THE BOOK--Playing The Percentages In Baseball

Hey Tango, I have been reading your site for a few months now and just read the e-mail exchange between Eric and Rob Neyer on his blog. I just had a question I was hoping you could answer for me. As a Yankee fan, I hear a lot about Montero being switched to first base before he reaches the majors. Do these positional adjustments suggest that even if he is worth -15 runs behind home plate, it is worth keeping him there over moving him to first?
Thanks,
Greg

http://www.sabernomics.com/sabernomics/index.php/2008/12/im-not-a-sabermetrician/

On JC’s site I added:

“And, learned first-hand in my interactions with them, SABRmetricians simply are not interested in the MR part.  So, no surprise, whenever they do bring it up, they do it in ways that bother economists.”

Rodney: I don’t think that your experience with sabermetricians is broad enough to make this statement about sabermetricians.  There are some who apply MR, by service class, in establishing valuation, including applying discount rates.

The safer thing to say is that both sides can learn more from each other.  But, there is already tremendous overlap.  You simply haven’t seen it.

Greg: you’ll have to tell me how you think he would do at 1B as well.

Well, let’s just say he’d be an average first baseman, because I don’t see any reason to assume he would be better than average, and I also don’t see any purpose to moving him to first base if he would be below average there.
Thanks

oh, and also, I understand that’s how the calculations would come out, it just seems a bit off to me.

So, he’s -15 as catcher, or average at 1B?  That’s easy: leave him at catcher!

I have a 25 run gap between the two positions.  Now, if he’d be above average at 1B, say like +10, then we’re at a breakeven point.

What’s the forecast for his hitting?

I agree 100% that comparing peer-reviewed articles to “informal online discussions” is a bit of an unfair comparison, and that the correct analogy is the vetted and published stuff, like in the Hardball Times.

Very well said.

Although only 18, I have Montero projected at a .340 wOBA, with 653 weighted PAs, about the minimum for reliability.

.340 is well below avg for 1b (.357) while much better than the acg c (.311). -9 offensively at 1b, +18 at c over 600 PA.

Was there any resolution to the discussion a week or two ago about Mirabelli and the replacement level for catchers? IIRC, someone suggested that the gap between average and replacement might be about 10 runs for catchers versus 20 runs for other positions.

dcj,

That discussion led me to write this on Hardball Times:
http://www.hardballtimes.com/main/article/replacement-level-article/

Whether you consider it a resolution is up to you.

"When it comes to the advancement of baseball analysis, the peer-reviewed research of academia is nowhere near the top of the list.”

With only a toe in each camp, I’d be hard-pressed to defend that statement.  I don’t think most of the online community is familiar enough with the 3-4,000 articles per year published in academia to assess how much it has contributed. Neither community pays enough attention to the contributions of the other.

There are 4,000 articles about baseball analysis published every year in academia?  I find that hard to believe.

Just to return to the substance of the Bradbury/Tango difference on Ibanez, what difference in method between these two very smart guys is leading JC to value Ibanez at about $46 million for 3 years and Tom to value him at about $10 million?

goto: we reference academic papers here all the time.  Perhaps most don’t reference them, and I can agree with you there.

Feel free to post links to various papers that you think will interest us.

Also, I’d love to see *one* paper that references work on Hardball Times or in The Book.

***

http://sabermetricresearch.blogspot.com/2008/12/who-is-sabermetrician.html

I posted this on Phil’s site (on which has lots of other excellent comments):

Good comments, allround.

My one issue with JC’s comment is that it reads almost as if that the academic process will yield better results. Clearly, there is fantastic work being done without care of an academic process.  And alot of this work is done in a collaborative manner, as each person is inspired by others.

The only precondition I would say that an academic and a sabermetrician needs is a deep understanding of baseball.  Too often, I see an academic (and sometimes sabermetricians) be a slave to the regression, even if it runs counter to something intuitive about baseball.

Another bias I see is that while a sabermetrician will be all too eager to read the work of anyone out there, including those from academia, I don’t see the same eagerness the other way.  Academia will rarely reference work done outside the academic world, essentially marginalizing 90% of the advancements in sabermetrics.

