THE BOOK--Playing The Percentages In Baseball

Well, he didn’t shy away from the question, actually picking it first:

The key fact is that you were an above average fielder, and there is a lot of value to being even an average shortstop for a full season. Keep in mind that the replacement level in the WARPs is very low indeed, what a AA player might do. It is geared towards what the worst teams in history actually accomplished.

I think he meant an average fieldig shortstop . And, if he was exactly average as a fielder at SS, his WARP1 would have been zero, as he’s saying.

Just think about that.  You have a guy that BP says is -39 runs in 401 PA (-65 runs if playing a full season!!!), who, if you have an average fielding SS in 1979, would be considered a “zero wins above replacement level”.

***

The next replacement-level question came from Anthony from Long Island, who seems to be the same genius I quoted on Leverage Index:

Anthony (Long Island): You use replacement level for defense, whereas most everyone else sticks to an average baseline. Since you’re apparently the outlier on this front, would you mind sharing your thought process on sticking with replacement level?

Clay Davenport: If you use an average player fielder baseline, you have to make an explicit adjustment for position - “an average 1B is 25 runs better than an average SS” in hitting. I think the difference in positional value should come from the fielding statistics, not the hitting statistics, and using replacement levels allows me to do that. The two should correlate - managers apying attention should respond to changes in fielding skills needed for a position by moving better or worse fielders into the role, taking either the hitting advanatge or hit that follows that decision.

He doesn’t have to use an “average fielding player” baseline.  There’s just no reason to use both a replacement-level at both hitter and fielder, as if they are two unrelated things that you can put together.

***

The really strange part is not that he sticks to his guns, but does so in the face of everyone else who studies the issue.  And without a very convincing argument.

Replacement-level has been defined generally speaking as a team with a .300 win level.  If Clay insists on using a .150-.160 level, then he’s got to use a different name.  Something like “WAA” or “WADA” for “Wins above AA”.

Not a very satisfactory answer. It’s certainly true that “there is a lot of value to being even an average shortstop for a full season,” but his further explanation, that replacement level is set so low because “it is geared towards what the worst teams in history actually accomplished” rings hollow. The 2003 Tigers have a cumulative WARP of 23, and the 1962 Mets a cumulative WARP of 28. Is the baseline the 1899 Cleveland Spiders?

The real problem, I think (which someone touches on in a followup question, and I believe it has been discussed here before), is that they want to maintain the fictions of “replacement level hitting” and “replacement level fielding.” This is convenient, as it gives a baseline for their “BRAR” and “FRAR” stats, but it isn’t very hard to see that it’s the wrong thing to do. Replacement level only makes sense when you look at combined skills, and a true replacement level player might be someone like Jack Cust or Joey Gathright (or similar players at whatever the right level is).

Oops, looks like you beat me to the punch and I could have saved myself some typing and just written “I agree.”

"The really strange part is not that he sticks to his guns, but does so in the face of everyone else who studies the issue.  And without a very convincing argument.”

I’m not surprised:  BPro has gone too far down the WARP road to now just tell the world, like Emily Litella, “Never mind.” But VORP is a pretty useful stat, and if you add FRAA you then have a pretty reasonable player evaluation (since replacement players are essentially average defensively).

Of course, that’s only IF you think FRAA has some validity.  I know that DSG is highly skeptical, but I haven’t heard his reasons.  What’s the assessment of FRAA/FRAR by folks here?

And he also talks about “historically”, meaning the 1899 Spiders, they of the 20-134 (.130) record.

That franchise was playing for .500 until that season.  They had this guy play a whole season at SS, who never played before, and just a tiny smidge after:
http://www.baseball-reference.com/l/lochhha01.shtml

This was their 1B, and his last season:
http://www.baseball-reference.com/t/tucketo01.shtml

This was their 3B, who barely played before, and would never play again:
http://www.baseball-reference.com/s/sullisu01.shtml

Their 2B has two seasons left:
http://www.baseball-reference.com/q/quinnjo02.shtml

Their OF had one season left:
http://www.baseball-reference.com/d/dowdto01.shtml

And the Spider’s position players was their strength.

