Sunday, April 07, 2019
Fixed v Custom Win Probability
?The win probability charts that I generate are virtually always based on two equal teams at all times. That means it starts at 50/50. Fangraphs has an option that shows the win probability based on the pre-game odds. So for example if Scherzer is pitching, the Nationals would start off at say 65% chance of winning.
Something interesting happens in that case. If you were to do Win Probability Added (WPA), meaning the change in win expectancy, over the course of the season, Scherzer should come out to exactly... ZERO! Why is that? Consider for example you had Superman, and your pre-game odds are at 100%. The game ends at 100%. So, Superman's value-added was... zero? Right. It's zero, over-and-above your pre-game forecast. And, if your pre-game forecast is perfect, then the value-added in-game will be zero.
Going back to Fangraphs, their custom win expectancy does not change based on who the batter is at that moment in time. So, in this case, Trout will end up with a huge value-added... just not as huge as you'd otherwise expect. This is because the pre-game win expectancy is spread out across all the players. So, in my Scherzer example, he wouldn't get exactly zero if your forecast of his was perfect, because the Nationals without him are still above average. It's a bit of a nuance.
This opens up something interesting. ESPN has recently unveiled that their win expectancy is indeed custom at the plate appearance level (actually at the PITCH level). And this means all the nuances I noted goes away. Indeed, in order to prove that their model works as intended, all you need is the WPA for each hitter and pitcher. If any deviation is consistent with Random Variation, then, great, we've got the perfect model. Any other deviation would mean either a poor pre-game forecast, or, there's a particular variable that has not been customized.
My best guess as to what might not be as customizable would rest with relievers. Since we don't know who will come in to pitch, then we are making guesses as to who will pitch. And so any deviations there would reflect that. And so, you should expect top relievers to have positive WPA consistent under the ESPN custom model, but just not as positive as the fixed model.
I hope all that made sense. If not, read it again. It should make more sense the second time.
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