle of players to play Francoeur’s innings, the Braves would have scored more runs and generated more revenue.

On to another confusion. I seriously doubt that any team would pay Jeff Francoeur $12 million, but it is still possible that the asset that is JF is still worth $12 million. This is clearly out of line with current salaries. In a perfectly competitive market, wages ought to equal net MRP.  I have come to the conclusion that the baseball market is not perfectly competitive, even at the free agent level. The degree of imperfection in competition is something that I am working to uncover right now. It’s an interesting issue.  The restrictions on the non-free-agent market may dampen the wages of free agents, but I don’t know by how much.

And despite the fixation that people seem to have with that $12 million number, I think the more interesting finding is that my estimates of his salary arbitration award expectation are similar to what the Braves offered.

You are incorrect to state that I do not fully explain the method in my book.

JC, you must have me confused with someone else.  I never stated that.

If you want to stay mad at that part of my analysis, you are free to do so.

Who’s mad?

Again, it is your responsibility to educate yourself on the basics. If you’re having trouble grasping what MRP is, then you should proceed with your examination of the model.

I’m not having trouble understanding MRP.

I don’t know why you addressed this whole post to me, since others are even more frustrated and confused than I was.  And I have your book as I stated twice in the comments, so I don’t need a library card.

***

We’re not asking for a full explanation, just some basics like: what does an average nonpitcher, starter, and reliever get?  How much for a full team?  Just a basic framework so we have some baseline to work with.

There are several people frustrated here in this thread and in your blog, and we’re doing our best to be kind to your work in the face of a result as clearly improbable as someone with Frenchy’s stats. 

My guess is that your total team MRP will come in at something like $150MM or $175MM, and that only 25% of that will be allocated to pitching.

And thank you for stopping by.  I’m sure the readers here appreciate it as much as I do.

I’ll make this my request for what JC can provide, so that we all have a basis for the results of the implementation of his framework:

1. MRP value leader ($ and name) at each of the 9 positions, the starting pitcher and reliever.

2. One guy at each position that have an MRP of zero, or close to zero (with at least 300 PA, or 60 IP).

3. The average team MRP, for each league, for a) nonpitchers b) starters c) relievers (or, collapsing b,c into pitchers).

JC: is this a reasonable request that I’m putting forward?

Tom,

I’m not going to parse exact language. In this post there is an implication that I am dodging explanations about my original method. Whether it was intended or not, it is there, my comments are justified.

In post 3, you cite three endnotes as what I mean by my request that a commenter read my book. The implication is that my explanation is a mere wave of the hand or the result of a few equations, when in fact I devote an entire chapter detailing the Scully approach and my modifications to it. The math is necessary, but not sufficient to underpin the method. Again in 19, you respond sympathetically to a commenter who hasn’t become familiar with the basic model when I tell him to read my book.  Your response implies that my book does not provide an explanation. If you do think that I explain the basics of my system in my book, then don’t leave it open to interpretation. It’s an easy thing to correct, whether the issue is implication or inference.

I’m sorry that if offends you that I directed some of my comments to readers in general than to you. You didn’t seem to be interested in clearing up misunderstandings.

I enjoy baseball and baseball analysis. I discuss it with many people, and I learn quite a bit from others. However, I find my interactions with you and many (but not all) participants at this site to painful because of consistent basic errors in logic, economics, and statistics combined with arrogance.  I don’t say this to be insulting, but to explain why I don’t participate on this site. You may feel the same way about me, and you are free to do so.  Discussions between us are a waste of my time and your time.  Rather than focus your energy on me, I suggest you move forward independently and do what you think is correct, and I will do the same. I see no benefit to further communication between us.

And if people don’t like what I’m doing, that doesn’t bother me. I have no problem putting my name and reputation on the line. I may be wrong about things, but I do not intend to be wrong nor do I wish to continue to hold onto beliefs that I later learn are wrong.

JC:

At no time do I ever make implicit negative points, here or anywhere.  (At least, I do my best to not do so.)

As I said in another thread, I say what I mean, and I mean what I say.  There is no need to parse my words, read between the lines, or anything else of that matter in any kind of negative light.  If I don’t express myself well, then I appreciate if the readers can read my words in a neutral manner (or, if charitable, a positive light), or ask for clarification.  For example…

The implication is that my explanation is a mere wave of the hand

...there is no need to make that implication.  You have TONS of footnotes, and so it is very easy for the reader to not see that footnote.  It’s an important footnote.  I simply pointed it out.  You could have asked me if I intended to make that point.  Indeed, that thought had never entered my mind.

***

You didn’t seem to be interested in clearing up misunderstandings.

Again, why take the pessimistic position?  Indeed, my post #30 is the clearest, most dispassionate post I have, a post that if you could answer in the same manner could actually move this issue forward for further discussion.

***

However, I find my interactions with you and many (but not all) participants at this site to painful because of consistent basic errors in logic, economics, and statistics combined with arrogance.  I don’t say this to be insulting, but to explain why I don’t participate on this site.

Well, making a summary opinion that can only be taken in a negative light, and having not supplied any evidence to support your opinion, is an insult.

After all, if I were to repeat your words, and direct them to you, how would you take it?  However, I set aside feelings and focus on the content. 

I reason that with a blog it is too easy for the reader to misinterpret things too much.  So, I either try to clear it up and move forward, or go around it and move forward.  The key is to move forward together. 

There is zero reason for any lingering or strongly-held animosity of any kind, with me, or on this site.

If Obama can say that he will give an outstretched hand to someone willing to kill him if that person would simply unclench his fist, then two nobodies like us can at least offer professionalism, courtesy and respect.

***

I see no benefit to further communication between us.

I think your readers and my readers would benefit greatly if we can move forward on tackling the issue.

***

Anyway, if we can consider our last two posts as mutual soliloquies and set them aside, can you go back to my post #30, provide the data, and we can all pledge (us and the readers) to move forward in as constructive and respectful manner as we can?

Those interested in the Scully paper being referenced can read it here:

http://www.cbe.csuhayward.edu/~lkahane/MHC349/349read/Scully%20AER%20’74.pdf

The problem I have with Scully’s - and by extension Bradbury’s - application of MRP to baseball is that they are treating fixed inputs as variable. A baseball team has 25 players on the roster, no more or less, and must bat and pitch/field until 27 outs are recorded (more or less). Nine players from the fielding team must be present.

Viewing Franceur’s production relative to the Braves simply not having a right fielder or sending someone up to bat in his lineup spot doesn’t tell us anything meaningful, because it’s an entirely theoretical concern divorced from reality. If McDonalds has an employee that doesn’t provide MRP greater than his salary, they fire him; if they can get additional MRP from another employee, they hire one. This isn’t true for baseball - the quantity of players a team can have and field for a regulation game is fixed.

In short, we can’t presume that a player’s MRP is positive just because he’s employed by MLB; a team can’t simply opt to not have a player for that spot because he doesn’t generate his wages in revenue for the team. It’s possible this is so, but I haven’t seen anything that’s convinced me of this.

The way I view player salary is to view players as independent contractors that provide a commodity (wins) to a team. That way you don’t run into the problem of inputs being fixed at the team level (although obviously the number of wins available is fixed at the league level).

I must say, I really don’t understand the discussion. Are we not all in agreement, including JC, that if we knew what kind of production JF would have provided last year, we would/could have replaced him with someone from the minor leagues (or some castoff from the major leagues) and paid him the league minimum salary?

Again, that is quite a different scenario than what we would have offered JF (as a FA or otherwise) before the 2008 season.  That would have been based on our 08 projection for JF.

How about if and when the discussion moves forward, we discard words like MRP and simply speak English?

If I have an MLB baseball team, there is only one known quantity and I must work from there.  And that is how many games my team will win if I filled my roster with players to whom I can pay the minimum.  Say that is 40 wins (I don’t remember the number off the top of my head).  Then I figure how much (net) revenue my team will produce.  That is ALWAYS the starting point (although I suppose I can use as a starting point average team revenue and 81 wins and average team payroll, but I think the replacement team framework is “cleaner").

Now, in order to figure out how much to pay a player who is better than replacement (assuming a free market - in other words, assuming that it is not a player who is still “under my control"), I simply figure out how much marginal revenue that player provides.  And that is how many extra wins he produces (along with, at some point, how much he increases or decreases my chances of making the post-season and things like that) plus his marquis value.  Period.

If you frame the question of “What was JF worth in 2008, given we knew what his stats would be” in the above context, then obviously he was worth nothing.  Even JC cannot dispute that sentence.

However, there are many other ways of defining and framing the question, “What was JF worth in 2008?” Using the word “MRP” even if we are all in agreement what MRP means in econospeak, does NOT help answer the question until and unless the question and answer are explained in more detail.  As is often the case.

Is that not right?

I must say, I really don’t understand the discussion.

This isn’t a discussion.  This is JC sticking his fingers in his ears and yelling “I CAN’T HEAR YOU” when people offer valid critiques of his work.

MGL/34:

If you frame the question of “What was JF worth in 2008, given we knew what his stats would be” in the above context, then obviously he was worth nothing.  Even JC cannot dispute that sentence.

JC, requoting from the top of this thread:

Even during his awful 2008 season, his marginal revenue product (MRP) contribution for his play in the field was approximately $12 million.

I would have to conclude that JC does dispute MGL’s sentence, seeing that JC does equate MRP with free agent dollars, as he said so here:
http://www.sabernomics.com/sabernomics/index.php/2009/01/pat-burrell-philanthropist/#comment-105649

In a competitive market, salary ought to equal net marginal revenue product, thereby eliminating any profit. If any profit exist when hiring a player, other teams have the incentive increase their bid until the wage is equal to the added revenue. This is basic labor economics and is not controversial.

So, to summarize: in a competitive market (meaning free agents), the net MRP will match the player salary.  And Frenchy’s $12MM MRP therefore would be what JC is saying a competitive free agent market will yield for Frenchy, if the teams knew that they would get his 2008 production.

In reality, this is untrue.  Indeed, he elsewhere states that Derek Lowe was one of the best pitchers in baseball, and he deserved his 4/60 deal he recently signed. 

So, my conclusion is that his model is severely imbalanced between position players and pitchers, and my questions in post 30, if answered, would lead us to more clarity and answers.  As I said, if JC can answer post 30, it would go a long way for both sides to be able to move forward.

I posted my take on JC’s method on my blog:
http://sabermetricresearch.blogspot.com/2008/06/replacement-players-vorp-salaries-and.html

Check out the comments, too—Rodney Fort, another respected sports economist, enters the discussion, but it appears we failed to convince each other.

The post also contains what I believe is a summary of JC’s method, as I understand it from his book.  Let me know if I’ve misinterpreted.