I also see a similar level of ignorance (disproportionately) from the older generation, whose knowledge of sabermetrics stopped when Palmer and James stopped publishing regularly.

The “underground” (i.e., internet, which is really the mainstream at this point) is where most of the great work is happening.

Yes, we’d love to have a stronger knowledge of economic and statistical disciplines.  But, as MGL said, we have day jobs too.

Looking at the comments at Phil’s blog, I see that gotowar was referring to articles on baseball and economics.  I am still surprised at the volume, but I guess put this way it is easier to swallow.

However, I think that baseball economics and sabermetrics are distinct disciplines.  Obviously there is overlap, but a lot of what falls under “baseball & economics” is not particularly sabermetric (ex. the economic impact of new stadiums on the adjacent business district), and a lot of sabermetrics is not economic (ex. developing a run estimator for extreme environments).

I do think that an economic approach to thinking is very helpful to sabermetrics.  But a lot of what we do is not really economics, and a professional economist is not any more well-equipped to provide peer review on it than any other intelligent person.

Not being an academic, it’s very difficult for me to access academic papers. If anyone knows where I can find these 3-4,000 academic papers that I’m missing out on, I’d be in their debt of gratitude.

But I agree with Patriot - a lot of sabermetrics isn’t economic, or often even particularly statistic. (BaseRuns or Pythagorean win expectation are two things that I don’t think really fall under the auspices of statistics at all.)

I think this is a good example of the sort of paper Tango is talking about:

http://arxiv.org/PS_cache/arxiv/pdf/0802/0802.4317v2.pdf

That’s Shane Jensen’s SAFE paper, and MGL’s work on UZR (and Pinto’s work on PMR) are both cited.

Then there’s stuff like this:

http://www.economics.pomona.edu/GarySmith/BBregress/baseball.html

Which is a nice article on regression to the mean for hitters and pitchers - except it uses batting average and earned run average.

I’m going to probably end up spending more time than I’d like on this.

Although JC does not give his exact methodology for valuing players, it appears, according to his FAQ, that he is using a $ per marginal win value that is team dependent and dependent on the number of expected wins that team will have, with and without the player in question.

So, for all we know, he may have Philly’s marginal win value at 10mm.

Arguing about a player’s WAR and his $ value are two completely different things if you are not using the same $ per win.  So there is somewhat of a misunderstanding in terms of JC’s and Tango’s $ value for Ibanez, as apples and oranges are apparently being compared.
Sabermetricians, or anyone who is doing sabermetric work, should argue about a player’s WAR and THEN argue about what each marginal win is worth, if they want.  Those things are separate issues.  You can’t argue about a player’s $ value without first establishing what $ per marginal win value you are using.

Of course, you cannot even argue that latter point until you explain or define what you mean by worth.  Tango simply uses the average (for all teams) going rate.  That is neither right or wrong.  It is just how he defines “value” (of the marginal win).  If JC wants to use HOW much revenue he thinks or estimates a marginal win adds to a particular team at a particular time, that is fine.  Nothing right or wrong about that.  It happens to be much less cut and dried, of course, but it is what it is.

There is one thing that Tango can do and JC cannot, however, using their respective methods for estimating or defining $ per win.  JC cannot really say that this is what a player is worth on the “open market” using some particular team’s marginal win value.  Those values presumably vary tremendously from team to team.  A marginal win for the Yankees next year might generate 10 mil in revenue while for the Royals it might generate .5 or 1 mm.

JC can’t even say that a player’s contract was a good or bad one for a particular team (unless he defines good or bad by the difference between that player’s team-specific $ value and what they pay him), using his team-specific $ per marginal win.  For example, if a player is 2 WAR and the Yankees sign that player for 16 mm, they likely overpaid for him even though that player might generate 20mm in net revenue for a cost of 16mm.  That would likely be a “bad” signing since presumably they could have gotten that same player or some other player or players who could generate those same 2 WAR for a lot less (if we accept the fact that the “going rate” for a WAR is 5mm or so).

The only caveat to that paradigm would be that if the Yankees can’t get another 2 WAR at the “going rate” and they exhausted all other possibilities, then it is “correct” for them to “overpay” for those 2 WAR if in fact that generates profit for them.