Their best pitcher had 1 season left, compiling a career 29-80 (.266) record.  Do we even see such a pitcher?  We complain about Joel Pineiro.
http://www.baseball-reference.com/h/hugheji01.shtml

Their next best pitcher pitched one season only:
http://www.baseball-reference.com/k/kneppch01.shtml

Their 3rd best pitcher had 4 starts in 1898, and then never pitched after 1899:
http://www.baseball-reference.com/b/batesfr01.shtml

This guy had a SIX year layoff, came back for the Spiders and two years later came back for 4 games:
http://www.baseball-reference.com/s/schmicr01.shtml

This guy never pitched before or after again:
http://www.baseball-reference.com/c/colliha01.shtml

This guy never pitcher again after, even though he was only 24:
http://www.baseball-reference.com/h/hillbi01.shtml

This guy, finally, has 100 career wins, but only had 10 starts for the Spiders in 1899:
http://www.baseball-reference.com/s/sudhowi01.shtml

Their top guy out of the bullpen pitched 7 innings after 1899:
http://www.baseball-reference.com/c/carseki01.shtml

Their #2 out of the bullpen never pitched again:
http://www.baseball-reference.com/s/stiveja01.shtml

Their #3 guy was legitimate, but only threw 37 IP:
http://www.baseball-reference.com/h/harpeja01.shtml

Next up is a guy with 2 games before, 0 games after, and 25 IP in 1899:
http://www.baseball-reference.com/m/maupiha01.shtml

After that, their OF threw 16 IP:
http://www.baseball-reference.com/m/mcallsp01.shtml

And what does this ragtag group of “baseball” players represent?  Nothing.  It doesn’t represent anything real in terms of comparison.  These players would not each earn the MLB minimum today.  I don’t even think half would be on the 40-man roster.

And why did the 1899 Spiders exist? 

http://www.wcnet.org/~dlfleitz/cleve.htm

The final blow to Cleveland baseball came early in 1899. Frank Robison, Cleveland owner, bought the St. Louis Brownls at a sheriff’s auction and decided that a good team would draw better in St. Louis than in Cleveland. He then transferred all of Cleveland’s stars to the Browns, which he arrogantly renamed the Perfectos. Pitching great Cy Young, batting champion Jesse Burkett, and all the other Spiders stars were replaced by minor-leaguers and semi-pros. Other teams followed Robison’s lead; the Brooklyn Dodgers bought the Baltimore Orioles, absorbed their best players, and renamed themselves the Superbas. Four different teams held stock in the New York Giants. Ownership of major-league teams represented a jumble of conflicting allegiances which resulted in the weaker teams serving as farm teams for the stronger ones.

By the way, readers of my blog proclaimed Willie Bloomquist the worst MLB under 30.

If we make him the ideal “replacement-level” player, BP has him with a career -38 runs relative to average.
http://www.baseballprospectus.com/dt/bloomwi01.php

We need to do a positional adjustment, but WFB has played everywhere.  He’s got 950 innings at a premium position (SS, CF), 1000 innings at a neutral position (2B, 3B), 200 innings at an easy position (LF, RF), 300 innings at no position (1B, DH).  If you apply a +0.5 win adjustment for SS, CF, -0.5 for LF, RF and -1.0 for 1B, DH, you get.... ZERO.  That is, WFB has played at a neutral position.

He has a career 1009 PA.  A full 162GP season has 700 PA, which would make WFB, per 162, -26 runs, or -2.4 wins.

If you had 9 such non-pitchers, you are at -22 wins.  So, a team of WFB with an average pitchers would win 59 games (.364).

I’ve always advocated a .380 level for nonpitchers and .410 for pitchers.  If we instead use .365 and .400, we get a team of WFB as .280.

And, other than him being from Seattle, I doubt any other team would have WFB on their team.

Calling .300 the replacement level works for me.

Using the fantastic PI, we have the answer:
http://www.bb-ref.com/pi/shareit/24hf

Among players with at least 300 outs made, Mario Mendoza had the second worst OPS+ since 1901.

There’s no way that that level of performance, plus average fielding at SS, is the level at which we want to compare someone.