In Phil’s link, Rodney Fort says this about JC’s model:

Might I suggest that you can both be incorrect?

JC stretches the definition of MRP to a statement about average values; this can never work. And you are right to doubt HIS interpretation of MRP (which is incorrect).

And concludes about VORP with this:

But, ultimately, theories are just theories until they are tested. I guess it’s time to see how you can put the VORP idea into action.

Let me know how it works out for you.

And anyone who has read my Sabermetric offseason threads for the past 2 (or is it 3 now?) offseasons, where I go case-by-case in virtually every notable free agent and arbitration signing, that readers here will attest to, I have shown that the WAR model (wins above replacement) works, and is linearly linked to salaries.

The only interesting cases is the level of discounts that non-free agent sign for long-term deals.

The only thing I didn’t do was write it up in a journal.  But, it is clear to me, and it is clear to MLB, and it is clear to MLBPA, that players are paid via a WAR model.

I don’t understand the pushback against this by anyone.

I don’t know what JC’s pitcher/hitter split is, but Phil identifies another important issue.  In rejecting the idea of replacement level, JC ends up with an extremely flat value (MRP) curve.  Leaving defensive adjustment aside, a player’s value is basically proportional to how many runs he creates.  So if Francouer created 61 runs and Pujols created 160 runs in a similar # of PAs, Pujols is worth 2.6 times as much as Francouer. (JC’s estimate is actually 2.2, $27M to $12M). 

If you look at the Scully paper JC references, he does the same thing.  Scully calculates the MRP for each point of SLG%, then concludes that an average hitter with a SLG of .340(*) and 1/12 (.083) of his team’s PAs “will contribute 28.3 points” to team SA.  Even leaving aside the issue of the correct relationship between SLG and runs (this was 1974, so we shouldn’t expect perfect sabermetric analysis), you can see the problem:  every point of SLG has value in this method.  Even a guy with a .270 SLG contributes something, and is half as valuable as a .540 SLG player (Scully shows exactly that in Table 1). 

* I stopped short at this example, but Scully was working with 1968-69 data when the average SLG really was about .340.  Hard to believe now.....

BTW, I MGL’s post 34 provides a solid argument that JC’s model is wrong.  It’s almost a proof by contradiction:

“Are we not all in agreement, including JC, that if we knew what kind of production JF would have provided last year, we would/could have replaced him with someone from the minor leagues (or some castoff from the major leagues) and paid him the league minimum salary?”

Regardless of the math, or the economics, or the specifics of the model, if a theory tells you that JF’s 2008 performance was worth substantially more than league minimum ... well, that’s gotta be just plain wrong, doesn’t it?

Which is why asking JC to provide this will give us resolution in 10 minutes:

2. One guy at each position that have an MRP of zero, or close to zero (with at least 300 PA, or 60 IP).

Colin posted this at JC’s site, which echoes Phil’s point:

JC, I am not trying to provide a paradigm shift in MRP. I am simply trying to argue that because of a specific condition - the fact that an MLB team must employ 25 baseball players, no more or less - that only applies to sports teams, the basic assumptions of MRP may not be valid. (I am not even arguing that they do not, simply that they may not.)

I don’t think this is an unreasonable claim. I don’t even think this is a radical claim - if the government passed a law tomorrow saying that a restaraunt had to have 25 employees, no more or less, when open to the public, wouldn’t that change the way MRP applied to restaraunts?

I wonder how JC and Rodney Fort would value Fantasy Baseball players?  I’m not trying to be facetious or sarcastic or anything.

The way I value it is based on replacement level: if you have 20 teams, and they have to select 25 players, then the 500th player will have a value of exactly $1 (no less, by definition, and no more, because he is the last player chosen).  Everyone else gets a value above that.  Everyone below that gets ZERO.

MLB operates in a similar fashion. 

Would the models of JC and Rodney agree?

Valuing all runs as if they are marginal runs, as Scully and Bradbury do, is really an incredibly basic mathematical/logical error.  To his credit, Fort seems to recognize this.  Even leaving aside the 25-man roster and replacement level debate, the approach fails to properly account for wins at the team level.  Consider three offenses in a 5 RPG context, that score 3, 5, and 7 RPG.  A 5 RPG offense must be worth 40.5 wins if we assume a 50/50 offense/pitcher split (just to keep things simple).  Scully/Bradbury say the 3 RPG offense is 60% as valuable as the average team, when it really only contributes 14% as many wins (6 wins).  Similarly, they would value 7 RPG at 40% above average value, yet such an offense would in fact contribute 65% more wins (67 wins). 

By applying the marginal value to all runs scored/prevented, the Scully/Bradbuy method is guaranteed to do two things:  1) create a value curve that is much too flat, undervaluing great players relative to bad players, and 2) overestimate value for all players in the aggregate (because what we call below-replacement production is being valued as equal to marginal production).  Combine the two and you’d expect JC’s estimates to probably be in the right ballpark for good players (the two errors offset each other), but to hugely overestimate the value of bad players.  And that’s pretty much what his results seem to be....

What’s weird is that when I look at JC’s results in his book, they seem ok.  Nothing outlandish (then again, I didn’t look too hard). 

But in his new model, he’s doing something very different, and leading to really impossible results. 

For him to say that the arb players get 77% less than they otherwise would as free agents is also an impossible result.  He’s saying they get 23 cents on the dollar, from years 4 through 6.  The answer is closer to 50, if not 60 cents on the dollar.

I don’t know why JC won’t accept our help here, as we’re all subject matter experts on this.  We’re being, I find, uncommonly charitable here.  Had anyone else posted those results, we’d have blasted him already.

I don’t know about you guys, but I have a soft spot for anyone who poses with his kid:
http://www.sabernomics.com/sabernomics/index.php/2008/12/happy-christmas-2/

In our earlier thread (http://www.insidethebook.com/ee/index.php/site/comments/all_rob_neyer_all_the_time/#41), Phil said that in his book JC starts out with an average team offense worth about $50M.  So an average position player might be worth something like $5M.  I don’t know how you get from there to JF being worth $12M.  Something has changed.....

Geez, I get distracted with other things (like, paid work), come back to this thread, and see it exploded....

Phil/#37 - thanks for the link and the explanation. That helped a bunch. The material I supposedly learned by taking microeconomics in college seems to have faded already.

Tango/#18 - A late thank you for pointing out what I missed in #3.

As to JC’s point about having a library card in #27… that assumes your library either has a copy of the book or can acquire one through interlibrary loan. And I have to say, I’m sure the former isn’t true here, and I’m not sure about the availability of the latter for my local public library out here in rural Nebraska. Regardless of his model, his tone seemed to smack of Effete Academic Syndrome. That could explains why his model probably works well within a theoretical framework but is so flawed when compared to reality.

Had anyone else posted those results, we’d have blasted him already.

Good point.  I do value JC’s insight as an economics expert, which is why I’ve bothered to post four comments at his blog, let alone one.

If you’re going to ask that non-experts read the book and get a degree in economics, why write a blog?

1.  Saying “I’m an expert in economics and you’re not” is perfectly legitimate when the issue is a subtle point in economics, and when the commenter obviously is in over his head.  This is not the case here.  It’s just as counterproductive for JC to say “you don’t understand economics” as it is for us to tell JC “you don’t understand sabermetrics.” We understand enough economics to critique JC, and he understands enough sabermetrics to critique us, if he chooses to.

2.  No matter how involved the analysis, and no matter how much expert knowledge you have, the results have to stand up to common sense and logic.  As a former pope said, “truth cannot contradict truth.”

JC has an involved method of determining MRP.  It turns out that the calculation of Francoeur’s MRP is very large, despite the fact that Francoeur could have been better replaced by a minimum-salary guy. 

Therefore, one of the following is wrong:

a) Francoeur is worth more than the minimum;
b) Francoeur’s stats could be replaced for the minimum.

And it’s pretty obvious that (b) is correct, isn’t it? 

I think JC has it backwards: it’s the more involved, more complicated, conclusion that’s likely to be wrong. 

3.  More generally, in any argument, it’s not enough to say why you’re right—you have to be able to say why opposing arguments are wrong.  It’s OK to ignore the stupid, ignorant opposing arguments, but there are always thoughtful, reasonable arguments from thoughtful, reasonable people.  Part of intellectual debate involves addressing those opposing arguments in good faith.

3.  JC’s book and blog are intended for a lay audience, not for professional economists.  Therefore, even if JC is right, and the economics do indeed lead to a completely counterintuitive conclusion, it’s JC’s obligation to explain why as best he can, isn’t it?  There are lots of truths in economics that seem to defy common sense, such as:

-- revoking tariffs on imports from country X is good even if country X won’t revoke tariffs on your own goods;
-- rent control laws hurt most tenants;
-- stricter security at airports may cost more lives.

All these are true, and have been well and logically explained by economists writing for lay audiences.  If JC really believes that JF is worth more than a minimum salary, it would be appropriate to explain to us why what seems to be watertight logic is nonetheless wrong.

Regardless of the math, or the economics, or the specifics of the model, if a theory tells you that JF’s 2008 performance was worth substantially more than league minimum ... well, that’s gotta be just plain wrong, doesn’t it?

Phil, again it depends upon what he means by “is worth.” Surely you don’t think that that is an unequivocable and unambiguous set of words, do you?

“Was worth” to whom by virtue of what as compared to whom and what?  Etc.  All I am asking is that JC explain what he means by “is worth” or MRP (other than the technical definition that we can all look up in Wikkipedia or in an Econ 101 textbook), using at least a few sentences as it pertains to players and major league baseball. That is not too much to ask is it?

I mean, and these are bad hypos, but after 78 posts excoriating JC, maybe he finally responds by saying, “What I meant was that no matter how bad a player is, if a team gives him 150 games of playing time, he provides 12mm in revenue as compared to X because of Y.” Or maybe he says, “Yes, I realize that his performance was not worth 12mm, but I found out that he is a popular player, and I estimated that an unpopular player with the same stats would have provided 12mm less than he did.”

Or, “Sure his performance, being 30 runs or so less than average, does not warrant anything more than a few hundred thousand in salary (we all know that), but what I meant was ...”

Or any one of 1000 other possible explanations.  You can’t continue to criticize someone and claim that he is wrong until he at least provides some explanation of what the heck is talking about. If he does not want to do that, all you can do, in this case at least, is to say, “That does not sound right.  I’d like to know what he means.”

If he still is unwilling or unable to engage in the discussion, then you drop it.  I mean, obviously he is a really smart guy and understands a lot about sabermetrics, MLB finances, and economics in general.  He is NOT going to say something absurd without a reasonable explanation. At least I don’t think so, and we should give him the benefit of the doubt.  I would hate to think that if I made a curt statement that on its face seemed ridiculous, that you guys would give me a chance to explain, and if I could or would not, then you would simply say, “Well, maybe he has his reasons.”