I thought (and wrote) that the issue with JC’s valuations is that they treat all runs equally.  I argued that you should treat the number of runs corresponding to replacement value of runs as worth zero (or the major league minimum), and only after that minimum are salaries worth the marginal value of the runs to the team.

Is that not true?  Is there some other difference between Tango’s methodology and JC’s?

The best thing is not to presume what JC does and does not do.

I have no idea how he’s handling aging, if at all.

I have no idea if he’s using a positional adjustment or if he treats SP and RP differently.

I do know he applies the 10% growth that I’ve been using.

Thanks, mgl, for the illuminating speculation on how Bradbury and Tango came up with such dramatically different valuations.  I would add one observation to your point about team-specific marginal values. If Ibanez was actually worth $15M/yr to the Phillies, for reasons unique to the Phillies, but only $3M/yr to an average team lacking the unusual characteristics of the Phillies, then you are right that the Phillies overpaid for an asset they could have recieved for less.  But it only takes one other team that the Phillies believe would value, and may pay, Ibanez at $15M/yr, for the Phillies to rationally pay Ibanez his full marginal utility to them.  And of course multiple market participants may have strong incentives to misinform the Phillies about Ibanez’ marginal utility to other teams.  Ibanez of course has an interest in making the Phillies believe that others are willing to pay close to his marginal utility to the Phils, the Mets (who don’t want to see the Phils get a bargain) may have a similar motive, and other teams and other agents may all have interests in characterizing Ibanez’ marginal utility to other teams as comparable to his marginal utility to the Phillies.  This set of phenomena may be related to the so-called “winner’s curse” in auction situations, in which auction winners tend to “overpay” because the winner tends will be the one market participant who most highly values the product being auctioned, rather than the core group of potential buyers whose consensus may better reflect a neutral market value but who won’t bid high enough to beat the bid of the extreme high outlier.

tango, in real life I’m a health economist and a huge baseball fan, so I mean it when I say I have just a toe in each camp.  I barely have enough time to keep up with my area, but I do squeeze in peeks at both online and academic baseball research. From what I’ve seen you and JC are some of the few who reference academic works.  And you are right that few academics reference non-peer reviewed work, but there’s a reason why.  Submit a paper with non-peer reviewed research cited, and that’s a guarantee that the peer reviewers are going to nitpick that part of the paper.  But, you’d be surprised:

Just one?

Will this one do?
http://66.102.1.104/scholar?hl=en&lr=&scoring=r&q=cache:udzY_8yPtfUJ:arxiv.org/pdf/0705.3257+baseball+and+lichtman

Patriot, I disagree.  SABR is baseball research.  I know many use the term more narrowly to focus on statistical estimation of onfield events, but I think that’s in error.  So, I would argue that all baseball economic research IS sabrmetric, while not all sabr research is economics.  So, yes, google scholar shows typically 3-5,000 peer-reviewed papers on baseball and economics.

That’s what happens when you tie tenure to publish or perish!

But it only takes one other team that the Phillies believe would value, and may pay, Ibanez at $15M/yr, for the Phillies to rationally pay Ibanez his full marginal utility to them.

I know nothing about economics and/or free market theory or whatever it is called, but is that correct?

A commodity will demand the highest price that someone will pay of all the possible suitors?  I don’t think that is true.  Doesn’t it depend on how much of the commodity there is and how many “high priced” suitors there are? 

For example, if there are 5 Ibanez and only one team who values them at 15 mil, while all other teams value them at 5 mil, what will he ultimately sign for and with whom?

I would think that the ultimate value of a commodity is close to its average marginal value among all suitors, no?

What if I am looking to buy some steel and the average price of steel based upon market influences is $10 per pound.  Everyone buys steel for $10 per pound and that makes them an additional $5 (through the profit they make when they sell whatever it is they are using the steel for).  What if I happen to be manufacturing something that allows me to make $100 per pound for that steel such that I could actually afford to buy it for $50 a pound?  Am I going to pay $50 a pound for that steel?  No!  I am still going to pay $10 a pound.  Maybe I might drive the price up to $10.01 but that’s about it.