I’m not surprised:  BPro has gone too far down the WARP road to now just tell the world, like Emily Litella, “Never mind.” But VORP is a pretty useful stat, and if you add FRAA you then have a pretty reasonable player evaluation (since replacement players are essentially average defensively).

Of course, that’s only IF you think FRAA has some validity.  I know that DSG is highly skeptical, but I haven’t heard his reasons.  What’s the assessment of FRAA/FRAR by folks here?

***

What I do when I want quick-and-dirty runs above replacement is add together FRAR and BRAA on the DT cards. FRAR adjusts for position and includes a reasonable replacement level; it’s when you add BRAR instead of above average that you get in trouble.

As for Clay’s fielding system, I think it’s pretty good. It has some issues: It looks at things like putouts for infielders, errors, and double plays, all of which are pretty much useless, but muddy up the results. The system is also VERY conservative, and thus tends to underrate great fielders. For example, Adam Everett is rated at just +22 runs above average over the past three seasons; using the detailed zone rating data listed on THT, he’s +68.

If you want more of my thoughts on various fielding metrics, I wrote a pretty detailed article for The Hardball Times last year on that very topic:

http://www.hardballtimes.com/main/article/evaluating-the-evaluators/

Hi, I’m Anthony from Long Island. I had submitted questions to Clay before entering a meeting, so I didn’t get a chance to ask a followup. Maybe you could clarify something for me then…

Let’s say the positional adjustment for shortstops is 39 runs. That means a replacement-level shortstop will be 39 runs below average? Or 39 runs below a position-neutral replacement level?

If I’m following things correctly, you and most everyone else compares a player to a replacement-level hitter at his position and an average fielder at his position, whereas Clay compares a player to just a general replacement-level hitter and a replacement-level fielder at his position. Is that right?

Now, two questions occur to me: 1) what research has been done--hopefully using play-by-play defensive metrics--to determine whether replacement-level players are average fielders or not? And 2) how do you feel about Clay’s assertion that “the difference in positional value should come from the fielding statistics, not the hitting statistics”? Even absent the double-counting problem, is there any particular reason why the positional adjustment should be made on the hitting side of the ledger?

Just asking the naive question here.
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Speaking of, if you click on my name it will link to a column written by Nate Silver a year ago about redefining replacement level. He seems to subtly make the argument that WARP is wrong, but nothing else ever came of his research. I wonder why Nate doesn’t use FAT instead of WARP & VORP in PECOTA.

Anthony, thanks for stopping by.  If you check out my blog (look for Category Fielding) you will see several entries on the subject.

I agree with Clay’s premise that the adjustment shouldn’t come from the hitting stats.  After all, that assumes that the avg 3B = avg 2B = avg 1B, etc.  This makes no sense to blindly accept that.  After all the avg QB does not equal the avg offensive tackle.  Nor is it even true that the avg SS = avg 2B in high school.  Therefore, what would make it so at the MLB level?  (And, in 2006, the avg 3B was better than the avg 2B.)

However, that doesn’t mean Clay found the right way to do it.

***

I once looked at the UZR of regular players and the rest, and, pretty much, the non-regulars were average fielders.  Even in the cases that they weren’t, we’re talking about a couple of runs here or there.  It would be a fair *starting point* to presume that a repl level off plus average fielding gives you repl level player at that position.

***

In any case, what I did is the following:
+1.0 wins: C
+0.5: SS, CF
0.0: 2B, 3B
-0.5: LF, RF
-1.0: 1B
-2.0: DH

Those are my positional adjustments.  So, a below-average fielding 1B (-1.0 wins) plus the adjustment (-1.0) gives you -2.0 wins of position+fielding adjustment.  Frank Thomas therefore comes out as -2.0, whether at 1B or DH.

Everett is +2.0 wins as a SS compared to the average fielding SS, plus 0.5 wins of adjustments (average fielding SS to average fielder at a neutral position).  If he’s a -2.5 wins as a hitter, that makes him an average MLB player.

I find this alot more straightforward than other things I’ve seen.

Anthony:  Silver’s article also shows that replacement players basically provide average defense (except at SS). 