That is all I am saying.

MGL:  I think you need to distinguish between JC’s conclusion and why he believes it is true.  There is no ambiguity in what he is claiming, which is that JF’s 2008 on-field performance generated $12M in revenue for the Braves.  I agree it’s not clear why he believes this to be true, and that’s what everyone is trying to figure out.  JC seems to feel he has already explained it clearly, others disagree.

Also, no disrespect, but because something isn’t clear to you doesn’t mean it’s unclear to everyone else.  JC has written previously about MRP and player valuation, so Phil and Tango are not responding only to this short post on Francouer.  I think they have a clear sense of what JC is claiming here (though, again, are not sure exactly how he arrived at this conclusion).

I am going to guess that JC is doing this:

MRP = LWTS * x + PA * y

While I would treat x = 0.4, JC is probably treating it as x = 0.1.

While I would treat y = 0.015, JC is probably treating it as x = 0.02.

So, suppose you have Frenchy as LWTS = -25 and PA = 650.

I would say:
MRP = -25*0.4 + 650*.015 = -0.25

JC might say:
MRP = -25*0.1 + 650*.02 = 10.5

These are just made up numbers to make the point.  It’s simply very possible that JC is giving an enormous weight to the PA, and very little to the performance.

And in this madeup illustration, in order for him to have an MRP of zero would need a LWTS of -130 runs.

Again, I have NO idea.  But it makes some sense. 

This is why all JC has to do is answer my post 30, and we’ll be done with this thread in 10 minutes, and hopefully, JC can improve his model so that we don’t get a result like we see with Frenchy.

Take all the emotion and adjectives completely out of this thread, and focus purely on the numbers.

***

Interesting, JC is speaking at Penn State:
http://www.sabernomics.com/sabernomics/index.php/2009/01/talk-at-penn-state/

Maybe somebody can take notes and report back.

JC on his blog says:

Mean MRP if PA>600:  $16.7 million
Mean MRP if IP>200:  $14 million

I think Tom is correct as to what JC’s results look like and why, but not his process. I think he simply uses RC-style LWTS.

I have a pretty good guess about what JC is saying, and I tried to summarize that in my blog post that I referenced above.

Basically, I think JC is saying that:

1. Francoeur’s batting performance caused the Braves to earn $12 million more than if he had created zero runs while using the same number of plate appearances (or outs—not 100% sure which, but I think it’s PA).  This is his MRP.

2. Therefore, because of the result in economics that says “MRP = salary,” JF is worth $12 million in salary.

I object to #2.  It seems to me “MRP = salary” is true only when certain conditions hold, those conditions having to do with a free market for number of employees hired.  Because that condition doesn’t hold in baseball—you have to have exactly 25 players whether you want to or not—I argue that instead of

“MRP = salary”

it should be

“MRP over replacement player = salary over replacement player”

This is the formulation with which JC and Rodney Fort disagree. 

So, basically, I think I *do* understand what JC is saying, and I think I have clearly stated my reasons for disagreeing.

And just to restate: I think my #1 above does correspond to JC’s definition of MRP.  And I have no reason to believe it’s incorrect, or that his estimate of Francoeur’s MRP at $14 million is incorrect.  My disagreement is with #2 alone.

Further to my post #55, I guess I’m disagreeing with Tango somewhat.  My position is that when JC defines MRP as being zero at 100 runs below average, that’s perfectly correct—after all, if they put ME in there, that’s exactly where I’d be, -100 runs.  If JF is at (say) -30 runs, he is indeed 70 runs better than I am, and his MRP can legitimately said to be the value of those 70 runs.

My objection is simply his assertion that the value of those 70 runs should be his salary.  I think that’s just plain wrong.  I think the issue is one of economic logic, not sabermetrics.

Phil, I don’t think that JC is accounting for playing time at all - if he’s using BsR to create his LWTS, which is what he says he’s doing now, he’s using LWTS denominated in outs above absolute zero.

Based upon what he’s written, and the Scully paper he keeps referencing, I think it’s pretty apparent he thinks that a player’s production is worth the same amount of money regardless of how many PAs/outs were used. So if Francoeur was worth (just spitballing here) 55 runs above zero, then he’s equally as valuable as a player who was +55 in 250 PA.

Phil:
Actually, JC is wrong on BOTH counts, not just the 2nd.  Valuing all runs created (and runs prevented) as though they were marginal runs is incorrect.  Take a team of Francouers, and equally bad pitchers:  3.4 RS, 5.6 RA.  It will win 46 games.  This team is about 350 runs worse than average, and 35 fewer wins, so 10 runs = 1 win = whatever $MRP you want to assign each win. But the Francouers used 1100 runs (550 on offense, so let’s credit the pitcher with preventing an equal #) to achieve 46 wins.  It took 24 runs to generate each win!  So you can’t say that a player who creates 60 runs generates half the revenue of a 120 run player—it isn’t true.  But that’s what the Scully/Bradbury method says.

Colin/57,

I’m going by JC’s book.  He starts by figuring what an average player would be worth if he had that number of JF’s plate appearances, then adds or subtracts.

Either way, it works out the same ... whether you create 55 runs in 250PA, or 55 runs in 600PA, if you start with “striking out all the time is 0 MRP,” then you wind up with the same MRP either way.

But you’re right.  Looking at my #1 in post 55, I should take out “while using the same number of plate appearances.” JC is assuming a zero MRP if you create no runs, regardless of plate appearances.

Guy/58: From the book, JC values runs more highly the more you score or save (p. 182).  So I’m not 100% sure that he thinks a 60-run guy generates half the revenue of a 120-run guy.  But I still think he doesn’t get to $0 MRP until he gets to zero runs, though. 

If he’s now valuing runs equally where he didn’t before, I agree that that’s a problem.  But the REAL problem is with #2, not considering that replacement players are the baseline, not zero players.  His #1 may be inaccurate, but that’s just a technicality.

Basically: if JC had used the equation

Salary - minimum salary = MRP - replacement level MRP

his estimate for Francoeur would have been close to zero, and we wouldn’t be having this discussion.  We’d still be able to look at how he values runs, and we might find something to criticize, but if you’re dealing with the question of how he gets such a high value for players of marginal ability, I’d say 95% of the problem is #2.

Phil:  A non-linear valuation of runs may help reduce the error of valuing all runs as marginal, but I think it still leaves you with a serious problem.  If you read the Scully paper, you’ll see he does literally value a .300 SLG player at 50% of a .600 SLG player. 

The average #s the JC comes up with (Tango/53) are revealing.  An average team of players would generate roughly 10*16.7 + 7*14 = $265M in revenue.  I think that’s more than the average team’s total revenue.  So that suggests his numbers are singificantly inflated.

Guy/61: Well, you guys have analyzed JC’s numbers more than I have, so I’ll defer to you.  If you say that JC’s individual numbers don’t add up to team revenue, there’s definitely a problem there.

What’s the average team’s revenue, by the way?  How much is JC off by?  Wait, I can find that ... here’s a 2007 Forbes list ... by eye, the average appears to be maybe $180MM.

So even if JC is off by (say) 50%, that doesn’t explain Francoeur.  JC’s model overvalues Francoeur by about 3000%.  I continue to argue that the 3000% comes mostly from equating MRP and salary without adjusting for replacement level, above and beyond any errors in the way the model values runs.

I have not read today’s posts, and I have to run for a while, but Guy, you are right (no disrespect felt) in that maybe it is just I who does not understand what he means and it is crystal clear to others.

I just don’t think that “on-field performance being worth something” has an unambiguous meaning, at all.  In fact, why would linear weights or some similar context-neutral measure mean anything to a team in terms of worth or value.  The ONLY reason we use lwts or a similar measure, is because it is the best, or at least one of the best, metrics for predicting (used properly of course) exact future value to a team.  For retrospective value, it is worthless and meaningless.

In fact, there is no metric that we can say with any certainty represents retrospective value, but a context-neutral one has to be at the bottom of the list, at least as far as the sabermetric ones.

We’ve had this discussion before in terms of “MVP-type evaluations.” Surely something like WPA or even RBI+R-HR more reflects a player’s retrospective value than something like lwts.  Why would lwts even enter the discussion in evaluating someone’s retrospective worth?

Surely, if someone played really well “when it counted” but poorly when it didn’t, by any measure and and stretch of the imagination, their retrospective worth would be high regardless of their context-neutral stats!

So maybe JC is talking about Francoeur’s non-context-neutral stats.  How was his WPA?  His RBI and Runs?  Did he come through in games and at times that meant something?

Even if the answer to those questions are “no”, again, there are many other scenarios whereby you can talk about “What a player’s on-field contributions are worth” other than the very irrelevant (to retrospective worth) lwts!

At best, the concept of what a player was “worth” or how much marginal revenue they produced as a function of their performance, is a hypothetical and theoretical one, and to some extent a philosophical one, with no clear answer..

Maybe I am missing something. 

From Wikipedia: (emphasis mine)

“In economics, the marginal product or marginal physical product is the extra output produced by one more unit of an input (for instance, the difference in output when a firm’s labour is increased from five to six units).”

and “Marginal Revenue (MR) is the extra revenue that an additional unit of product will bring.”

It seems pretty clear from this that if one can assume a static roster size, that adding Franceur must also mean subtracting another player.  So the MRP for “adding” Franceur would be something like the MRP of Franceur - the MRP of a player that can be had for the minimum league minimum.

I know most of you know this already.  Why doesn’t JC?

It’s more difficult churning through Scully’s equations than I first conceived of, mostly because he calculates SA (or slugging average) as:

TB/AB*1000

and win percentage as

W/G*1000

So (using the BDB) we get an average SA of 356 for the sample period of ‘68-’69. Playing time is measured as:

AB/tAB

Where tAB is team at-bats.

Using his value formula, assuming a full-time starter with an average SA, we get a value of $281,940.

So let’s look at Hank Aaron’s value to the Braves in 1969.

547/5460 = .1

That’s our playing time estimate. He had a SLG of .609, so we get:

609*.1*$9,504=$578,793

And the values I’m getting seem to line up with Table 1 of the paper.

Now let’s examine the case of Horace Clarke in 1968, who seems to be a reasonable proxy for Francouer, with -30.1 Batting Runs. (At second base, however; but Scully’s model ignores position altogether.)

254*.109*$9,504=$263,127

Clarke’s value is slightly more than Scully’s table would suggest because he had a higher-than-normal share of the Yankee’s playing time, due to his low walk rate (and thus higher number of at-bats) and the fact that the Yankees used him as a leadoff man that year.