In any case, arguing with JC or anyone about Ibanez’ dollar value without specifying the other parameters, not the lest of which is how many $ per marginal win you are assigning him, makes no sense.  What Tango and JC (or anyone) want to argue is how many WAR Ibanez is worth. And that would be a short argument since the range of reasonable answers is really quite narrow.

gotowarmissagnes, the problem (for me, at least) is that a lot of academic work on baseball is simply not very accessible. I spent a few hours this afternoon looking for academic papers on baseball (with the caveat that I wasn’t about to part with money for them) and it’s difficult at best. And some academic sites are asking for $14-$34 per paper - that’s the price of a decent baseball annual or a year’s subscription to a site like Bill James Online or B-Ref’s PI feature.

And even if they were all free, simply finding articles is like pulling teeth. Google Scholar helps, but even so I was only able to find a handful of pieces.

tango/22:

>“The best thing is not to presume what JC does and does not do.”

Well, isn’t the idea to identify where you differ so that you can try to figure out which approach is the right one?

Patriot, I disagree.  SABR is baseball research.  I know many use the term more narrowly to focus on statistical estimation of onfield events, but I think that’s in error.

The term “sabermetrics” was never intended by Bill James to apply to all aspects of research about baseball.  Defining all baseball research as sabermetrics is to make the terms so broad as to be useless.

SABR and sabermetrics should not be confused.  Bill James incorporated SABR into the name he chose to pay homage to the organization, not to unite all of the research done by SABR members (which does run the whole gamet of baseball topics) under that banner.

Yes, MGL that’s a little simplistic, but correct.  Take your first example where there is just one team that values Ibanez at 15 million and 5 that value him at 5 million.  If that’s the case, then the Phillies can get him for 5.1 million.  However, if there are two teams that value him at 15 million and 4 that value him at 5 million, then the Phillies are going to have to pay him 15 million.  His value is not the average value among all suitors, but the value you have to pay to outbid all the other interested demanders.  Think of each point on the classic demand curve as a person who had to outbid every person below them on that curve for that particular unit of the good.

Now, to your steel example, if you have a way of making extra profits that depends on monopoly, then steel should not go up.  But, if anyone else can enter the market and use steel that way, then they will and you’ll all be demanding steel as an input, and that will drive up the price of steel.

Yes, Colin I am sure it can be quite inaccessible in more ways than price!  Since my university pays the fees, if I connect through my office laptop, I get validated and into the journal right away or may just have to connect through our library, while I’m sure many of you would have to pay.  In many cases, however, if you find an abstract that looks interesting, you can write the author and they will send a copy.

You may remember, MGL, that Marvin Miller, when the players’ union first found itself with the prospect of free agency looming, was very happy that the owners sought to limit free agency to a relatively select group of players each year.  Miller recognized that if hundreds of players were thrown into free agency at once, they would become a commodity product and the owners could keep the cost of labor relatively low.  But free agent MLB players come on the market in a small supply, and as a result a player like Ibanez can hold considerable market power in an auction-like setting.  Experienced left fielders who can relatively predictably add x WAR for a team without a left fielder under contract are in short supply, and if such an asset is worth $15M/yr in marginal value to the Phillies, it isn’t going to take much to get them to pay that, even if they know that 27 of the other 30 teams only value Ibanez at $4M/yr.  Major league left fielders of Ibanez’ talents are not a widely avaialble commodity like steel.

Yes, I agree that supply and demand factor in heavily.  (I guess I don’t need to “agree” with that, as that is the principal basis for all commodity fluctuations in price, no?)

If that’s the case, then the Phillies can get him for 5.1 million.  However, if there are two teams that value him at 15 million and 4 that value him at 5 million, then the Phillies are going to have to pay him 15 million.

How can that be true?  One team, 5.1 mil and 2 teams 15 mil?  What about 3 teams?  15 mil also?  I don’t think this is an either or as you are implying - that one team means 5.1 and more than one team means 15 mil.  That can’t be.

If Ibanez provides 15 mil in marginal revenue to me and only 5 mil for all other teams, and I am willing to pay 12 mil for that 15 mil and they are willing to pay only 4 mil, then when Ibanez asks for 12 mil from me, I simply say, “No way.  Go play for 4 mil with one of the other teams. That is all you are going to get.  If you want to play for me, I’ll pay you 4.1 mil (or whatever) and not a penny more.” You will say, “No, I’ll sooner rot in hell than take your lousy 4.1 when I know I am worth 12 mil to you.”