It’s interesting to compare Tango’s and Silver’s position adjustments (assuming -20 is neutral):
Tango/FAT
C +1/+1
SS +0.5/+2
CF +0.5/0
2B 0/0
3B 0/0
LF -0.5/0
RF -0.5/-1
1B -1/-1
DH -2/-2

A great match except for SS, where Silver’s data would argue for a much larger adjustment.

When I do interpositinal comps, the easiest, by far, to do is the three OF positions.  All three use the same skills to varying degrees, and all three has an abundance of movement.  And, the end-result is always the same.  The fielding difficulty of LF and RF are virtually the same.  And the gap between the corner OF and CF is around 9 runs (a shade under 1 win).

If the RF hitters are better than LF hitters, it’s really irrelevant to the replacement level, exactly because the RF and LF positions are drawn from the exact same pool of players.

Anyway, according to UZR since 1999, of guys who played both LF and RF, they performed equally well at both positions.  This shows that the fielding pool has been evenly split.

Therefore, there’s no way that the LF/RF gap as Nate is showing is a full win.

BPro has gone too far down the WARP road to now just tell the world, like Emily Litella, “Never mind.”

That’s a pithy thought.

It might be similar to Bill James’ Win Shares.  It was apparent to me that Loss Shares was an absolute requirement, and if you work it out, Barry Bonds would end up with negative loss shares, and that’s probably why James didn’t do that (i.e., can’t figure it out, so I’ll just not present that half of the equation).  I heard he’s now on record as saying that his original version of Win Shares is not workable, and that his new version has Loss Shares.  Presuming he’s not going to have negative loss shares, what he’ll end up with is exactly what I proposed: win advancements (WA) and loss advancements (LA), which is WPA (WA-LA).  Pujols for example had 18 WA and 9 LA.  An LA is essentially .027 x outs.  WPA is linear weights divided by 11.  Solve for WA.  If I were to do WPA historically, pre-1957, that’s how I’d do it.

Anyway, we’ll see how long Clay will be so insistent.

Guy, that’s an interesting comparison. My gut instinct would be to lean more towards Nate Silver’s evaluation of shortstops, except that would mean a shortstop is worth four more wins than a DH. So David Ortiz or Travis Hafner would have to be worth ~40 runs more than Derek Jeter (okay, 30 runs if you assume awful defense) with the bat to be worth more. That’s wild.

Tango, how does the Fans’ Scouting Report judge starters and bench players?

Anthony, that’s a great question.  Next on my todo list is to finally consolidate the 4 years of Fielding Scouting Report I have, with MGL’s UZR, which he may be releasing publicly.  Should be exciting stuff.

I am very much interested in seeing how much information the Fans Fielding Report adds to UZR in terms of projecting future UZR. Of course, the “problem” with that is that UZR may be biased such that it is more reliable than accurate.  In other words, lets say that the Fans Scouting Report adds nothing to UZR in terms of projection accuracy.  That does NOT mean that the fans know nothing more than UZR data provide in terms of fielding skill.  UZR may simply project UZR well but that UZR is not really a great indicator, even in the long run, of fielding skill.

That was just a theoretical problem.  I fully expect fan rating to add something significant to UZR, in terms of projecting UZR, especially for small samples of UZR data.  In fact, I think that Tango already got that result.

It is interesting that sometimes observation can trump data in the short run.  That is not always the case.  If the “observation” is actually an observation of the data itself, that will probably NOT be the case.  If the “observation” is of the underlying skill that the data is a proxy for, then that may be the case. 

If the data (in this case, the UZR itself) is fairly accurate in terms of being indicative of the underlying skill (I think that it is - others will disagree), then in the long-run the observation will add little to identifying and quantifying the underlying skill. In fact, it might add noise and be worse than useless.

Sorry to change the subject, but Tango sort of did in his last post.

Plus, I don’t usually weight in much on the “WARP replacement issue.” I think it is a non-issue.  Anyone can use any replacement level they want, as long as they define what they mean by “replacement.” If Clay or BP wants to define it as the worst player or players in the history of baseball, that is fine by me.  That is not a very useful construct of course, which makes their position silly, whether they properly define their replacement or not.  The principal reason for using the replacement concept is to figure out what players are worth as compared to “freely available talent.” “The worst in the history of baseball” is obviously not the same as “freely available talent” - not even close.  So unless BP/Nate explain what for they are using “the worst ever in baseball” as their baseball, theirs is an untenable position.  Why they stick to their guns is one of those mysteries in life.