So the arguement that Scully’s model makes is that Clarke, the hitter with the lowest SLG among all players with 500+ at-bats in our sample, was worth only $20k less than average.

The largest determinant of value in this system seems to be playing time, rather than performance in any meaningful sense. And it appears that JC’s model views production the same way.

MGL:

http://www.sabernomics.com/sabernomics/index.php/2008/12/how-i-value-players/

The basic method is detailed in my book. The method I use in my book values hitters using OBP and SLG., but now I use linear weights (Base Runs).  Pitcher are valued according to strikeout, walk and home-run rates.

These estimates are adjusted for home-park influences. I also add an adjustment for defense. In some cases I assume the fielder is average for his position, in other cases I use the Plus/Minus system to adjust for defensive quality.

By Plus/Minus I’m pretty sure he means the Fielding Bible.

It’s not that we don’t understand what JC is doing here. Or how he defines “his play in the field.”

We should expect the MRP of a team to be close to double what the average team payroll is.  Remember, that the MRP is based on how much he generates as a free agent. 

So, you should expect that if the team payroll is $90MM, then the MRP would come in around $180MM.

In terms of actual salary, the free agents gets 100% of their MRP, while arb players get less (JC says only 23% which is very very low), and slave players of course get barely above average.

Tango/Phil:  I’m not sure it makes sense to assume the sum or marginal revenues equals total revenues (MRP = ARP).  Related to that, is it true that 100% of revenue is created by players?  Does everything else—the ‘capital’ of owning a MLB franchise, management, marketing, player development, a stadium, etc.—create zero revenue? 

Phil:  While I agree replacement level is a more useful way to think about player value, it isn’t essential.  As Tango and I have both argued, if you have the right number for the average player, and the correct marginal revenue impact of each run/win, you don’t need replacement.  And Francouer will still end up with approx. zero value. 

I think you underestimate the problem created by valuing all runs at the marginal rate.  You concede that JF created $12M, compared to a .000/.000/.000 player, because with the latter player the Braves lose 60 runs and 6 wins (roughly).  But by that logic, the Braves’ hitters, which scored 743 runs, created all 72 of the team’s wins and all of the MRP.  But then, what about the fielders and pitchers?  You see the problem?  This is why Bill James needed to zero out win shares at about 50% of average production—you can’t work with marginal values and then apply it to total production.

Guy, I also question the assumption that players earn all the MRP.

I’ve written a fairly long response on my blog.
http://lanaheimangelfan.blogspot.com/2009/01/ballplayers-and-their-marginal-revenue.htm

To piggyback on Guy’s point, let’s take the case of one of our typical FAT players - the sort of guy who can float between MLB and AAA. We could - if we had the info - figure out his MRP for both teams using MLEs.

Measured in runs/wins/etc. his production at MLB is lower, but his MRP would be higher in MLB (figured using the JC method.)

I would argue that this difference in revenue is due almost entirely to those things that Guy mentions, and such should not be revenue attributed to the player.

Guy/68:

1.  I think you’re right—adding up marginal revenues for each player doesn’t necessarily give us total revenue for the team.

2.  Yes, that makes sense: it must be that the value of runs declines fast as your team becomes worse and worse.  So the “zero” mark does need to be somewhere above zero—such as half of the average, which you point out was Bill James’ method.

Maybe I *didn’t* interpret JC’s method correctly.  Maybe his zero point isn’t really zero, but actually somewhere above zero, but still too low.  That would still explain why he has Francoeur worth so much: his zero level is too far below replacement level.

I agree with you and Tango that you don’t need to explicitly consider replacement level—it’ll work out automatically if the rest of your numbers are correct.  But the rest of the numbers DEPEND on replacement level.  Average salaries would rise if minimum salaries rose.  Average salaries would drop if replacement players got better.

Replacement level is determined by the pool of available talent.  Replacement salary is determined by the collective agreement.  But *average* salary is an empirical observation.  So I’d argue that it’s “purer” to start at replacement and work up, rather than starting at average and working down.

That is: from replacement level and salary, and an estimate of the marginal value of wins, we can predict what every player “should” be paid if owners are rational.  But we can’t calculate anything on the basis of *average* [free-agent] salary without ASSUMING that owners are rational.

Suppose that owners are irrational, paying all players $1 million more than they’re worth (for whatever reason).  Then, by starting with the average and working down, you’d find that Jeff Francoeur (assuming he’s replacement level) is worth $1.39 million rather than just $390,000!

You see what I’m getting at here?  Using replacement level salary lets you do a theoretical calculation.  Using average salary requires you to make the assumption that the market is efficient, and that can lead to big discrepancies at the lower margins, which is where the Francoeur discussion is.

It’s the MLB minimum salary and replacement level that drive average salaries, and not the other way around.

Having thought about it, and after considering Guy/68, I should probably retract my claim that I know what JC means by MRP.  I don’t think I do know.

In an non-baseball context, I know what MRP is: it’s the difference in revenue between if you hire the guy, versus if you leave the position unfilled.  But there’s no such thing in baseball as leaving a position unfilled. 

So what *does* JC mean by MRP?  I assumed he meant the difference between playing the guy and playing a .000 guy, but Guy has persuaded me that maybe I’m wrong.

Just for the record: if there were no minimum salary in MLB, and no roster size limit, then every player WOULD earn his MRP.

Suppose you have 30 identical teams with 25-man rosters.

Suppose a guy comes along who can save a team one run—maybe he’s a LOOGY or something, and he’ll only play a few games.  Every team would bid on him.  If one run is worth $400K, no team will pay more than $400K for him.

Now here comes a second LOOGY.  He’s worth one run to the 29 other teams, but maybe only half a run to the 30th team (they already have a LOOGY, the one they just signed).  So one of the other 29 teams bids higher, and gets him.

Same thing happens for each of the other 28 LOOGYs who come along.  Now, every team has a 26th man LOOGY.

Here come 30 more LOOGYs, same quality as the first set.  Now, each of these guys is worth only half a run, because they’ll only play when the first LOOGY has already been in the game.  Each of the 30 teams winds up with one of these guys, at no more than $200K.

Here come still another 30 LOOGYs, same quality as the rest.  Each of these guys is worth 0.1 runs (because they won’t get much playing time).  At $400K a run, no team is willing to pay more than $40,000 for one of these guys.  Some of them sign, but some of them can make more money becoming accountants, so they quit baseball. 

Finally, there’s one more set of 30 LOOGYs.  This time, they’re only worth $38,000.  This time, ALL of them realize they can make more money as accountants, and all of them quit baseball. 

The marginal LOOGY that actually got signed had an MRP of $40,000.  What do they make?  Somewhere between $38,001 (below which they’ll quit) and $39,999 (above which the team doesn’t want to pay them). 

That is: they do make their MRP.  (Yes, they may make $39K while their MRP is $40K, but that’s a rounding error.  If I made the example less coarse, it would have been exact.)

Note also that the first and second rounds of LOOGYs, the non-marginal ones, ALSO make $39K or so.  Why?  Because we assumed they’re no better than the third round, and the difference in runs is simply due to them being less redundant.  They have no negotiating power, because if they want more than $39K, management can tell them to buzz off and grab a guy from the third or fourth round.

Which confirms the economics: players make the value of the runs of the LAST (marginal) player signed.

----

But again: this works ONLY if you have no minimum salary and unlimited roster size.  If you have a roster limit, it breaks down, because the 26th player is worth ZERO.  That means the 25th player would be paid only $39,000 (just enough to prevent him from running off to be an accountant).  That’s likely less than his MRP.

And the minimum salary means that the 25th player needs to be paid $390,000.  That must still be less than his MRP, because otherwise you’d just fire him. 

Except ... that you MUST have a 25th player, so you can’t fire him.  So his MRP might actually be LESS than the $390,000 you’re paying him.  Or, it might be more.  There’s no way to tell from the armchair.

And, what about the other guys, the superstars?  As I argued, they are paid their MRP above and beyond what the 26th guy would produce, plus the minimum salary.

Rally, nice analysis.  Another good analogy is the movie industry.  A big production company can make a film using no-name actors and pay them union scale—a “replacement level” cast.  With enough marketing and a distributor, the film will generate revenue.  With a good script and soundtrack, it might even make a profit.  But is it meaningful to say that the no-name actors generated the revenue? 

JC likens Francouer to Keanu Reeves, to make the point that a bad actor can generate money.  The analogy obviously fails, because Reeves is a huge plus at the boxoffice and undeniably creates revenue (meaning he is extremely talented in the only terms his employer cares about, which is selling movie tickets).  In any case, Francouer is not Reeves—he’s the baseball equivalent of a struggling actor who waits tables to pay the rent, and who would gladly work for nothing to appear in a Hollywood film.

Last thought:  JC’s theory is that Francouer is paid less than $12M only because he is denied free agency.  So let’s imagine that all players became free agents next year.  Does anyone seriously think that any team would pay $12M to a player expected to put up JF’s 2008 numbers, or that such players would earn nearly half of what Pujols would command?  The question answers itself....

My response to the Keanu analogy:

I don’t think that’s the appropriate comparison though, JC. Francoeur’s level of performance in 2008 was more akin to the sort of actor who plays the part of “Cop #3″ or “Woman With Baby,” the sort of actor you can find a half-dozen of if you pull the fire alarm in half the apartment complexes in New York.

Baseball is, as you note, an entertainment industry, and what you tend to have - in sports, music and film - is a sharp talent curve, with a few stars and a large number of people just looking to break in. At the bottom point of the talent curve, what you have is more people willing to work for league minimum/union scale/etc. than you have jobs, and very little differentiation between them in potential revenue.

And Phil, I don’t think you’re wrong that what JC is attempting to measure is MRP compared to .000/.000/.000. (That’s how Scully does it, and from what I remember of JC’s book he follows the same model, simply adding OBP to the equation as well.) We all recognize why that’s wrong, but I don’t think Bradbury does - Guy/61 points out how team revenues end up being overestimated, probably for that very reason.

Yes, I think that is what JC is doing - he is comparing JF to a non-player or a player with zero stats.  And yes, of course that is “wrong.” And yes, replacement level is THE ONLY true baseline because it is the only known quantity.  I know for a fact that I can fill my roster for 390,000 times 25.  Once I know the lwts or OPS of a FAT player, then I know 2 things:  One, how many wins I will have, and two, how much money it will cost.  From there, everything falls into place.  In order to figure out how much to pay each player who is better than replacement and knows he will get paid more than the min salary, I only need to know how much extra revenue that player generates over and above how much revenue I would generate with a team of replacement players (and 40 wins).  Simple.

