THE BOOK--Playing The Percentages In Baseball

Tuesday, August 21, 2007

WPA: one says goodbye, another says hello

I’ve been late in continuing my answer to an earlier post regarding the real-time and retrospective look at the play-by-play of a game.  Basically, the answer is:

Do sequencing and timing matter?  If you had a game with 1 inning (each with 27 outs), and only 1 base (i.e., HR or out), then the tracking of win probability at the play-by-play level will be fairly unimportant to the hitter.  It would seem unlikely that anyone would care, or anyone would feel, that if it’s the top of the inning, and you scored 5 runs with 13 outs, that it would be any different than if you scored 8 runs with 10 outs.  At the pitcher level, or more specifically, at the pitching-changing level, we’d care more, but only from a manager perspective.

From this perspective, the in-game tracking of scoring is really irrelevant.  What we care about is the final outcome.  Unless of course timing matters.

Even if timing matters, how much of the leverage do we want to give to the batter.  As I’ve stated at other occasions, the best stat around is WPA/LI (WPA divided by Leverage Index), which is the same thing as wOBA by Game State.  With a man on 3B and less than 2 outs in a close game, a strikeout is a killer.  The underlying premise of wOBA is that the average positive value is always exactly 1.  That is, a walk is worth on average 0.72 positive plays, but could be worth 0.50 in some cases or as much as 1.00 in the case where a walk and HR are worth exactly the same (bases loaded, tie game, bottom 9th).  A HR could be worth as little as 1.0, on average close to 2.0, and probably as high as 3.0 or 4.0.  But the point is, we don’t give the leverage to the player.  We have a specific wOBA stat for the specific game situation, but, it doesn’t inflate the impact based on the inflated value of the Leverage Index.  That’s why it’s WPA divided by LI.  From this perspective, sequencing matters, but timing does not.  Since we’re also reasonably confidant that a player can’t “rise” to the occasion to any great degree, it would appear to be foolish to credit a player’s PA for ten times its value, simply because it was his turn at bat.

What you are left with however is the “luck” bucket.  Take for example this game, where ARod hit a grand slam with 2 outs, bases loaded, down by 1 in the bottom of the 9th:
http://www.fangraphs.com/plays.aspx?date=2007-04-07&team=Yankees&dh=0

A typical HR adds around +.13 wins per PA.  This particular HR however added +.72 wins.  However, his WPA/LI was +.72/10.9 = +.07 wins.  This is what the win value of a typical double would be.  And, it makes sense.  They only needed 2 runs to win, not 4.  The effect of the grand slam HR was exactly the same as a two-run single.  If we only give ARod credit for +.07 wins for the HR under the “timing doesn’t matter” scenario, we are left with the other +.65 wins to be accounted for and distributed somehow.  We can just create a new bucket for the player ("clutch" or “timing") or for the team ("timing" or “luck").

The great thing about a site like Fangraphs is that it gives it all to you:
http://www.fangraphs.com/statss.aspx?playerid=1274&position=3B

ARod’s WPA/LI is +4.8 wins this year, and he’s had another +0.8 wins based on the leveraged-timing of his performance.  You can add the two to give you WPA (+5.6 wins), or you can do whatever else you want with it.

Since hitters can’t be selected to be placed in certain hitting spots (PH notwithstanding) it would seem foolish to use WPA for them, when WPA/LI does really what you want it to do.  The same applies for starters.  Unless you believe in one or both cases, that players can rise to the occasion, and therefore they deserve to have the full impact of their “timing” values attributed to them.

For relievers and PH, it’s a bit different, since managers are using them based on the game state.  They do have an influence since a better player will implicitly force his manager to use him in the higher leveraged situation.  However, as noted Book Blog poster Guy pointed out, those situations will exist regardless of which reliever the manager can choose from.  And, he certainly makes a good point.  Guy’s idea, why I endorse, is to basically give a portion of the “timing” value to the reliever, a portion of which is based on how much he contributed over what a peer-replacement would have otherwise done.  This would satisfy both camps: that part of the “timing” value was strategically earned, and part of it was pure luck.

WPA can exist in various forms.  As presently constructed, they are ideal for in-game tracking, strategy, and betting.  Post-game, on a player basis, we should deal with two numbers, WPA/LI and Timing, as these numbers, separately, tell us what we want: how well the player performed to the situation, and how much additional hope/despair he gave the fans for the timing of his performance.