THE BOOK--Playing The Percentages In Baseball

I don’t have time to skim, but isn’t that conclusion a tautology in a world with market pricing of free agents, market-associated arb salaries and mlb-delineated pre-arb pay?

Maybe I’m missing something here, but unless substitute players are really scarce, isn’t this what we should expect?

I mean, I would expect that the Yankees would pay the same as the Royals for Cracker Jacks, so I would expect them to pay similar amounts for a league-average outfielder.

I guess some possible arguments are:

1) A win for the Yankees brings in more revenue than a win for the Royals, so the Yankees should be willing to pay more for that win than the Royals.  (If there are enough players out there, though, it still doesn’t seem to me like they would have to overpay, just like they shouldn’t have to overpay on Cracker Jacks unless there is an extreme shortage.  There’s nothing putting pressure on the Yankees to overpay for a win unless there are no quality free agents left to pick from.)

2) Free agents will want to play for good teams, so the Yankees can pay less for the same player than the Royals.

3) Cost-of-living should require the Yankees to pay more than the Royals?  (I think some players who were reluctant to move to NY, even just during the season, put clauses in their contract for this, but it doesn’t seem to be a big issue in general.)

I’ve said it a million times, that the Yankees (or whoever) just need to offer a dollar more than everyone else.  Not literally of course.

And like the cracker jack analogy (how much they sell cracker jacks at Yankee stadium for does not affect their price), if I am going to buy steel to make something (a car, saw blades, whatever), how much I make off that product has almost nothing to do with how much I pay for the steel. I will pay market prices.  Obviously how much I make from the steel I use factors into the price of steel, just as how much the Yankees make from a marginal win factors into the price of that win for everyone, but that is not the question…

Someone sent me a PDF version.  Here is what I see:

We model (the log of) an individual player’s salary as a function of his OBP, SLG, fielding average (FLDAVG), whether the player is eligible for salary arbitration, whether he is eligible for free agency, and his fielding position.

Good job mostly.  One day, academia will realize that UZR is available on Fangraphs.  But, I love that they put the player’s fielding position, which is a huge plus.  I’d have preferred the arb-eligibility be 1styear, 2ndyear, or 3rdyear, but, let’s make due with what’s there.

We create a set of dummy variables for fielding positions based on the model developed by Hakes and Sauer (2006). They create categories for catchers, infielders, outfielders, and first basemen/designated hitters.

Ah, music to my ears.  This is the exact model I use.

We use local revenues from 1999, measured in millions of dollars.

They use “local revenue” to establish the market size.  Not necessarily a good choice, because the local revenue is also linked to their recent win%.  I’d have preferred a local-revenue parameter after adjusting for win%.  The Indians and Tigers, for example, likely switch between medium market and small market based on how well their teams have done.

This suggests...that players who have reached free agency eligibility earn higher salaries than players who have not reached this point. The statistically insignificant revenue term, however, indicates that playing on a team with higher revenue does not translate into a higher salary.

So, this is what the start of this thread is about.

The remaining position variables indicate the salaries of various positions relative to first basemen. The only statistically significant variable is infielder, suggesting that infielders earn more, all else equal, than first basemen.

I can believe it for outfielders, but certainly not for catchers.  I can only presume this is based on the limited dataset by catchers, or you have some unusual representation by catchers in 1999 (IRod, Piazza or whatnot).

They also note that rich teams in arbitration pay more:

This translates into a salary difference of more than US$500,000 when the player reaches arbitration eligibility between the poorest and richest teams, holding player characteristics constant.

I can only surmise it’s because the rich teams are more willing to submit higher offers, and the player is willing to submit higher requests.  Kinda like a game theory situation going on here. THIS is the most interesting finding in this paper.

Thus, we would not expect players on low-revenue teams to earn less than players on high-revenue teams, but we would expect low-revenue teams to have fewer high salary players. Because the winning salary bid may be only slightly higher than the next bid, high-revenue teams may acquire many more free agents by outbidding low-revenue teams by small amounts.

This is the “duh” comment that MGL is making in post 3.

The effect is not in the differing dollars-per-win, but simply in the number (and total dollars) of free agents signed.

***

Also, the variables for FA and arb should not be “added”, but be a multiplier.  For example, if arb players earn 50% as much as free agents, then, I think, their model won’t capture this.  It will simply presume that the FA baseline is the same amount above the arb baseline whether you are a star or a scrub, while I’ll contend that the FA will sign for double what he’d sign as an arb.  So, I think the authors miss this in their model.

All-in-all, a decent enough paper, and I learned something regarding the arbitrator and/or team/player submission offers regarding large/small market teams.

The next step in view of this fascinating result, is to see if teams/players submit higher offers, or if it’s the arbitrator that chooses the higher offer disporportionately. 

Seeing that the vast majority of cases are NOT in front of an arbitrator (90% or something), then I have to believe that teams/players are engaged in game theory (which we already knew), but also includes a market-bias. 

And that is the most interesting thing I learned in this paper.

"Also, the variables for FA and arb should not be “added”, but be a multiplier.”

Isn’t this a pretty huge problem?  It seems to me you want to make FA the starting point, add variables for arb year, and exclude the pre-arb players entirely (their compensation effectively has zero relation to their performance).  I always thought this was a major flaw in the Sauer paper.

One reason the position values might not make sense is their use of fielding average.  Catchers and first basemen all have Fld% around .99, while IFs (especially 3Bmen) and OFs are much lower.  You really need to standardize by position (or exclude). 

Still, interesting stuff.....

And no vindication to my WAR model in this paper.

Tango:  What are you saying in #6?

Also, does this paper shed any light on the issue that Hakes and Sauer addressed, i.e. whether teams undervalued OBP pre-Moneyball, but not after that?

He has another “interesting statement” up there today that might be of interest to you

Feel free to link to his blog:
http://www.sabernomics.com/sabernomics/index.php/2009/03/another-interesting-statement/

I don’t find that interesting either.  Teams pay more for players when they are in the sweet spot of getting more games courtesy of the playoffs. 

Here’s a couple of good articles on the subject, courtesy of Vince Gennaro:
http://www.hardballtimes.com/main/article/player-value-the-postseason-effect/

http://www.hardballtimes.com/main/article/diamond-dollars-the-economics-of-winning-in-baseball-part-1/

Nate Silver also had a good article on the topic a few years back, if someone wants to look for it.

Does this mean that teams are not doing a good enough job of driving up the price of players for the Yankess, or are the teams just driving the price up on each other somewhat equally?

Is dividing things up into “catchers, infielders, outfielders, and first basemen/designated hitters” better than further dividing into 2B, 3B, SS, CF and C? There may be a good reason to do that there way that I don’t understand. But in some salary regressions I have run, I sometimes get opposite signs for SS and 2B (where the magnitude is the same in absolute terms). I did not include revenue data or fielding pct, but I did have hitting stats, free agent/arbitration status and position dummies. Here is the link on what I have done

http://cybermetric.blogspot.com/2008/06/have-second-basemen-been-underpaid.html