Tuesday, September 1, 2009

Replacement Players And An Apparent War: Sabermetricians vs. Economists???

When I think about statisticians, economists, managers, and sports enthusiats, I think compatibility, co-workers, discussion, working together, etc. That doesn't seem to be the case when it comes to the debated Replacement Player metric often discussed on sabermetric websites. I had a post dedicated to that discussion, as I am somewhat stuck in the middle on the issue. However, I wasn't planning on posting it without some discussion with economists way smarter than me or with sabermetric folk way smarter than me as well. Below, I'll just say my general thinking on the topic (though, I'm not an Economist or a Sabermetrician, so take it with a grain of salt).

I definitely don't agree that a Replacement Player should be paid $0, but I also DO NOT think the idea of valuing zero-sum outcomes using a replacement metric is outlandish. I mostly think the disagreement comes when converting the replacement metric(s) into valuations or salary (which are different things). I also believe that there are some differences between valuing players in a fantasy model vs. valuing players in real life. The Replacement Player works great in fantasy, but not when revenue is coming from an external source (or, is not a totally zero sum occurrence). Anyway, what prompted this was a recent generalization by JC Bradbury on Sabernomics (one of my favorite Blogs) that claimed Garrett Anderson is a league average player (I really think readers blew this out of proportion, as Bradbury was mostly speaking as a Braves fan). The Book Blog has a thread about the issue, and I posted my opinions as follows:

"From my experience with economists, I’m not totally convinced they all ‘flat-out reject’ the idea of the replacement player [a claim made earlier in the comments]. In fact, I think the replacement theory has its foundations in a good economic place (despite my mentioned qualms with it in the past). I generally just think it goes astray with the assignment of $0 value to a replacement level player and the fact that paying $0 this just does not happen in the world of competitive bidding where players can choose to play or take on another profession.

I think the fact that the player is contributing production at the MLB level inherently creates significant value for that team and therefore more salary to that player (like when we see a good player go from a small market to a large market). It may not be value above other teams, but while the Game of Baseball is asbolutely Zero Sum, the revenue function is not necessarily so. I feel this is where the real-life valuation diverges from using the Fantasy Model, where ‘revenues’ come directly out of other fantasy owners’ pockets.

I also feel there is the general disagreement from most economists (and I have to mention here that Fort and Bradbury don’t seem to have the same view, as exemplified by the discussion at Phil’s site, linked above...I can speak for neither) because of the competitive bidding process and what the value of maintaining the ‘absolute’ level of talent in Major League Baseball is. There is going to be a larger cost to having players like Willie Bloomquist rather than a team of high school players on the field. MLB makes millions of dollars precisely because they are able to pay the highest prices for all talent, and get the best talent available. The reason the level of replacement player exists for MLB where it does is only because MLB pays the highest price for talent. Otherwise (for example, if it paid $0), the talent would go elsewhere or find something else to do.

In addition, there is significant time and money spent playing baseball for those who are at the minor or major league level. I’m willing to bet a lot of money that the ‘Reservation Wage’ is a lot higher than most people suspect.

This time/money is spent specifically for the reasons mentioned above: the players are expecting a ‘payout’ and ‘probability of reaching that level of payout’ that maximizes their return on investment. This level of payout (like in a tournament or promotion model) needs to be significant enough to continue to attract that talent and induce players to put forth effort to produce the highest absolute level of baseball play (at least in its simplest form). Otherwise, the expected payout would not likely come out above players’ reservation wage (as averaged over his career).

From the standpoint of replacement player, it almost seems as though many people who advocate $0 value see fielding the 25 player minimum as a sunk cost of sorts, or a fee to participate in MLB (25*$400,000, or $10,000,000 payroll minimum). If there is no expected return on investment into that $10,000,000, then I guess that would be the case. But I think that’s a VERY hefty price to pay ($300,000,000 for 30 individual owners in MLB) to simply be able to negotiate with the Players’ Union.

With that said, I tend to think values from the past year on JC’s site are pretty inflated and agree that a team of Jeff Francouers being paid $12 million each would be hard pressed to see a profit [I will insert here that I love JC's site, and his book is one of the main reasons I got into statistics, economics and sports research]. While I feel that there is value simply by being an MLB club, it doesn’t go all to the players. But given that they are the product, a significant amount probably should to maintain the product quality. But that’s a completely non-analytical point of view at this point (I’m just ‘eyeballing’ it). I can’t really criticize without knowing anything more myself.

I really don’t think the above reasoning is totally incompatible with the Replacement Player metric. I think the disconnect simply comes from the conversion to value or salary and how Marginal Value is assessed (as MGL mentions above) at that level. Does anyone think those concerns are completely out of line? I really like the topics discussed here, and mean no harm at all in any questions I pose. I am simply a curious person and think there are plenty of smart people here.


That seems like a silly and misleading question. *Most* people intelligent enough to be involved in analyzing sport performance (I say most, because I know it’s not all) recognize that the use of a .100 batting average as 1/3 production of a .300 average is an incorrect assumption. But then again, I’m just a recently converted Wolverine, so you should probably ignore me."

I guess I'll mention that Patriot has his own Blog (Walk Like A Sabermetrician)as well, and is a thoughtful reader in my opinion. He's got a fun to read Blog, and i like it. Unfortunately, he's a Buckeye. But I'll let that slide.

The reason I post this here is I'm curious about others' opinions on this topic (whether you be a casual observer, a stat nerd, an economist, or just smarter than me in general). The idea that a replacement player is valued at $0 and paid $0 doesn't take into account opportunity cost and the need for the league to maintain a certain quality level to continue to attract fans. I feel like there is a lot of hostility and rash generalization toward Economists from Sabermetricians (and sometimes the other way around as well). I'd love to hear input from any angle other than "You're a stupid idiot, idiot!", because I get that a lot already.

ADDENDUM: It seems that in the past, I have been grossly misinformed about the $$ value conversion of a 'replacement player'. According to Tango, there is not an assumption that the replacement player is paid $0. However, in the past, I had been told the value is $0. Period. And salaries are generated from a baseline of $0. It still can be an arbitrary metric, with plenty of uncertainty, but I have much less problem with it if this is the case. I think overall, it's a productive discussion here. The $400,000 intercept is much more reasonable, in my opinion and I either made a mistake, or was misinformed. Either way, the intercept (in terms of where it lies on the talent distribution) is up for debate/uncertainty (I think most would agree), but not to the extent of millions and millions of dollars.

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