Anyone who computes a player’s MRP, value, or whatever you want to call it from the standpoint of not having anyone, or as compared to a player who hits zero, is being, well, ridiculous, since we KNOW that we can get a much better player than zero for 390,000.  I own a store.  I can make $100,000 a year.  In order to do that, I must have a cashier.  I pay that cashier around 8 bucks an hour.  Without a cashier, I make zero money. My cashier is not worth $100,000!  A replacement cashier gets paid around min wage (that is because it requires no skill, the pool or cashiers is a zillion people, and for some businesses, a cashier only earns a business an extra 8 bucks an hour), and I go from there.  Same thing with baseball.

But, if JC wants to say that JF is “worth” 12mm using his model, whatever that model is, that is fine with me and it should be fine with everyone else.  If he wants to say that an average team would (happily) pay a player 12mm if they knew that they would get JF’s 2008 stats this year AND his playing time, well, even he cannot believe that. So his “value” or “MRP” must mean something else, or else he is delusional.

MGL, I understand and appreciate wanting to give Bradbury the benefit of the doubt here, but I think he’s being very clear about exactly what he means. Again, from his own blog:

[blockqoute]In absence of some external force or cognitive bias, teams will pay players a salary equal to their net marginal revenue products (MRP). Non-free agents earn less than their MRPs, because their movement within the labor market is restricted. Free agents ought to earn their projected MRPs (there is a lot of variance in these projections) in the competitive labor market, and no team ought to pay a player more than his estimated MRP value, even if it has room in the budget.

Bradbury is in essence claiming that a player’s free agent salary is equal to his MRP. He is claiming that Frenchy’s MRP in 2008 is $12 million. I don’t see any way around the conclusion that JC believes that as a free agent someone of Francoeur’s value is worth $12 million.

This is not news. Fellow economist Andrew Zimbalist wrote in his review of Bradbury’s original text:

http://www.bizofbaseball.com/index.php?option=com_content&task=view&id=1768&Itemid=40

But the fatal problem is that Bradbury’s methodology unwittingly identifies a player’s average revenue product, not his marginal revenue product.  By his reckoning, all of a team’s revenue is attributed to the players, leaving nothing left over for front offices expenses, stadium expenses, minor league operations, or profits.  Given this misstep, it is not surprising that Bradbury finds players at all levels (under reserve, arbitration eligible and free agents) are paid less than what he estimates they are worth.

I don’t see any reason to conclude that any of us in this thread are misunderstanding JC or using any definition for value other than his own. I’m sure it’s nice to think that he couldn’t be this wrong about the issue.

But I think that he is, and there are economists who agree! (Anthony C. Krautmann noted the same problem with a Scully-style MRP analysis of baseball players in a paper published in 1999 in Economic Inquiry - it provides inflated and unrealistic estimates of player value.)

Also note that Pujols and Frenchy both had around the same number of PA.  So, we can safely ignore the playing time component, and focus on their hitting relative to each other.

That gap is around 90 runs or so, whether you use RC or LWTS.

JC also told us that Pujols’ MRP is 26.7 and Frenchy is 12.  That difference is 14.7MM$

So, 14.7/90 = .16

That means, JC values each run at .16MM$.

All we need now is to scale using PA.  If you use RC, then you need to add .005 runs per PA.  If you use LWTS, then you need to add .024 runs per PA.

Let’s see what this means.  I’ll use the figures from Fangraphs.

Pujols: 641 PA, +69 runs, 146 RC
Frenchy: 653 PA, -23 runs, 56 RC

MRP(Pujols) = .16*69 + .024*641 = 26.4
MRP(Frenchy) = .16*(-23) + .024*653 = 12.0

OR

MRP(Pujols) = .16*146 + .005*641 = 26.6
MRP(Frenchy) = .16*(56) + .005*653 = 12.2

***

That sound reasonable as to what he’s doing?

If he has 0 RC in 650 PA, the second equation says MRP = $3MM.  The first equation says the LWTS has to be -100 relative to average for MRP=0.

***

Also note that I’m not considering fielding + position.

***

He also said the mean MRP for pitchers over 200 IP is $14MM.

There are 32 pitchers who qualify in 2008.  Their simple mean ERA was 3.53 and FIP was 3.64.  JC says he uses something FIP-like, so let’s say these guys in his pool have an ERA of 3.6, compared to the league average of 4.3.  That makes these guys 0.7 runs per 9IP better than average.

The average number of IP for these pitchers is 214, which if you divide by 9, is almost 24 full games.

He also has top pitchers similar to what I have, so around $24MM for a guy with an ERA of 1.5 better than league average and 24 full games.

So, if we presume the following:

MRP = 14 = x(.7*24) + y(24)
MRP = 24 = x(1.5*24) + y(24)

We get x = 0.52 and y= 0.22

That means each run saved generates half a million in MRP.  And each 9 innings generates 220K in MRP.  At what point is MRP 0 for 24 full games?  When runs saved is -0.42 runs per 9 innings relative to average.  That becomes JC’s replacement level.

***

See? The marginal run for pitchers is half a million, very close to what I have it, while for hitters it’s 160K.

As far as I can interpret using these pieces of data anyway.

Tango:
I don’t think JC values top pitchers nearly as highly as you do.  See his list here for 2006-2008:  http://www.sabernomics.com/sabernomics/index.php/2008/12/baseballs-most-valuable-pitchers-2006-2008/.  Santana, for example, is valued at $14M per season.  It seems to me that he’s valuing runs at about $210K/run, and just works up from zero.  For pitchers, that suggests he uses a zero value at something like 2 R/G above average. (With the caveat that he may not value runs linearly, so this is an approximation.) So I don’t think he’s necessarily being inconsistent in valuing runs scored vs. runs saved.

The result, as I think we all agree, is a much too flat valuation curve.  A good illustration of how absurd this is:  Jake Peavy’s last three seasons ($36M) are valued the same as three years of Frenchy 2008.  It’s hard to imagine JC really thinks that makes sense.  He’s just dug himself a hole at this point....

Tango brought up fantasy baseball earlier, and I think that’s a good way to illustrate the problem created by the Scully/Bradbury confusion of marginal and average.  In a fantasy league, it might take 20 RBIs to gain one point.  If owners on average pay $260 for 52 points, 1 point is worth $5.  The Scully/Bradbury model then says 1 RBI = $.25, so if Ryan Howard delivers 120 RBI that’s worth $30.  Run this for every category, and maybe he’s a $90 player overall.

The problem, of course, is there isn’t enough money to pay $90 for Howard.  The average team might have 800 RBI, which is a total of 40 marginal points, but that team will only earn 6 actual points in the standings.  The difference between marginal and average is much more radical in fantasy baseball—an extra 200 RBI might improve a real team’s wins by 30%, but in fantasy it’s the difference between 1 point and 12 points. But the principle is the same.

Guy,

I missed that list.  One thing in JC defense is that he does use a 10% increase in revenue.  So, Frenchy being 12MM in 2008 would mean a guy with the same stats in 2007 and 2006 would come in at a 3yr/33MM (not 3/36, not that it makes much of a difference).

That would be around Felix Hernandez, 2006-08.

Rally’s response:

http://lanaheimangelfan.blogspot.com/2009/01/ballplayers-and-their-marginal-revenue.html

My most recent comment on the issue (still in the moderation queue at JC’s blog):

Here’s where I run into problems, JC. From 1994-2007, the average MLB player hit .267/.334/.424, while the average corner outfielder hit .275/.347/.457. When we look at free agent corner outfielders making the league minimum during that time period (not cost-controlled players, players who had already reached free agency) they hit .265/.336/.423, or right about the league average. (Looking at STATS, Inc. Zone Rating, they were also pretty close to average on defense as well. ZR isn’t perfect, but I think it works well enough in group studies.)

[My estimates of players making the league minimum may be slightly off - a player who plays 1/3 a season at 3x league minimum will show up in my sample, because I lack service time data.]

So if these players are worth more than the league minimum in MRP, why aren’t teams bidding them up to their MRP? (Or even to some fraction of their MRP?) Why instead are they paying them zero plus the league minimum?

I think the answer is that these players have an MRP of $0, or close to. And here’s why I keep asking what you mean by marginal - this is how I am thinking of a free agent’s MRP:

The MRP of a team’s free agent players is equal to team revenue minus what team revenue would be with zero free agent spending.

There are two aspects to this - teams bring certain capital (stadiums, territorial rights, brand equity) to the equation. Then teams spend a certain amount of money on player development - minor league salaries, player development personell and scouting, draft bonuses, Latin American academies, etc. A team that does those things will have some revenue, without spending any money on free agent salaries.

So players who make the league minimum aren’t worth nothing, but they aren’t worth anything above and beyond what a team is willing to pay to develop and promote talent through the draft or amature free agency. In this instance, then, our replacement players/freely available talent (assuming that as a pool they are no better or worse than the pool teams have due to player development) have a MRP of zero, because they don’t generate any marginal revenue above that produced by a team’s initial investment in player development; thus, these players are paid the minimum.

[The confounding factor here is arbitration-eligable players, who are paid a percentage of their MRP relative to free agents.]

Given that thinking, it’s hard to see how a corner outfielder batting .239/.294/.359 can have marginal value above what a team’s spending on player development should produce. If the Braves’ farm system can produce a player who can hit better than that, or can find an equivelent player in FA, (and looking at BP’s minor league translations, I think that’s a good possibility), then having Francouer produce at this 2008 level actually produces a negative MRP - the Braves have fewer runs/wins (and given the premise of estimating MRP based upon estimates of runs/wins, less revenue) than they should given their investment in player development.

[Note: the use of the term replacement level doesn’t mean that a player below rep-level in a specific metric, like VORP, necessarily has an MRP of zero. I think there is still room to revise and improve the concept of replacement as is currently defined by sabermetricians.]

As far as moving on - I feel that by discussing this with you, I’ve actually been made to think a lot more clearly about these issues. I’ve also been exposed to points of view I hadn’t before, like Scully, Krautman, Fort and Vrooman (or at least, Fort and Vrooman’s response to Rottenburg). And I’ll admit that some of the concepts introduced from those papers have seeped into the arguement I presented above. If this conversation isn’t providing similar value to you, I truly am sorry. But from discussions here and elsewhere, it seems that there are people other than me (people who have read your book as well) who are having the same issues that I am. Maybe you’re entirely right and I’m not - and in that event, the most you have to gain from this is an understanding of a certain point of view that needs remediating. I hope you get at least that from this.

At this rate I could get an article out of this pretty easily.

And I think that JC has decided I’m not worth the headache anymore - that comment has been in queue for over 24 hours, he’s posted and approved other comments since then… yeah, I definately get the feeling that my contributions over there are no longer appreciated.