Eventually you will agree on some price between 4 and 12. I have no idea what that will be.

With two teams, there is more of a demand, but those two teams will NOT bid his price up to 12 mil (the max for both teams), I don’t think.  That just would not be good business for those 2 teams.  One time one team will get him for 6 mil (or 8 or 10 or whatever) and the next time, the other team will get him for the same.

All those 2 teams have to do is to say to themselves, “This guy is worth 4 mil to everyone but us and one other team.  I refuse to pay him 12 mil even though it is worth it to me.  If I lose him I lose him.”

No matter what, those 2 teams will split X number of players.  They can either split those players at their max, 12 mil, or they can split those players at 5 or 6 or 8 mil (or 10). Why would they do the former?

But, as I said, I have no formal training in economics, and I am talking out of my ***, so I could be wrong.

I realize that teams are not allowed to “collude” but I would certainly have an unwritten agreement with all teams like mine who can afford to pay Ibanez-type players 12 mil that we won’t pay more than 6 or 8 or 10 mil, if all other teams can and will only pay 4.

And I think that is what happens in reality.  That is why you don’t see the Yankees pay CC much more than any other team and you won’t see Boston or ANA pay Teixera much more than any other team.  They will pay more, but not 4 or 5 times more (not even 2 times more) even though the value of a marginal win to them is probably worth 4 or 5 times that of many other teams.

Keep in mind that while FA are limited, especially certain classes of FA, there are still a plethora of ways that a team can spend their money to improve their club.  Signing FA is not the only way.

Therefore, teams like the Yankees and Boston, and other high $ per marginal win teams, can pass on players.  They don’t have to bid them to the max.  The supply of marginal wins (either through FA or through player development or through signing bonuses, etc.) is fairly liquid and plentiful.

Actually, MGL, if we want to get past ECON 101, it’s even more indeterminate than your last posts imply, because now we are getting into both details of industrial organization economics and game theory.  So, as you note (and for talking out your a**, you have a good intuition for the key factors), the result will depend heavily on the exact specification of demand and supply.  The number of teams demanding will play a critical role, and as that number goes up, it becomes harder and harder for the market to avoid bidding the price up to the marginal value.  There’s no deterministic solution and multiple theories about the relationship between oligopsonistic markets and price.  I’m not an IO economist, but if I have some time, I can try to post more (I’m leaving town for my mother-in-law in 2 days, and she lives in a cave without internet access, as most ogres do, so I may need to connect later).

The supply conditions, as you note, are closer to, though probably not identical to a more competitive market, especially given the union involvement and the pressure they put on players.  Teams are trying to produce wins using a factor input, players.  While there are alternatives to FA, there are few alternatives that have an immediate payoff for next year’s wins.  Because of the distribution of marginal value of wins, different teams will be located at different points along the curve.

And, then, there are of course the game theoretic aspects of the problem--who has what information, and how well can they exploit those informational advantages.  Under certain frameworks, (for example, auction environments), it’s actually the case that the player could get MORE than their marginal value (the “Winner’s Curse” situation).

So, that’s a long-winded way (hey, I’m an academic economist), of saying that your intuition that it’s more complicated than my simplistic addition to the earlier simplistic outline is right.  It’s a very complicated market characterized by less than competitive conditions on both sides, including market power in both supply and demand, and informational complexities.  The theoretic result, if we were to outline all those conditions, would likely be the usual economic answer..on the one hand, the player could get $5 million; on the other hand, he could get $15 million.  Then, we’d send an RA to run a few million regressions, and go have a beer.

Given our discussion, I would be remiss to not mention that the seminal article, one often cited as the initiation of sports economics, was by Simon Rottenberg in 1956.  It was entitled ““The Baseball Players’ Labor Market.”