As well, to say that “real” backup or replacement players, at any or all positions, have defensive skills that are 10 or 20 runs below average is simply and absolutely, 100% not true - of course.  I don’t know if they are saying that, but if they are, they are dead wrong.  So this is really a non-issue, issue as far as I am concerned. IOW, there is really nothing debatable here.  To tell you the truth, I did not understand Clay’s repsonse to Tango’s question at first read and I am not going try and take the time to understand it.

I agree with MGL’s basic point that the value of talking about “replacement level” is to set it equal to the min salary.  Willie Bloomquist for example would fit the bill, as a guy anyone can have, the 25th player on the roster.  There must be a hundred guys like him in the minors, guys who can’t hit, but who get by on their athletic ability.

The next point is to recognize accomplishments, the area under the curve, where the top line if the player’s production, and the bottom line is the minimum production (i.e., wins above replacement).  But, others can draw that line at .500 or even .600, so that when talk of Hall of Fame comes around, a guy like Koufax comes out pretty good if you compare his “above the line” performance if the comparison line is a .600 pitcher, and that maybe Don Sutton doesn’t look as good.

The problem is when Nate develops MORP (dollars above replacement) by basing it on Clay’s WARP (wins above replacement), when the two replacement levels are not the same!  Nate is looking at the first paragraph and Clay is looking at the second.

The final answer is that you start with the question.  Develop your metric based on that.  Don’t start off with a metric, like WARP, and then try to figure out how to use it.

In any case, it’s hard to deal with BP, since sometimes you can deal with each as individuals, and other times, you are dealing with the “entity”.  Clay is wrong about WARP, and Woolner is wrong about leverage, but good luck trying to change it.

Here’s a fan page on WFB:
http://www.sportsargumentwiki.com/index.php?title=Willie_Bloomquist

Just to weigh in on an issue that is tangentially related: I certainly agree with MGL that anyone can use any replacement level they want, but BPro consistently misuses WARP by applying it to club economic analysis.

I also don’t feel that “Freely Available Talent” is a useful replacement level for analyzing club economics.  It may be fine for rotisserie leagues, but rotisserie doesn’t have a lot to do with real, true club economics.

To me, any assessment of replacement level that is used to analyze major league financials and economics has to recognize that ballclubs are going concerns, with drafts, minor league systems and players not yet eligible for free agency.  That makes the replacement level much higher than WARP’s or freely available talent.

I made that point to Vince Gennaro, who used WARP for his new book, Diamond Dollars.  He was nice enough to compare WARP and WSAB in a sidebar in his book, but didn’t really address my issues.

I’ve always preferred using “average” as the starting point.

For example, the average payroll would be 80 million$, with revenues of 140 million$ (no idea what it is in 2007).  A standard rule would be that every extra win adds 2% to revenues (though with revenue sharing, not true these days). 

Anyway, every win is worth 2.8 MM in revenues.  Let’s say that the team gives 80% of that to the player, or 2.2 MM per win.

Now, let’s look at it from the replacement viewpoint instead.  The minimum payroll would be 0.4 x 30 = $12MM.  That means the average payroll is +68MM.  The average team is also .20 wins per game x 162 games = 32.4 games.  68/32.4 = 2.1 MM per win.

Even without needing to know anything about replacement level, you can work out the finances.  So, the concept of replacement level is useful as a shorthand, but hardly a requirement.

If you look at marginal revenue product, which most economists and many businesspeople would (and should), then you need a meaningful measure to relate to it.  Performance above average isn’t the right comparison for marginal revenue product—the right replacement level is.

There’s nothing wrong with saying marginal revenue above average.  That is, given an 80 MM payroll and 81 wins, how much would you pay to get to a team talent level of 86 wins.

If it’s a purely linear relationship, then you can extend forward and backward, forcing the line to go through the mean point.

If it’s not a linear relationship, then you need a marginal $ per line at every point.  That is, you need 1 MM per win to go from 81 to 82, and 1.1 to go from 82 to 83, and 1.5 to go from 83 to 84, etc.