Thinking some more about Phil/73, I don’t think that roster limits and minimum salaries are really the main issue here.  If you allowed teams a roster of 30 players, most would probably add a couple of specialty relievers and a couple position players with good defensive skills (or maybe a pinch-hitter).  But they would all get paid very little, and other players’ salaries would change little.  The important constraints are 9 men playing at a time, 9 innings per game, and 3 outs per inning.  You win by putting the best 9 guys on the field as often as possible.  And even with bigger rosters, the vast majority of PAs and IP would continue to go to the players who get them now.

JC believes Francouer has value because he created 60 runs.  And 60 runs ARE valuable—a team would gladly pay $12M to add 60 runs to its offense next year.  But a team hiring Francouer isn’t awarded 600 extra PAs in which to score runs.  Francouer must take those PAs from another player, and thus his contribution is only the difference in production, which in this case is effectively zero because no team has a worse hitter consuming those PAs.  Goodyear can keep adding workers as long as someone buys the tires, but a baseball team can’t.

Join the club Colin.

Anyone who has a post moderated at JC’s site is free to post it here, uncensored.

I like the way that Guy put it.  You could make the roster sizes 100 players, but there are 27x162 outs available for the hitters regardless.

Colin:  JC may just be holding your comment until he has time to write a reply. 

If any of the journal articles you mention are available free online (aside from Scully), could you post links here?  Thanks....

Guy/85: you’re right, it’s an oversimplification ... it works if you assume that all players are equal in talent, but having more players gives you better matchups and you can earn a couple of runs that way.

Actually, Guy, I think JC may have closed the comments. The comments box has disappeared on my screen for that post. It still shows for his other posts.

I found the Krautmann article here:

http://findarticles.com/p/articles/mi_hb5814/is_2_37/ai_n28734871/print?tag=artBody;col1

Thanks, Eli.  Maybe I’m missing something, but I think Scully makes a basic error when he takes the coefficient for the marginal impact of a player’s productivity and applies it to all production for all players.  In sports, the marginal productivity may exceed average productivity (which I assume is rare in the “real” economic world).  Basketball provides a more stark example:  a regression would show that each 30 points scored/prevented (approx) adds one win, and another regression would tell us each win is worth $X.  Scully then says a player’s revenue is X * Points/30.  However, a team will score 95 points a game, generating over three marginal wins per game—6 times their actual wins!  And of course the Scully model would also contain a defensive variable, so now players are producing 12 marginal wins for each real win.

The same problem could apply to the revenue model, compounding the problemn.  A marginal win may generate $3.5M in baseball, but that doesn’t mean 81 wins will generate 81*3.5 = $283M. 

Is this right, or am I misreading Scully?

I think you’re right, Guy. Quoting Zimbalist again: “But the fatal problem is that Bradbury’s methodology unwittingly identifies a player’s average revenue product, not his marginal revenue product.”

Not all revenue is marginal revenue. I’m reading over the state’s audit of the Brewers’ finances, and it’s a pretty fascinating glimpse into the structure of a team’s revenue. This is less true of more successful franchises, but for the Brewers, a significant portion of revenue was either revenue sharing or league-wide revenue. I really think that you need to exclude that revenue from the regression when coming up with marginal revenue figures.

So essentially what you want is local revenues - attendance, concessions, parking, local TV contracts, etc. And I think you want to further isolate it from other things that contribute to local revenue - stadium, player development, brand, etc.

The interesting thing is that the more revenue sharing there is, the lower the $ per win, which is why players go crazy against revenue sharing (the union anyway).

Yeah, you end up with a handful of welfare queens like Loria in the mix.

One of the concepts I’ve come across recently in Rottenburg’s “invariance principle,” in that the distribution of players among teams doesn’t change when things like free agency or drafts are added - the teams with the most incentive to win games will find ways to get the best players regardless.

(This may be an oversimplification - I’ve yet to get my hands on the actual paper and so I’m reading about it second hand for an audience that seems to already know about these things.)

Something to keep in mind when arguements about salary caps come up. I’ll try to lay my hands on Rottenburg’s original paper sometime and read it.

I broke out his book and begun crunching the numbers, even using his own math, the 12 million is wrong and I am sure from his silence he knows it.

I am following his book on all calculations:

Total Revenue of Atlanta using his MSA model = ~127 million.

According to book this should be split in half between pitchers and batters or 63.5 million each

Francoeur got 10.7% of his team’s available salary from his at bats.  He gets 6.78 million from that. 

Fuzzy math coming up.  Since JC won’t answer what a league average player is, I just look the over league average for 2008 of:  OBP = .333 SLG = .416

OBP and SLG are the two values in his book that he uses to determine a player’s run producing value.

Francoeur’s 2008 were: OBP = .294 SLG =.359

He is definitely below league average player so he should get less than the 6.78 allowed from his at bats.

No idea were he is getting the 12 million from.  It would be ~10% of the entire teams salary in his model.  I hate to say this, but until he puts the numbers to paper, I am just going to consider him a joke/fraud.

Total Revenue for Atlanta = 127m - that seems very low to me. 

Most likely whatever formula he had in the book worked back when it was published, but he’s updated it to account for the massive increase in revenue since then.

As for the rest of it, JC would be wise to listen and learn instead of deluding himself into thinking he’s the expert on this, and that he doesn’t have to take any of us seriously until we submit and publish a peer reviewed paper.

This is simple stuff.  He’s making it a lot harder than it should be, and making so many mistakes in the process that it’s hard to know where to begin.

The book was published in 2007, not “that” much change since then.

Didn’t realize it was that recent.  As I get old, I have lost my sense of what happened when.  It all just sort of jumbles together.  If I had to take a guess, I would have said he published the book in 2003 or something.

Still, 127 total revenue for Atlanta seems wrong.  They’ve supported 80-100 million dollar payrolls, and I thought team’s generally spend less than 50% of revenue on payroll.  Is that local revenue, excluding National TV deals, MLB.com, and other shared revenue?

His equation:

MSA = population of metropolitan area = 5.3 million for Atlanta
RS = 753
RA = 778

(0.126)* (RS-RA) + (0.000665) * (RS-RA)^2 + 3.88 * MSA + 109.02
-or-
(0.126)* (-25) + (0.000665) * (-25)^2 + 3.88 * 5.3 + 109.02

Rally:  I think Scully only used gate and local TV revenue.  Maybe JC is doing the same.

My guess is JC is now using Scully’s method:  just subtracting a player’s total Run contribution from the team total.  Francouer created about 60 runs in 2008, worth about $10M with these coefficients (maybe JC credited him with a defensive contribution, or has modified the coefficients.) An average hitter would be worth about $14M.  The problem, as I argued before, is the players then produce far more than 100% of the actual revenue (the Braves’ hitters alone would have an MRP of about $135M using these coefficients).

In any case, his old method of starting with the average player and going up/down from there was a much better approach.  But then you first need a method for establishing the MRP of an average hitter, to give you a baseline.

Jeff:  Can you do me a favor.  Try the following run differentials:

-200 runs
-100
0
+100
+200

And report back the results.

If I’m doing this right, the revenue is higher at minus 200 runs than when RS=RA.

Tango: you’re doing it right.  But I think JC must have a mechanism for keeping the sign negative on the RS-RA^2 term when RA>RS.  If you do that, -200 runs costs you $52M in revenue, +200 runs is worth $52M.

He must keep the (-) sign some how.  i just re-checked the book and he doesn’t mention doing it in it.

Here are his numbers when he doesn’t keep the sign:

-200 131
-100 124
0 129
+100 148
+200 181

Correction on #104, if the sign is (-) it will become (+).  The graph looks like a J and is Figure #17 in his “old” book.

I did a little back tracking of numbers to find some of the other values for his equation in the first book.  It looks like the average player is around 83 RSBA (runs scored from BA) and Francour created 85 RSBA according to JC numbers, so he is due just over 6.78 million mainly for the innings he played.

JC has a talk and slides available:

http://www.sabernomics.com/sabernomics/index.php/2009/01/thanks-to-penn-state/

I’m finishing up listening to JC’s talk.  Nothing all that different from what we’ve discussed here, meaning he’s still missing the boat on what “marginal” should actually represent.

Actually, JC spends about a minute at the very end talking about the correct margin.

Not exactly word for word, but close:

“Ctain players who are lower quality have more substitutes… But maybe lesser pitchers, maybe like a Randy Wolf—a team might say well look, you’re worth a lot to us, but we can go out and sign some of these other players.  Some people have argued,’well couldn’t you just go out and pay a player the league minimum?’ Possibly.  But from the estimates that I’ve seen, teams are going to be willing to pay more than that, even for players who are not all that good, and the talent pool is thin enough.  But the fact is that we have to remember that there are substitutes out there and that might affect player salaries.”

Yup, that just might affect player salary.

So, Francouer 2008 is worth $12M, while Sabathia and Teixeira are each worth $16M?  Even assuming the latter two are in 2007 dollars, this isn’t even remotely coherent.  And he clearly doesn’t get the idea that the 750th best player must be worth zero (league minimum), which every fantasy player in the world understands.  JC’s got some work to do.

And I guess Colin was right that JC had terminated their discussion.  Too bad.....

Just found the link over here.  Good hour plus of reading out of it.  Everyone here makes interesting arguments.  I’m not convinced by any of them.

Sounds like a lot of outrage toward JC.  I think there may be difficulties coming from both sides.  JC gets a lot of flack for high valuations (including from myself in the past, though for different reasons) without a lot of defense.  I know for a fact that he does get fed up with that.  Maybe some has to do with unfufilled expectations that he has the ability to answer certain qeustions.  As an academic, he believes in using a full array of evidence to defend himself.  He may not have time (or the ability, considering contract stipulations with books in progress) to do this on a blog site.  He does it for fun and to a general audience. 

While I disagree with the explicit claim of ‘replacement level’, I also do believe that, of course, not all revenue is generated through player statistics on the field.  It’s a tough question, and while obvious answers seem, well obvious, each explanation I’ve seen still falls short (including Phil’s subtraction of minimum salary on his site, JC’s total revenue model and average MRP calculations, as well as using replacement players: this simply puts a label on something that means nothing...similar to an intercept in regression...interpreting something like this becomes problematic and can lead to misleading conclusions).

I absolutely agree that a player at Francouer’s level can be replaced for cheap.  But I think that fielding a team has more complications than just statistics.  As explained in one comment I saw, deliberately fielding a team of ‘scrubs’ may not be profitable.  This is a corollary to my argument about the Tigers on Colin Wyers’ first valuation article on THT.  I don’t think the total revenue model OR replacement level model is really able to account for what is going on with salaries.  Maybe some day I’ll have time to check it out myself, I honestly don’t have time.

