THE BOOK--Playing The Percentages In Baseball

Just to be clear (as someone who has only done a little regression analysis but is nonetheless teaching a couple of students how to do it) the problem is that this study is pretending things like OBP and PA can be combined linearly while that doesn’t make any sense, right?

If their equation had things that might be combined linearly to determine value (1b, 2b, 3b, BB...) they’d likely come up with an equation that made more sense (although there would still be problems like 3b acting as a stand in for “speed” more than representing the value of an actual triple).

We’ve basically been doing things like looking at how K% from years Y-1, Y-2 and Y-3 determine K% in year Y.

We’d also be interested in seeing how things like 1b, 2b, 3b etc predict R and RBI and (as I understand it) that might be okay but trying to combine things like lineup position and team offense levels in a linear equation with 1b, 2b and 3b would be problematic.

Is that basically, right?

Right, treating PA and rate stats in the same equation the way they are doing is terrible.  Not to mention the arb and FA parameters as well.

The reason you create a model is to… model reality.  And this is how it works:

salary = playing time * (wins minus baseline) * FA_Arb_multipler

That is it.  That’s all it is.  That’s the model.  Now, you just have to figure out how to best represent each of those parameters.

I’ve done it already in my WAR model, and it works pretty darn well.  It matches reality.

When I see a model like proposed in the paper, I see how it deviates from my model.  Mine works.  If it deviates from my model, I need to see how it does it better, either by simplifying it (which is practically impossible), or being more intelligent (which is definitely possible).

I’ve yet to see a model that does either.  Indeed, the model in the paper is so outrageous, that I’m disappointed how much traction the conclusions to the paper is given.

Kent: Mr. Simpson, how do you respond to the charges that petty vandalism such as graffiti is down eighty percent, while heavy sack-beatings are up a shocking nine hundred percent?

Homer: Aw, people can come up with [a regression] to prove anything, Kent.  Forty percent of all people know that.

FYI, Sauer and Hakes did a followup paper using some post-2004 data:  http://pirate.shu.edu/~rotthoku/papers/anomaly.pdf.  They go beyond SLG/OBP to look at BA, BB%, and Power separately, which is an important improvement I think.  But the salary model remains basically the same, so it will still make your head hurt.

I’m enjoying this blog while I patiently await the start of the Yankees game tonight.

I wholeheartedly agree that practitioners of regression tend to make horrible mistakes in application and graver errors in interpretation.

One must be especially careful not to extrapolate a regression model to vectors in high dimensions that are “far” (in some mathematical sense) from the fitted data vectors. Nonsense usually emerges even for good models appropriately derived.

In this case, the salary of 1.65 M attributed by the model to the “free agent outfielder with 600 PA in 2000, who hit like a pitcher (say .180 SLG, .160 OBP)” is weird not because the model is wrong (which it very well might) but because such outfielders don’t exist in practice. For who would let such a player bat 600 times? These players only exist in theory and as such they are only wild extrapolations from which conclusions should never be drawn.

One that that is so easy to forget, even for those well trained in statistics, is applying a regression model to data that is beyond the scope of the data used to create the model. You can never treat a regression model as something that is valid for all time and space unless it was modeled over a sample representative of all time and space. Of course, no model could ever do that.

While these criticisms regarding the bastardization of plate appearances are certainly valid, I concur with the point from #5 and #6 above: you can’t extend the regresssion beyond observable data points.  Suggesting an outfielder who hits like a pitcher would get 600 plate appearances simply isn’t plausible.  Well, unless you employ Jeff Francouer.

Any player peforming at or below the baseline will contribute zero, so regardless of playing time, the product is still ero, and he shouldn’t be projected to make more than minimum salary, unless he is named Francouer.

So, it is real life that there a few very unproductive players who are overvalued, at least for a few seasons.

Q:  What’s the most dangerous thing a math teacher ever said?

A:  A function can be written to describe every data set in which for every X value there is one and only one Y value.

I agree that the model’s failure to properly value nonexistent players isn’t necessarily evidence of a problem.  But in this case Tango’s example does highlight a real problem, because if you plug in the stats of real replacement level outfielder (something like .300/.400) you’ll get a salary of around $3 million, about 10x what it should be.

The models just don’t value either OBP or SLG nearly enough.  According to the multi-year model, gaining 150 pts of SLG and 150 pts of OBP combined only increases a player’s value by about 75%.  Is a 1.000 .OPS player paid just 75% more than a .700 player?  Obviously not.

Yes, my point was not that it breaks down at the very extremes.  I always say that you can’t extend an equation beyond the data it was based on (hence my disgust for using team data to test runs created, and then apply RC to players).

No, the point is how far I haev to go to find an equivalent to a .340/.400 player with 400 PA, if I give the other guy 600 PA.  Basically, I can’t even find a guy so bad that he would be valued worse than the .340/.400 400 PA guy.  It’s not that it breaks down at the extremes, but it simply breaks down period.

In WAR parlance, it would be very easy to find an equivalent for .340/.400 with 400 PA for a guy with 600 PA.  I can’t do it with the model presented in the paper (for the 2001 year).

The idea that you can add PA as an extra parameter like you would add a rate stat (!) is preposterous to say the least. 

I can find a ton of real-life absurd results from each of the equations they posted for each year.

I’m not sure including PAs is a problem.  Because log(salary) is the dependent variable, an incease in PAs effectively multiplies the value of the hitting stats, as it should (though it’s not linear, which it should be). 

However, it’s not clear why increases in SLG or OBP should have a muliplicative impact.  100 points of OBP should have a fixed value, but in this model it’s worth a bit more coming from a high SLG player than a low SLG player. Anyone know why economists like to use log(salary)?