Here’s an analysis of his paper:
http://www.vanderbilt.edu/Econ/wparchive/workpaper/vu06-w06.pdf

Phil 19/25:
I certainly agree that treating all runs equally is a mistake.  A player who generates 15% of his team’s runs is obviously worth far more than 15% of that team’s total offensive value. But I wonder, is that what JCB actually does?  I know he has argued that replacement level is not a useful or necessary concept (and like you, I disagree).  Still, if his valuation method uses a baseline of average performance, and then adds/subtracts value from there, he should still arrive at very similar values.  Are you sure that he is using a zero baseline rather than the mean?

Guy,

That’s how I read “Sabernomics,” and nobody has corrected me.  My most recent comments are here.

I’m just wondering if I got that wrong, since nobody is mentioning it.  But IIRC, I think I wrote some comments to that effect on JC’s site, and he disagreed with me.

Anyway: my argument is: a player who creates exactly replacement value is worth the league minimum, say $400K.  A player who creates twice replacement value is worth millions, a lot more than $800K.  If you value every run the same, even the below-replacement runs, you can’t help valuing the guy who creates 100 runs at twice the value of the guy who creates 50 runs.  And that can’t be right.

JC uses an exponential function.  It’s in his book.  When asked to give us the input parameters for Ibanez, JC said he didn’t have time to walk through an example.  Until he actually gives his readers something to parse and analyze, we’re going to go in circles trying to figure out what he’s actually doing.

Phil:
Valuing every run the same is OK, IF you use average performance as a baseline.  For example, if you say the average full-time LF is worth $8M, and every win is worth $4M, then a -20 run player is worth zero (or $400K), and a +20 run player is worth $16M (all numbers for illustration, as Tango likes to say).  I have no idea if that’s JCB’s approach, but it’s a valid one and should get you to approx the same replacement level (if teams are paying players correctly).

But it sounds like JCB has left his method somewhat oppaque, perhaps so as to protect him from criticism from sabermetricians like the two of you.  Of course, your work isn’t as “rigorous” as that of academics, so sports economists can dismiss it and go about their business.  Sigh....

Right on Guy’s first paragraph.  Indeed, for those who don’t care at all about replacement level, that’s how I approach it: start with average, and give average a starting salary that is appropriate.  And when you draw your linear line back to where salary=0 (or 400K), that tells you exactly what the wins below average is (and it’s going to be close to 2).

As for Guy’s second paragraph: some people like to have a good, bloody (above the belt) intellectual thick-skinned scrap and have a beer afterwards to laugh about it, and others don’t.  I’m in the former group, but not everyone is.

Tango/38:

“start with average, and give average a starting salary that is appropriate.  And when you draw your linear line back to where salary=0 (or 400K), that tells you exactly what the wins below average is (and it’s going to be close to 2).”

What linear line?

Create a graph, where the x-axis is wins above average, and the y-axis is salary. 

Put a point on the graph where x=0 (which is NOT the y-intercept), and y=$8MM.

Now, draw a line, from that point, backwards, so that it hits the y-axis at y=$400K.  The value of x will be -2.35 wins.

YOUR question will be “why is it -2.35, and not -3, or -1 or -5”.  That’s a good question.  Before I answer, are you ok with the above?

I picked up “The Baseball Economist” (not Sabernomics, as I incorrectly wrote), and here’s what JC did:

Start with $54.5 million, which is what an average offense is worth.

For each player, multiply the percentage of his team’s plate appearances by $54.5 million.  This gives you what the player’s MRP would be if he were average.

For each run the player is above or below average, add or subtract the value of that run.  JC assumes that each additional run is of higher value than the last, so it’s not a straight multiplication.

(As Tango and Guy note, JC doesn’t give his non-linear function for the value of runs.  But I don’t think it matters much for this argument.)

That means there is no guarantee that the value zeroes out at replacement level.  And if you look at some of JC’s evaluations, it shows.  Brandon Fahey in 2006 comes in as having been worth $1 million, despite JC having him as creating 3.15 runs per game. 

Does that make sense?  It seems to me that Fahey’s MRP is the league minimum at most—if the Orioles had known what he’d have produced, he probably wouldn’t have had a job.  They’d have got themselves a replacement player for $390K instead who would have done roughly the same. 

