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Wednesday, January 26, 2011
Win Probability: pre-allocation method
Brian asks:
Don’t miss Andrew Foland’s 5-part tour de force on how to incorporate pre-game estimates of win probability with the in-game estimates. Awesome job, and I really appreciate the time Andrew has put in. This is something I’ve been asked to do for a while. I think it’s a great idea, and I developed a very similar method to do it.
However, I would be reluctant to make it the ‘official’ WP or WPA model. If the Patriots have a game against a weaker opponent pegged as a 70/30 match-up, and Tom Brady plays lights-out, should he only get 0.30 WPA instead of 0.50 WPA? Should he be penalized for being favored pre-game?
I’ve talked about this in the past, and I guess Brian post-dates those discussions. No problem, as I presume lots of readers don’t go through my archives looking for stuff like that.
Ok, this is how it works. Suppose that Halladay is pitching, and the Phillies are at home. Let’s say that they have a .750 chance of winning. In order to go that, you need to “preallocate” a certain number of wins to Halladay, to the Phillies being at home, to Rollins, and Utley et al. Then, you let them accumulat their +.250 wins or -.750 wins depending on whether they win or lose.
And what happens after one million games? Well, Halladay’s in-game WPA will be exactly ZERO. The sum of his pre-allocated WPA will be exactly equal to his talent level. In short, given enough games, adding up a player’s in-game WPA is useless.
But:
1. That is deathly boring
2. We really don’t know what his true talent level is for each game
3. There aren’t enough games to get a zero for in-game WPA, and now the whole thing will look strange
So, rather than doing the extremely complicated method of preallocating wins on a player by player basis, simply start everyone with ZERO pre-allocated wins, and let them earn their in-game WPA without knowledge of their talent level or their team’s talent level. When you sum it up, you will obviously get zero pre-allocated wins, and the in-game WPA will be their entire impact.
If you are a professional bettor, well, you desperately need pre-allocated wins.
Check out the archives. I have a few threads on the topoc.
Am I correct in understanding that, by charting pre-allocated wins during play, you create a graph which basically reflects live, updated gambling odds? Sort of an up-to-the-play Vegas line?
That doesn’t seem too terribly boring, but I’m probably missing something.