Regardless, the idea that you need a “replacement” level isn’t a requirement.  You don’t need replacement, but the appropriate baseline level, at every point, for whatever it is you are trying to do.

I don’t see it, Tango.  A player with +1 WAR in 500 at bats is worth more (in marginal revenue product) that the player with +1 WAR in 100 at bats, if you assume the player most likely to replace either one is below average.

80 MM in payroll, which we’ll split as 45 MM for nonpitchers and 35 MM for pitchers.  The average nonpitcher get 5 MM per 162 GP (700 PA).

So, your +1 WAR in 500 PA would be say -0.43 WAA.  Your +1 WAR in 100 PA would be say +0.71 WAA.

Player 1: 5MM/700 * 500 + 2.2 * (-0.43) = 2.6 MM
Player 2: 5MM/700 * 100 + 2.2 * (+0.71) = 2.3 MM

As you can see, it didn’t matter whether you started with the WAR (which is the same) or a combination of WAA and playing time.  In either case, you get around the same number.

sloppy me.  If I used 2.5 instead of 2.2 as my multiplier, I’d get the exact same answer in both cases: 2.5 MM.

I meant to say WAA in my post instead of WAR.  What is the multiplier based on?

That’s not the type of financial analysis I’m talking about.  I want to compare a player’s marginal revenue product with his marginal cost, using his marginal performance as a bridge.  You basically took a given salary “budget” and spread it between two players, if I understand correctly.

Ok, then that’s:
Player 1: 5MM/700*500 + 2.5*1 = 6.1MM
Player 2: 5MM/700*100 + 2.5*1 = 3.2MM

If player 1 is +1 WAA with 500 PA, then he’d be +2.4 WAR.  Player 2 would be +1.3 WAR.  Multiply each by 2.5 MM per win, and you get the above figures.

Here you have two different processes each giving you the same result.  It presumes that MLB has allocated its payroll budget properly. 

And my marginal $/win is 2.5MM per win, around the mean. 

The replacement-level process presumes a marginal $/win of 2.5MM per win, starting at the 0th win.

As it turns out, we have the same answer.  I like my way, because I don’t even need to bring up repl level.

It presumes that MLB has allocated its payroll budget properly.

Exactly.  That’s my problem with what you’re doing.  I want to do it right: compare marginal revenue product to marginal cost, as Vince does in his book.  I believe this is what BPro did in BBTN, as well as JC in his book.

The absolute right way to do it, I think, would be to derive MRP for a specific team based on its economics and winning percentage, then compare a specific player (performance and cost) to actual replacements available, either on the roster or in the market.

For more generalized studies, I don’t see a way around a “replacement” concept mathematically.  And my point is that neither WARP nor FAT are appropriate for such studies because of the fixed costs of talent development.

If you are going to do it the “right” way, then you have a host of variables.  Not only the winning percentage, but the paths of winning percentages, and the expectation of winning percentages.  What that market can support, and what other places the fan might spend his money other than baseball.  You are trying to infer this:

how much more marginal revenue will be generated by an extra expected .001 wins per game, given all these other conditions that I know about this market, and based on the current context that I find myself in.

In Montreal for example, the fans are very fickle.  The town is used to a winning atmosphere, and has tons of other places for their entertainment dollar.  If the Expos are considered “it”, as they were in the 80s, the fans will come out in droves.  They come out even more, because of the perceived talent base.  And, being knocked out in the last series in September pre-1981 made them believe even more they were on the cusp.  Every .001 wins added at that point would have generated alot more money than 1995 and onwards, because of the fire sale that preceded that year.  Even if they were a 90-win team, the .001 wins added wouldn’t have been worth the same.

Then don’t forget you have revenue sharing, which means not every dollar goes to the team.

Even if you were to say “let’s drop Ryan Howard for nothing”, your replacement player will come from the minor leagues, which itself is a product of spending.  Say if your player development costs are 20MM to 30MM, you wouldn’t necessarily treat that as a “fixed” cost.  Ryan Howard languished in the minors for many years.