JC argued that if an average team earns $109 million, you should divide that equally by the number of runs.  I argue that you should divide it by the number of runs ABOVE REPLACEMENT.  The runs below replacement are available at a fixed cost of $390K per player.

Now, it could be that JC’s exponential algorithm just, by coincidence, winds up with $0 or $390 exactly at replacement value.  But (a) I don’t think it does, (b) if it did, it would be one hell of a coincidence, and (c) if you look at the players who are actually at replacement value, JC has high salaries for some of them that don’t seem to make sense.

Tango/40: Is $8MM an empirical observation of the salary of the average full-time player?  If you tell me where the $8MM came from, I’m good so far.

Now, it could be that JC’s exponential algorithm just, by coincidence

I think it works out like that.  I seem to remember seeing his formula in the footnotes section.  I can check when I get home.

***

If the average team spends 90MM (and 10MM of that is for minimum salary), of which around 58% goes to nonpitchers, and you have 8.65 “full time” nonpitchers per team, then: (90-10)*.58/8.65 = 5.4MM.  The free agent premium is almost 100%.  So, a free agent would get say 5.4*1.8 = 9.7MM.  Add in the 400K of minimum salary, and you get 10MM.  That’s what an average player should get, on the free agent market, if he plays 162G.

(I said 8MM, but that was based on data from 2006.  Things pick up fast every year.)

Tango/43:

1.  Sure, check the footnotes, I’d appreciate it.

2.  OK.  I didn’t need the details, just the fact that the $8MM figure came from observing what teams actually spend.  (FWIW, JC’s estimate came from team *revenues*, not from expenditures on salary.)

BTW, do you agree that the value of Brandon Fahey’s 2006 should not exceed the league minimum?  I could be wrong about that—maybe 3.1 runs per game is still above replacement level.

Presuming 4.8 runs per game, then 3.1 runs per game is -1.7 per 27 outs below average.  Times 18 such games, and you have 31 runs below average.  Presuming an average fielder at an average neutral fielding position, that’s a bit below the replacement level.

Replacement level is around 75% of average offense, more or less.

So I was doing some post-Christmas/birthday returns and exchanges - finally have The Book on order, BTW - and I thumbed through the MRP portion of “The Baseball Economist.” Holy jimminy cricket.

So far as I can discern, his formula for deriving team runs scored based upon a regression analysis is:

(3.013*obp) * (1.688*slg) * 1000

OMGZ.

Trying to duplicate his process (running a linear model of OBP and SLG against team runs scored) I come up with:

(2.728*obp) * (1.931*slg) * 1000

instead, based upon the sample years that he listed (2002-2005).

I’m willing to accept the premise that I’m doing something wrong with the regression, except that my AAE is close to HALF of what I get using Bradbury’s weights, 48 to 28. (Correlation for both seems to be the same, 0.949.)

Either way - a regression-based run estimator giving a 30-40 run error on team run scoring in-sample?!?!? Even something like Basic RC grades out better then that, with an AAE of 25 runs.

Estimated LWTS, based on Bradbury’s OBP/SLG regression and the plus-1 method from 2002-2005:

1B: 0.544
2B: 0.802
3B: 1.059
HR: 1.316
BB: 0.190
Out: -0.205

Those are… pretty mediocre, really. Undervalues the walk, overrates the double… underrates the home run?

Using the results of my regression instead:

0.564
0.830
1.097
1.363
0.197
-0.212

Very similar - I’m pretty confident at this point that the difference between mine and his regressions is either in datasets (I used the BDB) or in how OBP/SLG were figured.

Either way - presuming I’m interpreting his brief notes correctly - this almost has to be the one of the worst run estimators I’ve ever seen. I’d love to be wrong here.

Those are bad Linear Weights. Regression should never be used to generate coefficients for run estimators. On his website, JC states that he now uses linear weights:

“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.”

"(3.013*obp) * (1.688*slg) * 1000 “

The two terms are being added, not multiplied, right?

The two terms get multiplied. If a team has a .330 OBP and .425 SLG, there runs estimate is:

(3.013*.330) * (1.688*.425) * 1000 = 713 runs

This is similar to Tango’s OPS run estimator. If you divide the OBP coefficient by the SLG coefficient you get 1.78. So you now have (1.78*OBP + SLG) * Multiplier. Tango figured out the multiplier using .27 for every PA. If a has 6000 PA, then the multiplier is .27*6000 = 1620.