I also believe that comparing how MLB works to Fantasy is a huge mistake.  They are quite different worlds and while we like to think that playing fantasy gets us close to running a real team, it’s not. 

Everyone has some work to do.  If we didn’t then no one would be having discussions and everyone could simply just know the answer.  I believe there’s something to what everyone is thinking, but bringing it all together seems to be difficult.  We’re somewhere in the middle, and it may be impossible to quantify what to do about it.  It’s fun hearing everyone’s discussion, though.

There’s a pretty easy way to settle this: by actual experiment.

Suppose we had JC give his function of how revenue relates to wins (and it doesn’t matter if it’s a little off).  And suppose we have him give us a list of how many wins each player produced in 2008 (and again, it doesn’t matter if it’s a little off).

If JC likes, we could populate the teams with a certain number of arbs and slaves—if JC thinks it’s appropriate.

Then, we have an auction of all the players; when you get a player, you get his known 2008 stats, with the number of wins that JC previously assigned that player.  You are allowed 27*162 batting outs total.

At the end of the auction, we figure out how many wins each team bought.  We use JC’s function, whatever it is, to determine how much revenue that number of wins brought in. 

Then, every participant receives (or pays) the difference between his revenue and his total payroll, paid by (or to) the other participants.  (It has to be for real money, of course.)

In the true spirit of experimental economics, we repeat the auction as many times as necessary for everyone to learn the game, so that eventually the results become stable.  Most likely, in equilibrium, everyone breaks even, or comes close to it.

Then, we see how the salaries came out.  Did Francoeur actually generate bids of $12 million?  JC says he would.  I say he won’t.

BTW, in one of my posts, linked to in comment #37, I posted a simple version of such an auction and why I think replacement value matters.  Rodney Fort said the example was too contrived to be meaningful.  Well, this is our chance to have a real-life simulation, based on JC’s actual formulas.

JC wouldn’t even have to participate—if he gives us his function of how to turn wins into revenues, we could get a bunch of people—on both sides of the debate—and just run the auction.  It would make a great article for JQAS.

I’m not sure you’d need people.  Just bootstrap it with the sample of players out there, if you’re convinced it’s a sample size or distribution problem.  You could specify revenue streams for each team based on whatever you think is right (whether it’s Forbes, etc).  Specify some maximization problem based on ‘market size’ and simulate some auction though an algorithm.  Seems like that would be less expensive.  Less fun I guess, though. 

This way you take out any bias toward JC, or any individual player and how many at bats they get.  We could also get an idea of how player values vary from team to team.  It could be decided solely on their performance in 2008 (or, if you want something more useful, their projection for 2009).  Unfortunately, if you only use one model, and it already says Francouer is worth $12 million, then our result would most likely tell the same or a similar story.

Why just use Bradbury’s model?  Why not put everyone’s to the test?  I know there are simulation games out there.  Use a platform like that, but specify team values and revenue based on the teams’ current states.  Get that peer reviewed by econometricians, economists, statisticians, business experts, etc. (like in any peer reviewed journal).  Quite an undertaking.  Anyone have time to put together a simulation like that?

The difficulty under both situations is that we would have trouble really accounting for the differing strategies used across teams based on their market behavior.  People won’t necessarily simulate that well, as they don’t have the proper information.  Of course, a computer can’t either without that same information that the people would need to give it.  That’s why this is such a difficult problem.

Millsy/112: The reason you have to use JC’s model is that if you use any other model, JC can just say your assumptions are incorrect.  And if you use an algorithm, anyone can say that the algorithm is wrong.

If you’re disputing JC’s model, you have to let JC specify all the parameters of his model.  And you have to have humans, and it has to be for real money.

#110.  I thought that JC’s work could actually be very useful in the baseball discussion.  Take a pure economist’s view and look at the economy that is MLB.  It would be nice to be able to find where baseball economy model is different from baseball ecomony real world. 

His salary model in his first book is actually seems to predict Francouer’s salary much more inline with other people.  In the first book, I could follow the logic (and somewhat agree with it).  His new method (magic?) that says Francouer is worth 12 million, makes no sense. 

I have been pretty hard on him, but if he is going to make such a claim, which not one other person in existence agrees with, he should try to back it up.  I previously liked his approach and what he does of the discussion of baseball the money involved with it, but his stubbornness to not show how he is getting these high valuations or just admitting he is wrong is just rubbing a lot of people in the wrong way.

The incentives are extremely skewed though. 

Even if you have people making decisions based only on the model, wouldn’t we expect the outcome to create a world in which Francouer really creates $12 million in revenues? 

Based on the fact that he was on the field, in that slot, Francouer helped produce a specific amount of revenue to the team.  They could get this for cheaper most likely, and I believe JC absolutely concedes that point (if we’re solely basing off performance).  What he does imply is that the Braves can sign him for $3 million and not lose any money.  Maybe they could save some by sending him down and bringing up Joe Blow to sit on the bench.  Would they make more money that way?  Maybe...but we don’t really know.  Maybe Joe Blow was a top minor leaguer.  Maybe he’s not ready yet.  Maybe doing this, in the long run, will cost the Braves more than $3 million.

I’m not defending any particular person here.  I just don’t think basing a world exactly off a model, using the same data the model used, will do anything but produce the model.  It is based on average MRP...therefore basing the Pirates decisions on ‘average’ wouldn’t pan out anyway.  JC suggests his estimations are just that: estimations.  I can’t really comment on the accuracy of the model...I don’t know.

MY PROBLEM is that when there is a limited supply of players, say, at the level of Jason Giambi to Albert Pujols and everywhere in between, these teams don’t totally discount the stats put up ‘within’ replacement level.  In addition to this, assuming that every prospect in AAA is just there for replacement is a mistake.  There really are NOT infinite ‘replacement’ players.  Many of these guys are in the minors for a reason: to develop into Major Leaguers.  There is investment in that.  Just because they could perform at Francouer’s level doesn’t mean they should be moved up right away.  There’s long run and short run considerations here.

However, I do not believe that all profits should go to the players.  Some will have more leverage than others.  If your’e really bad, you probably don’t have much.  If you’re a rarer breed, you will have more leverage to cut into those profits and be closer to your total revenue produced to the team.  This is precisely why a set replacement level doesn’t work very well.

There is, of course, inherent value in the franchise being part of the league and its revenue sharing.  But without putting those players on the field, there is no MLB that people would want to watch.  That’s why we have strikes, minimum salaries, and Scott Boras.

I think Phil has a fantastic experiment idea.

The major problem I have, using JC model (first book only), Atlanta has 64 million to spend on batters and Fran gets 12 million of that or 19% of the teams salary available for hitters.  This is where I have problems with his math.  Since there are other, better, players on Atlanta, the 12 million is way out of wack and this is using his data/methods.

I would love to see Phil’s system go into effect.  Heck, I will use JC’s original method (book 1) against his current one and feel I could come ahead.

I guess I’m unclear on the actual structure of the study.  I think it’d be a fun experiment though.  With any model.

Phil does have an interesting idea.  However, it won’t work here because JC won’t reveal his new model.  Maybe it could be used to test some other model.

BTW, from JC’s book, here are the first few guys I found in 2005 who JC pegged as having an MRP about the league minimum (min 100 PA).  I’ve added their RC27 from Baseball Reference (which might be different from JC’s measurement of their offense on which his MRP is based).

Mondesi, $470K, 155PA, 2.9 R/G
Macias, $410K, 190PA, 2.5 R/G
Jimenez, $410K, 119PA, 3.5
Thames, $510K, 118PA, 3.6
Treanor, $360K, 154PA, 2.6
Castillo, $300K, 114PA, 3.2
Ryan, $310K, 131PA, 2.6
Offerman, $380K, 118PA, 3.4
Womack, $380K, 351PA, 2.7

Observations:

-- These guys should all be at replacement level.  Most of them are substantially lower than that.

-- PA seem to have a value in and of themselves, as the more PA you have for a given level of offense, the higher the MRP.

Oops, correction to #120.  These guy’s *salaries* should be no higher than replacement level.  I don’t actually know what their MRP should be, because I don’t know if JC’s MRP is based on .000/.000/.000 or what.

However: We can conclude that salary should *not* equal MRP here.  Because if you take three of these guys, and add them up, you get a replacement-level player’s full season (worth $390K), but an MRP over $1 million.

JC has now turned off comments forever:

http://www.sabernomics.com/sabernomics/index.php/2009/02/removing-the-comments-feature/

I blame Colin.....

Guy, if I could claim credit for that, I would.

Seems like a knee jerk reaction to lots of criticism.  There is no doubt that there is always going to be lots of “noise,” some of it quite bad, in a comments section, and the owner of a blog certainly has a right to have or not have a comments section.

But it also seems to me that if you are going to write something you think is important, you have somewhat of an obligation to let your readers comment and you simply have to put up with whatever they dish out.

An example is Neyer’s blog.  The quality of the comments are pretty poor in general, in my opinion, probably because it is on a mainstream site (ESPN.com). And there are several people who love to lambaste Rob and even get personal (sort of) sometimes. Yet he bites the bullet and even occasionally responds.

Finally, if JC does not like to read the comments, he is under no obligation to do so.  So why would he disable them?  Is his skin that thin?  Oh well, as I said, it is his blog.

Neyer, Posnanski are ideas of professional bloggers.  They let their audience speak for themselves. Jon Weisman is a similar blogger who has simple and direct guidelines:
http://latimesblogs.latimes.com/dodgerthoughts/

Thank You For Not ...
1) using profanity or any euphemisms for profanity
2) personally attacking other commenters
3) baiting other commenters
4) arguing for the sake of arguing
5) discussing politics
6) using hyperbole when something less will suffice
7) using sarcasm in a way that can be misinterpreted negatively
8) making the same point over and over again
9) typing “no-hitter” or “perfect game” to describe either in progress
10) being annoyed by the existence of this list
11) commenting under the obvious influence
12) claiming your opinion isn’t allowed when it’s just being disagreed with

They don’t usually (or ever) get involved in a back-and-forth with them. 

Our comments policy, lifted directly from USSM:

Think of this place as something like a college classroom. We’re in charge, we pick the topics, we set the rules, and we try to foster as much intelligent discourse as possible. If this isn’t your cup of tea, there are plenty of other sites out there for you to try—we’re not going to be for everybody, and we’re not going to try to appeal to the masses.

We are involved heavily in the back-and-forth.

JC’s comments policy is not at all the way most bloggers would lay down the law:
http://www.sabernomics.com/sabernomics/index.php/comments-policy/

I find that policy very stifling, which is not what one would expect from either a professional blogger or a professor.  And if I applied that policy here, his post #31 would not have seen the light of day.  So, he simply has not gotten the hang of blogging yet.