Comparing Ryan Howard to the equivalent of Bloomquist has no real basis in reality, since that’s not how teams operate.  They don’t pick up players from the scrap heap.

Given all that, my two-second method will yield results with the scrap heap method, and generally speaking, with the super long process.  If I was working for a team, and involved in their economics, then I would model reality, and develop that model appropriately.

Until then, Occam’s razor.  That’s why I like my way.

Replacement level talent sometimes come with fixed development costs and sometimes not.  Rule 5 and 6 year minor league free agents are examples of the latter.

It is difficult to assess FRAA/FRAR, as the method of calculation is proprietary.  Subjectively, I consider it less accurate than pbp in evaluating fielding skill.  You know when Willie Mays is rated at 3 runs above average per season from age 25 to 30, you’ve got some work to do. My sense of it is that the park and pitching staff adjustments are still considerably off.

Rule 5 players: there’s obviously not enough of them.  You can’t make the same Rule 5 player the repl level player for every team.  You’d need a pool of say 100-150 players to make up the replacement pool.

Tango, your solution is fine, but doesn’t handle the issues that the researchers I mentioned have raised.  Those are the financial analyses I am addressing.  Just because something is difficult doesn’t mean it shouldn’t be tackled.

My comment regarding fixed costs wasn’t helpful.  My point is the one I raised originally: baseball clubs are going concerns with draft choices and players who have to play for them for six years, the first two to three at nearly minimum wage.  If a researcher uses FAT for their replacement level, that is too low a baseline because all teams have a better pool of talent available to them without incurring what are typically interpreted as incremental salary costs.

I’m not saying not to tackle it, nor am I saying that there isn’t a better solution.

I’m saying that my approach is better than the current approach, simply because it’s… simpler, and it gets you the same result.

The better solution is one that addresses reality (much as you are describing it, but with even more parameters), as I’ve outlined in my quote post#29.

Tango, it doesn’t get you the “same” result.  It gets you a result based on certain assumptions, which may or may not apply to specific clubs.

Your solution is good for certain things, but not for any of the studies I mentioned.  It’s doable.  That doesn’t make it better for studying what the authors I’ve mentioned wanted to study.

My point remains: for analyses that strive to reconcile marginal revenue vs. internal marginal cost, replacement level is a necessity, and FAT is too low a replacement level (to say nothing of WARP).

Dave,

I don’t get your anti-FAT stance. I guess it depends on how you define replacement level:

(a) The level of play you would expect from a player replacing your regular starter, or

(b) The level of play you could acquire by paying the minimum salary to a player who replaces your regular starter.

It seems to me that option (b) makes much more sense. Phil Hughes might make it into your pool of replacement-level players, but he is neither easy to acquire nor cheap. Hughes required a $1.4 million signing bonus, development in the minor leagues, and quite a bit of luck on the Yankees’ part. Someone like Mark Bellhorn costs nothing and gives you a pretty certain level of production. For me, a replacement-level player is essentially a guy that would be playing on an expansion team that didn’t want to expend more payroll than it had to.

(BTW, I don’t want to put words in your mouth, so tell me if I’ve misinterpreted your definition of replacement level.)

I’ve had this discussion before, and it’s important to define “replacement”.  Rather than use that word, simply use the neutral “baseline” level.

You can indeed compare someone to an under-23 1st rounder as his baseline level.  The key is to associate the appropriate cost level to that baseline.  Rather than the typical 0th dollar price, you can associate say 3 million$ to that baseline level.

While Rule 5ers cost 50,000$ plus the minimum salary, and so, you can mark someone above that price (and quality level), there aren’t many of those around.  Or, how much would it cost to get an equivalent-quality player from an opposing team for an equivalent Rule 5er.

The basic equation is player-quality above baseline-quality times price-per-quality plus baseline-price.  We don’t need to set the baseline-price as close to zero as possible (by choosing the baseline-quality level appropriately), if we can derive that baseline-price the “right way”.

Thanks, David.  My argument isn’t related to the relative salary of players, though that would have to be factored into the analysis.  It has more to do with how baseball teams are actually run.  As I said, teams are going concerns with minor league systems and drafts feeding their major league teams.

