skyking162

One more regarding WPA volaility… My current best estimate of the importance of any game-situation is to measure the variance of the potential changes between the current game situation and the situation at the end of the inning. With a couple tables in Studes’ WPA Spreadsheet, it’s possible to know the probability of any number of runs scoring the rest of an inning.

Because WPA is known for every state of the game, you can compute the standard deviation of WPA changes to the end of an inning. For each possible change in score, subtract the current WPA from the end of inning WPA, square it, multiply by the likelihood of that many runs scoring, add up all the possibilities, and then take the square root. I ran through a couple calculations in this drawn-out post and posted tables showing the varying importance of game-situations in the seventh through ninth innings in these two posts: 7/8 and 9.

That’s a review of what I’ve got right now. What I think is an even better option is to compare the current game-state to the possible changes as a result of the current plate appearance, not all the way until the end of the inning. This approach really focuses in on the atomic events that change a baseball game. In order to run calculations on the volatility of plate appearances, you’d need a table with the probabilities of each of the 24 base-out states transitioning to a different one. For example, you need to know that the probability of two outs/runner on first becoming two-outs/runners on second is .08 (I’m making that up). You’d also need to include some additional inning-ending states: three outs with zero, one, two, or three runs scoring.

The calculation would be similar to the end-of-inning approach, except that you’d compare the WPA of the current situation with the WPA of each of the 28 potential game-states. And then take into account the probability of each change occuring. It’s a slightly more complicated calculation as there are 28 possible changes compared to the 20 realistic score changes during an inning. However, a more difficult part is finding the 24×28 transition matrix in the first place — some analysis of play-by-play data is needed, I think. And to me, the next-to-impossible part is figuring out how the 24×28 changes based on run environment.

Thanksfull the plate apperance approach is Tangotiger’s Leverage Index (LI), a calculation he’s going to present in an article shortly (with necessary tables, I believe). One difference that I know of is that Tango scales LI so that the average game-state has a LI of 1.00, with higher LI’s representing more important situations. According to this post, he also computes a version of LI using absolute values instead of standard deviation. Standard deviation seems more statistically valid, but I couldn’t explain why.

I promised Frank (and myself) a more intuitive an explanation of why we should heed these calculations when considering reliever usage. That’s my next WPA post, I promise. Probably.

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These links are via the home base of WPA, the Baseball Graphs blog.

I already pointed out the Nintendo recreation of the 9th inning of Game 6 of the 1986 World Series that uses Vin Scully’s actual call as the audio, but Lookout Landing posted a WPA graph and summary of the whole game. Buckner comes in at -.68 wins (lack of fielding plus lack of hitting) and Bob Stanley grabs the silver medal with -.31 wins. If you consider the fact that the Red Sox could have clinched the World Series with a victory, but dropped down to a 50% chance of winning the Series in Game 7 by losing Game 6, Buckner’s suckitude decreased Boston’s probability of winning the Series by 25% on the error alone. One missed play cost the Red Sox a quarter of a World Series. Of course, that’s a lot less blame than most Boston fans attribute to Billy B.

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Sox Watch is a blog devoted to tracking the WPA of the Red Sox, but with a couple cool twists. Since FanGraphs is tracking the WPA of all games, Sox Watch is “only” calculating year to date totals. First, the site posts daily updates of player WPA totals, like today’s. Second, the site posts daily updates of WPA by category — starters, relievers, position players, and opponents’ errors, like today’s. Remember that 0 is a league-average .500 winning percentage.

Schilling and Beckett both have over +1 win each, Papelbon’s right behind Beckett thanks to his high-leverage opportunities, Loretta’s the top-rated hitter due to his heroic walk-off homer a couple nights ago, and Youkilis is the second clutchiest on the team. Bring up the rear is Mike Lowell, more than countering the contributions of Mark Loretta. Hmm, who saw that coming!?

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Here are the standard deviations for the interesting parts of the seventh and eighth innings. Notice that there aren’t any red spots before the ninth, although my cutoff for red was rather arbitrary. The ninth inning charts can be found here.

For the original article about what led me to try standard deviations, click here. (Yes, it turns out that the expected change in WP for any situation is exactly 0% — this assumption is how Studes calculates WP in the first place.)

The next step is to compare P values for each situation with these SD values to see which situations each system weights as more important relative to the other one. I’m happy to share my SD worksheet with anyone who wants to take a look — all bugs have been removed.

Also, check out this roundup of WPA usage around the blogosphere over at HardballTimes today.

Top 7

Bottom 7

Top 8

Bottom 8

There’s a new version (1.6.1 it’s called) of the WPA spreadsheet available from Baseball Graphs that fixes a formula mistake in the later innings.

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Thanks to Studes’ updated WPA spreadsheet, I was able to calculate the standard deviation of the change in win-probability for each game-state. Excel’s array functions are my new best friend.

Here are a couple screenshots, one of the top of the 9th and one of the bottom of the 9th. The run differential along the top is from the home team’s point of view, and the InnBaseOut column translates as Inning-HalfInning-BaseSituation-Outs. For half-inning, 1 is top and 2 is bottom. For base-situation, it goes like this:

1 - none on
2 - first
3 - second
4 - first/second
5 - third
6 - first/third
7 - second/third
8 - loaded

I color coded each situation based on importance. Green is 15% to 25%, yellow is 25% to 35%, and red is anything higher.

Top Ninth

Bottom Ninth

I’m surprised to see so much color with the losing team trailing by as many as four or five runs, albeit with a bunch of runners on base. Those cells do pretty much represent situationsn with the tying run at the plate, though.

I haven’t spent too much time looking over specific situations, yet. I’ll try to post the more important sections of some other innings later today. Any interesting observations to make?

Note: I’ve found multiple errors in my formulas — not sure if they affect the 9th inning or not. I’ll fix them shortly.

Update: Just one more error to go, but none affected the tables already posted.

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The Washington Post is updating a win-probability graph in real time as part of its coverage of Nationals games. No summary of how much each player affected the game, however. Hat tip to The Nats Blog who’s also tracking something similar to WPA for every Nationals game.

Studes has a new version of his WPA spreadsheet available for download. The input sections are all the same, but the backend has been reorganized to make it more obvious how the calculations work. Best of all, a full win-probability table is included that can be modified for different run-environments.

SI.com has an excerpt from The Book discussing use and success of pitchers for three-run saves. Nothing ground shattering, but an interesting read. I’ve yet to order my copy of The Book, but I’m really looking forward to it.

Here’s a blog that’s attemptingn to track and present WPA totals for all Tigers games this year. He’s falling behind a little bit, unfortunately.

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