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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Sky is a baseball fan and racket sport afficianado living in upstate NY. His favorite color is orange and is just about ready to give up on his life-long dream to become the next Magnus ver Magnuson (World's Strongest Man). His favorite baseball teams are the Yankees and Red Sox, proving that there's hope in the Middle East.
April 19th, 2006 at 11:04 am
That’s pretty interesting, Sky. I find the results surprising, too. It also seems to say that one and two runs leads, and maybe even three-run leads are definitely more important than tie games. Perhaps this reflects how major league managers really think.
Seems to me it indicates that something should be layered on top of these results — perhaps the probability of an average pitcher (or even below-average) pitcher even getting into each situation.