What’s the point of the parenthesis if all the terms are multiplied?  What’s the point of having 3 constants multiplied separately, when you can just represent them as one number?

When you divide by the OBP component by the slugging component you get 1.78*OBP*SLG. I mistakengly said 1.78*OBP+SLG.

It isn’t very accurate at predicting runs. If you plug-in a .400 OBP and .500 SLG, you only get 1017 runs, 6.27 RPG. A team with a .400 OBP and .500 SLG would probably average 8-9 runs per game.

Tom, I simply took his weights and tried to best-fit an equation around it. The way he lists his weights is confusing. To be honest, I eventually started thinking of it in terms of RC instead of a linear run estimator.

I’ve took a look at the regression and read up a bit on MLR, and apparently the missing term of Bradbury’s weights is the intercept. Using my own regression, I come up with:

2591*@obp + 1957*@slg-915

As my best estimation of the formula. Now we’re at a AAE of about 21 runs.

As far as the formula Bradbury used, I can’t duplicate it precisely unless he says what intercept he used. My best guess is it’s 952, which would put us at an AAE of 20 runs.

It’s still a miserable-looking construct, and I’d have to see how it applies to individual players before I could draw too many conclusions. If terps is right and he’s using LWTS now it really doesn’t matter.

What I’m trying to say is:

(3.013*obp) * (1.688*slg) * 1000

OR

((3.013*obp) + (1.688*slg)) * 1000

It cannot be the first one, since the parens are useless, and having three constants all multiplied by each other like that is equally useless.

Anyway, presuming the typo in the original post, and that this is the actual formula:

((3.013*obp) + (1.688*slg)) * 1000

Then this is identical to:

= (1.79*OBP + 1.00*SLG) * 1000 *1.688
= (1.79*OBP + 1.00*SLG) * 1688

There are some 39 PA per game times 162 games, or around 6300 PA per team

So, we continue:
= (1.79*OBP + 1.00*SLG) * (6300 * .268)

If you replace the 6300 with PA, you get:
= (1.79*OBP + 1.00*SLG) * (PA * .268)

And that’s pretty much what I said it was last year in a long blog post.  The difference is that I use PA, while the original formula used a constant.  That is enough to increase the value of the walk to what it should be.

(1.79*.330 + 1.00*.425) * 1688 = 1714

Am I missing something here? Because that looks like 1,000 runs too many.

And here’s the old thread referenced:

http://www.insidethebook.com/ee/index.php/site/comments/why_does_17obpslg_make_sense/

So it’s like I said - this gives you the slope, and you need to subtract the intercept for it to actually come out looking like runs.

Yes, naturally you need the intercept.

David Berri supplies his thoughts on the matter:
http://dberri.wordpress.com/2008/12/21/week-15-football-rankings-and-a-sabermetric-debate/
to which I reply:

“In other words, if you participate in the group, then you are a Sabermetrician.  If you are not part of the club - even if you are doing legitimate analysis of baseball - then you are not a Sabermetrician.  “

To the extent that this statment applies to “all” sabermetricians, then I reject this statement in its entirety as not being at all representative of who I am and what I do. 

To the extent that this statement applies to “most” sabermetricians, I think this statement is also wrong. 

Though, before such a claim is made, evidence should be provided, as any good sabermetrician would tell you to do.  Otherwise, this statement is pure opinion, based on anecdotes, small sample size, and selective sampling.  And the statement is worth exactly what that level of sampling would give it.

Doing some noodling around on team revenues, and here’s the correlation between total revenue (per Forbes, 2002-2007) and some various things:

Population - 0.576
Win% - 0.395
RunDiff - 0.419
RS - 0.429
RA - -0.179

Population figures derived from the most recent US Census figures. (Canadian teams currently excluded; I’m working on including that at some point.)

It seems like the main ways to get the cash in is to be in a big market and score runs; winning appears to be third. (The fact that run differential outperforms win percentage is probably because the spread in run differential is so much larger than the spread in win percentage, rather than being a meaningful difference.)