THE BOOK--Playing The Percentages In Baseball

I think I sprained my neck reading this!

MGL, as you likely prefer the Vegas scenario, the one-line summary is to (a) create a model of all known variables such that (b) over a million games the impact of each player’s performance in terms of change in winning odds, aggregated, will be exactly zero.

Very interesting!  So down by 1 in the 9th, with Coco leading of, and then Ortiz and then Manny… there is some traditional (non-Vegas) WPA associated with Coco getting on base.  (let’s say .1 wins).  And let’s say all things considered, Pedroia is available to pinch hit and is 20% more likely to get on base.  If Francona makes the switch, we can credit him with getting .1 wins with 20% better likelihood.  Or, .02 wins for Francona for making the switch.

HOWEVER, with Ortiz and Manny on deck, instead of two “average” historical major league hitters, Coco getting on base is actually worth .15 wins.  And thus, Pedroia getting on 20% more often makes it 20% more likely that the Sox get those .15 wins.  So Francona instead gets credit for .03 wins instead of .02 if we look at the Vegas scenario.

Does that make sense - or better yet, is that correct?  That seems like a non-zero sum way to evaluate people via WPA with the inclusion of all the variables.

The Vegas odds would include the chance that Pedroia would have possibly come to pinch hit, much like you include the chance that Hoffman or Mo would possibly come in relief.

Everything is zero-sum.

I don’t think I understood whether you were doing the first scenario (full preallocation) or the second (no preallocation).

A thought: Say the Cards are in Atlanta, and Pujols sees Jimmy Carter in the crowd.  He’s always wanted to meet Jimmy Carter and he’s decided to leave the game to go meet him.  (I don’t like saying, “Pujols gets hurt.” But that’s what I’m really talking about...) Clearly, Tony LaRussa will have to send someone not-quite-as-good out to play 1st and hit in Pujols’s spot and the Cards win prob will have to be adjusted downward.  To whom do we credit/debit the WPA?  The trainer?  Pujols?  Jimmy Carter?  God?

Are you assuming method 1 (with full preallocation)?  In that case, you debit Pujols, since he was preallocated a certain amount presuming a certain number of PA.

This would be like Santana coming out after 1 pitch.  He was preallocated a huge amount, and will be deallocated that same huge amount in-game.

Pizza cutter, I’d say Pujols.  I’m not trying to advocate some fancy new amazing perfect system for evaluating stuff, just throwing around ideas.  But given it was Pujols’ conscious decision to leave (and like it was Francona’s hypothetical conscious decision to pinch-hit someone).

Tango, maybe I’m talking about something where you’re examining the process of the decision-making, not the results.  In which case, if you make the “right” decision every time, you never lose.  That’s how I try to evaluate Theo’s moves - sometimes you get lucky (Ortiz), sometimes unlucky (Renteria), but since the process was correct (in my opinion) in both instances, he gains points for both deals.  I was just trying to put an in-game, objective spin on it.

Would a WPA method that treated batters differently be computationally tractible? 

Standard WPA uses historical data to estimate a situation run-scoring matrix, and a situational win-probability matrix.  All WPA calculations depend on the same two matrices.  The system assumes (1) all plays are independent; and (2) all innings are independent.

When evaluating the WPA of at bat, if you want to consider the line-up surrounding the at-bat (e.g., Pujols is up next vs. Perez is up next), you would have to come up with different situational run-probability matrix for each at bat.

You’d also have the problem of innings affecting one another.  If a pick-off at first means Pujols bats first next inning, as opposed to last this inning, your prediction for runs next inning has changed.

Further, that dependence doesn’t stop next inning; an event in the first inning can affect the likelihood of Pujols batting again in the 10th.  And in order to calculate the value of the event in the 1st inning, you’d need to project out to the 10th.