In any case, my post 30 way above is an open invitation to JC to provide us with the very basic data we seek.  He can insult me all he wants, as long as he at least delivers the goods.

Here’s Dave Berri on JC’s comment policy:

http://dberri.wordpress.com/2009/02/15/king-james-and-kobe/

One problem with eliminating comments is we can’t see how the readers of these blogs feel about having their right to comment removed. Still, Bradbury is well-known enough that I was able to find some reaction on other sites.  And the conclusion reached by some is that Bradbury turning off the comments suggests that he is afraid of criticism. Such an argument, though, has problems.

Bradbury and Mankiw are both academics.  Consequently the argument that these two are afraid of criticism is difficult to believe.  Professors spend a fair amount of time critiquing the work of students.  This habit of critiquing students often carries over in our interactions with our colleagues.  In other words, criticism is a big part of academia.  So it’s unlikely someone who has found success in this environment (like Mankiw and Bradbury) would have trouble with criticism. 

For a more plausible explanation, let’s turn to basic economics.  As I noted in discussing Mankiw’s policy in 2007, simple cost-benefit analysis explains this behavior. Reading comments imposes a cost.  For this cost to be justified, the comments have to provide some benefit.  And apparently, both Mankiw and Bradbury have concluded the benefits fall short of the costs.  In sum, the removal of the comments feature on these two blogs says less about Mankiw and Bradbury and more about the perceived quality of the comments.

I’m a pretty good Googler.  And I looked pretty hard.  The only place on the entire planet that I found that made any comments about JC’s policy is in this thread.  So, Dave is almost certainly talking about Posts 122 through 126.  (Why would Dave not link directly to the threads he’s referring?)

I disagree with the inference Berri wants to draw regarding academia, that somehow academicians are more thick-skinned than the rest of us.  The presumption must be that each group of bloggers has the same thickness of skin, until evidence is presented otherwise.

More to the point - instead of starting from the overall premise that academics take criticism well, why not respond to the claims of specific criticisms that Bradbury doesn’t address?

Nobody’s alleging that Bradbury is afraid of criticism because he shut down comments, at least not as an “if x, y” relationship - most of us were claiming that Bradbury is afraid of criticism BEFORE he shut down comments.

I would also offer that it is possible that certain academics could be unafraid of criticism from other academics, but afraid of criticism from the masses.

It is one thing to be critiqued by one of your peers; it is another to critiqued by an outsider in a field in which you are supposed to be the expert.  And of course I don’t mean to imply that this impulse would be limited to academics.  If Tango or Colin or MGL registered their disagreement with something I posted on my blog, I would be much more open to it than if it was from an anonymous poster with no “credentials”.  The hypothetical academic and I are both open to peer group crticism, with the only difference being how we define our peers: the academic considering his peers to be other academics, and me considering my peers to be other sabermetricians (a much more nebulous group definition than “academics”, and yet one all the same).

-- Academics often give and take criticism in their normal line of work.
-- JC Bradbury is an academic.
-- Therefore, JC would never be afraid of taking criticism.

That syllogism just doesn’t wash with me.

Also:

“And apparently, both Mankiw and Bradbury have concluded the benefits fall short of the costs.  In sum, the removal of the comments feature on these two blogs says less about Mankiw and Bradbury and more about the perceived quality of the comments.”

Well, yes ... it’s a tautology that the benefits fall short of the costs—that’s why any human changes any course of action, because the costs of the old way outweigh the benefits. 

However, it doesn’t necessarily follow that the only way the costs outweigh the benefits is for the comments to be of poor quality.  It could be, as commenters here have implied, that the criticisms are so valid that they impose a cost on JC in credibility.

I’m not saying that’s actually what’s happening, of course, just that it’s consistent with Berri’s cost/benefit tautology.

I say this as someone much more sympathetic to academia than a lot of people here--I am currently a grad student in a Ph.D program--but the idea that being a successful academic, or academic economist, indicates that one takes criticism well is beyond absurd.  Indeed, making yourself sufficiently unpleasant that no one wants to challenge you in public is a perfectly workable strategy for an academic.

Berri just earned the title of “horrible economist” in my book. I don’t disagree at all that Bradbury’s refusal to endure further blog comments can be explained by “basic economics,” but Berri seems to think the job of an economist is merely to point out that actions have an economic incentive and to quit without any analysis whatsoever.

Bradbury published a book, and that book seems to have been wildly discredited by his own blog posts. The comments on his blog - which, as far as I have seen, were intended in the spirit of peer review to correct a whopper of an error - magnified and continued that process of discreditation, since Bradbury’s response was to stick by a flawed work (for a wide variety of exceedingly obvious economic factors). The comments subjected to Bradbury to a number of costs, and his only out was to turn them off.

Berri swoops in and argues against a seemingly non-existent view (Bradbury simply “is afraid of criticism” - something I don’t recall seeing on The Book Blog or elsewhere) by pointing out that there is a simple time cost to comments. We already knew there was a time cost - Bradbury had been repeating it over and over because he was already moderating all comments - a self-imposed time cost.

How can Berri just flat-out ignore that Bradbury turned off comments only after being outright hammered on his “The worst player in baseball was underpaid by $12 million” post? How can he act as if his colleague has merely made a market adjustment, as if turning the comments off is like discontinuing a company’s least successful brand of snack chips because they break even instead of profiting? (It would seem that the snack chips have rather been linked with salmonella.)

Oh yeah, because Berri is subject to the same “basic economics” that dictate keeping your mouth shut when a product similar to your own is discredited in the marketplace. Berri’s either a) randomly stumbled upon some other blog that, apropos of nothing, has been complaining about Bradbury turning off his comments or b) is eliding the actual and obvious criticism of his colleague because the criticism is detrimental to his own economic interests.

Berri has the gall to cloak Bradbury as an honest academic. Screw that. There is a distinction between academics and economists. No matter what price you are paying an economist, you can never tell how much the advice you’re getting is worth. There is always an obvious question of, “If you know so much about the economy, why aren’t you using that knowledge to profit off of it instead of sharing it with me?” And of course, the reality of such a question means we can rarely believe with great certainty the economist’s response to such a question. We cannot point to the same dilemma when discussing academics in many other fields.

Bradbury has shown that his “academic” expertise, econometrics, has, at the very least, HUGE problems in its attempts to bolster knowledge about baseball. Berri has chosen to ignore this in order to defend his colleague against criticisms that he does not identify. Berri’s nothing but an accomplice.

Maybe not afraid of criticism but annoyed

I finally got my hands on a copy of the book again, and was able to read over the chapter and the footnotes a few times. Using the Baseball Databank, I was able to put together a reimplementation of his work:

http://basql.wikidot.com/baseball-economist

Except for the regression intercepts, all constants used come from either Chapter 13 or the footnotes. (I had to tweak the intercepts to make RS/RA come out to the league average, about 20 for RA and 9 for R.)

If you put Francoeur’s 2008 line into that, what does the system say? He says he changed the system (not sure to what degree exactly) since that book came out, so maybe there’s a big difference in salary “earned”

If I dummy in a straight 10% increase in revenue per season, I get $3,986,316 in MRP for Francoeur’s 2008 season.

Or put it this way - a hitter with an MRP between $200,000 and $400,000 has an average OBP/SLG of .264/.284, which (doing a lot of really shaky back of the envelope math) comes out to a RAA_700 of about -56.

Yep.

JC has revised his estimates for Francouer. He admits that his old system was “giving credit for non-marginal revenue contributions and over-weighting defense”:

http://www.sabernomics.com/sabernomics/index.php/2009/10/should-the-mets-offer-jeff-francoeur-arbitration/

The valuation of players in terms of runs, wins, and dollars is so incredibly easy, it’s a shame that we have someone as bright as JC trying to make it seem like it’s more complicated than it is.

I mean, even his “74% less” for arb awards.  Is he talking about 1st-year eligible, or all arb players?  In the past, he made it seem like it was “all”.  Now? He doesn’t say. 

Anyway, at least JC is benefitting from us, and as long as we can set everyone right, that’s all good.  It was a tough battle with Clay to finally acknowledge WARP had the wrong baseline, and JC is going to give us a battle too it seems.

I’m not convinced WARP uses the right baseline even now. (Of course, since they haven’t been publishing the sortable WARP report since at least yesterday, it’s hard to say what baseline they ARE using right now.)

JC’s revisionism is galling, at least to me.

At the time, I generated some estimates of Francoeur’s worth that projected he was worth around $12 million, and should expect around $3 million in an arbitration award. Understandably, this upset some people (including me) for the sake of the sheer size of the number.

How did that upset him? And it would be nice to see him offer some sort of apology for all of the commenters he insulted in the process (I include myself here).

And of course he still doesn’t get it:

The $6.8 million estimate says he’s worth well more than that, but the estimate is misleading. The MRP estimates give credit for the playing time, and Francoeur’s managers have played him far too much. ... He’s no Natural, but he is a useful player who can serve in a platoon/reserve role. But, that’s not how the Braves or the Mets used him. Since his first full season in the majors he’s averaged 666 plate appearance a year. While this number may be appropriate for the anti-Christ, it’s not the number of PAs that any manager should be giving Jeff Francoeur. Jeff Francoeur should probably play 50% is what he has played, cutting his MRP estimate in half.

Sigh. The problem isn’t Francouer’s playing time (well, at least THIS problem isn’t) but how the model values playing time.

Well, let’s give JC credit for acknowledging a previous error.  The new valuation of Francouer seems plausible, if you credit him with good defense in 2009 (which I think plus/minus does).  It will be interesting to see his revised model, assuming he lays it out at some point.  (Although I agree with Colin that the comments about playing time still hint at a flawed valuation model.)

On the other hand, I find JC’s post on finding a “Duncan effect,” like his “Mazzone effect,” remarkable:  http://www.sabernomics.com/sabernomics/index.php/2009/10/the-duncan-effect/.  He claims that Duncan reduces pitchers’ ERAs by 0.35 (I think for Mazzone it was around .50 or .60).  Now, a coach who could do this would deliver about 6 wins to a team, and be worth upwards of $18 million a year.  If Duncan has anything like this kind of talent, his current salary would represent a gargantuan market failure.  To me, this is just implausible.

And let’s look at Mazzone:  after JC discovered his amazing talent, he went to Baltimore and bombed, and now doesn’t even have a job.  Are we to believe that 30 teams are letting $25 million worth of coaching talent sit unemployed, when he could be hired for a few hundred grand?  Rather than repeating his analysis for other coaches, JC should be trying to figure out why his calculations might be wrong.