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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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.