So, unless I’m confused (which happens somewhat frequently), instead of being able to leverage the independence of events and innings, you would have to do a ton more math.  For instance, Inning 1 can influence inning 2 in only 9 ways (by changing who leads off inning 2, assuming no pinch hitting, no subs, no injuries, etc.), but since that inning affects inning 3, etc., there are 9^8 (9^# of innings - 1) possible ways in which the events in inning 1 can affects the rest of the game.  And unless someone is very clever and comes up with a way to simplify the problem, one would need to evaluate all 43 million effects in order to determine the long-term effects of an event in the first inning.

cdm, right on.  Unless you are a gambler, where such analysis would be required (full preallocation), that’s the reason I prefer as much non-preallocation as possible. 

The concept that the players are identical on both teams is extremely appealing from a programming standpoint and explanatory standpoint.

And in the end, given enough games, you will end up with exactly the same results for Pujols using either of the two methods.

Where you gain the most, by far, is the one-game analysis.  That aside, since we typically look at things at the seasonal aggregated level, who the heck has time to program the perfect preallocation model?

It’s good to know what the frameworks are.  But, time must lead this solution.

CDM

If you look at market based systems, such as those at Tradesports then they will give you the “gambling answer” to a large degree as the markets update in real time.

You can read more about it in a Hardball Times column I wrote:

http://www.hardballtimes.com/main/article/prediction-markets-redux/

John

John,

Sure, as you mentioned in your column, those markets make pretty good predictions.  On an interesting aside: the variance between the predictions made by Vegas this year and actual game outcomes is only slightly greater than what you would expect by chance alone.  Over 1455 games this year, the variance one would expect by chance: 341.17.  Vegas variance: 343.32.  Thats crazy good.

But thats not solving the problem. Its using a whole bunch of gooey gray neural networks to estimate the solution without any real introspective understanding as to how the solution works. Its a purely descriptive model, without any predictive aspect. It doesn’t tell me, for instance, how replacing Kason Gabbard with Clay Buchholz would affect the likelihood of the Red Sox holding onto their one run lead going into the fifth.  For instance The “true” gamblers WPA solution would tell me that, if it were tractable.

-cdm

I really like that this is being discussed because I think it has a lot of potential.  I like using Fangraphs live WPA charts when watching games sometimes but when I’ve got #7-9 hitters coming up in the 9th and we’re down one run I’m pretty sure we are going to lose.  I can’t really help on implementation but the simpler it was the better (even at the cost of some accuracy I think).

While I agree that with Tango that the non-preallocation makes more sense to track and follow as fans, we’re forgetting a very important subset of gamblers: managers.

If you’re a manager/strategist thinking about using WPA to evaluate strategy, you’d be nuts to consider at least a little bit of pre-allocation.  Otherwise, a bunt/don’t-bunt decision would be evaluated exactly the same whether you had - ahem - Aaron Rowand or Albert Pujols on deck.  And that’s just nuts!

A manager is in the gambler class, for sure.  A fan evaluating in-game decisions is in the gambler class too.

So given that, do you believe that there is a hybrid of no pre-allocation/full pre-allocation that is necessary for using WPA to analyze strategic moves?

"If you have Eckstein hitting in front of the pitcher, or hitting in front of Pujols, the value of his performance is greatly affected. A walk is far more valuable if you have someone who can leverage it.”

“And in the end, given enough games, you will end up with exactly the same results for Pujols using either of the two methods.”

Tango:  I may be thinking about this incorrectly (often the case with WPA), but I’m not sure both of these statements can be true.  Traditional WPA is totally ignorant regarding the future—it “knows” only what has come before.  A leadoff walk—given a certain inning/score state—always has the same value. 

But in the “gambler” version, you seem to be taking account of varying probabilities in what happens next.  A walk by Eckstein has more value than a walk by the Cards’ #8 hitter, because Pujols is on the horizon creating a kind of “pre-leverage.” Won’t the two methods give you different assessments of Eckstein’s value?  And perhaps Pujols’ as well?

It should give you roughly the same, depending on the amount of synergy.

To Frank Thomas: Tim Raines preceded by Frank Thomas is better than a pitcher preceded by Frank Thomas. 

To Tim Raines: Raines preceded by Thomas is beter than Raines preceded by a pitcher.

The Raines+Thomas combination would provide more than additive impact because of the synergy.