If a team were to drop out of the free agent market altogether and just play players they acquired through the draft and/or minor league development, how much would they win?  That is the relevant baseline.

Why?  Because it’s much more related to the actual decisions that ballclubs make.  Very few ballclubs choose between FAT and a potential free agent.  They usually have options to them, within their own system, that are superior to FAT.  FAT ignores actual major league baseball realities.  That’s why I believe FAT is too low a baseline for true economic analysis.

For a team that completes ignores the free agent market, we’ve already touched upon this:
http://www.insidethebook.com/ee/index.php/site/comments/competing_on_payroll/#7

(I don’t know why some of those entries in the thread don’t display.  I see them in the database.)

The important line is this:

If I look at the bottom 7 teams by payroll index, they averaged .352 for their payroll index.  Their winning percentage was .438.

For all intents and purposes, those teams could be classified as the non-free-agent-dabblers.  If the average payroll is 80MM, then they spend 28MM. Let’s also presume that the low payroll teams happen to spendthe same on player development as the higher payroll teams.  (Which may be true, especially when you factor in the signing bonuses.)

So, to go from .438 to .500 (a gain of .062 wins per game, or 10 wins per season), a team will need to spend an extra 52 MM on their player payroll.  So, a 5 MM per win cost. 

Now, let’s extend this backwards.  Let’s say a team will have a 16MM payroll, which is 64 MM less than average.  At a cost of 5 MM per win, such a team will be -13 wins, or have a .420 record.

Let’s take a team with nobody on it (forget the minimum salary).  They spend 80 MM less on payroll and 20 MM less on player development.  That’s 100 MM savings, and all they can get is all the undrafted college players.  They’d get 20 wins less than average, or a .377 record.

That can’t be right.  So, what you have with is the cost per win is very high to begin with, until you reach a certain point, say a .300 record.  Then, the cost of talent to go from .300 to .500 is fairly low.  And then the talent level of players .500 and above rises dramatically.

Hmm, that last paragraph didn’t make sense.

An all-undrafted college team would play say for .150 (let’s say), or be 57 wins below average.  To get to the .438 record (10 wins below average), they need to spend 48MM (28MM for players and 20 MM for player development).  So a gain of 47 wins will cost only 48MM, or 1 MM per win. 

To go from .438 to .500 will cost 5 MM per win.

A couple of points:

- I don’t think your sample of seven teams would represent what I’m talking about.  They all probably acquired some of their talent through the free agent market, or developed players in their system via trade of players they had previously acquired through the free agent market (see Marlins, Florida).  I believe that a team that relied solely on the draft and minor league development would have a lower W% than .438.

- Also, your final change (all college players) ignores the economic reality that I’m trying to bring to the discussion.  No team would do that; MLB wouldn’t tolerate it.  I think the better approach is to take for granted that all teams have drafts and minor league systems, and the costs associated with them are for all intents and purposes fixed costs, with some discretion for the high-bonus draftees and perhaps players in their fourth-to-sixth year.

I’m giving you both.  Whether you find any value for the .150 to .438 jump is up to you.  You don’t need to use it in your analysis.

As for the teams I selected as not really being the non-dabblers, that’s ok.  You can still use it as a basis.  Maybe it’ll turn out that the non-dabblers are really a .380 team.  And that a non-dabbling team would have a payroll of 30% of the average (24 MM).  So, a gain of +.12x162 would cost 80-24, or 2.9 MM per win.

You’d also have to figure out how much teams spend in player development.  It could be that the Royals, Pirates et al actually spend much less than the Mets, Cards et al.

But, we all understand the framework at this point.  You can build a model of a team from .000 to .700, and how much it would cost to get to .100, .200, .300, .400, .500, .600, .700.  If you want to start the analysis at the .200 level or .300 level, that’s what you do.

I’m giving you both.
Thanks!

You’d also have to figure out how much teams spend in player development.  It could be that the Royals, Pirates et al actually spend much less than the Mets, Cards et al.
Yes, good point.  My assumption would be that fixed player development costs are also sensitive to market size, but not as sensitive as marginal revenue from performance on the field.

Or, who knows, inversely-proportional.  Maybe the A’s need to spend more than the Dodgers on player development, etc.