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Kalman Formulas

 
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student



Joined: 19 May 2007
Posts: 1

PostPosted: Wed May 23, 2007 10:39 pm    Post subject: Kalman Formulas Reply with quote

I was trying to make predictions of wnba games by this method (it's great fun to me lol): http://www.rawbw.com/~deano/articles/kalman.html

The author mentioned that the rating of two teams should be adjusted based on their actual performance according to

http://www.rawbw.com/~deano/articles/kalman/formula.html

I've been trying to predict wnba games using his method but I don't know how to update team rating based on actual performance, please help. (I'm completely lost when I read the sentences in bold below)

"Using a prior variance of 20 for both Chicago's ratings and the Celtics' ratings, the variance of the expected ratings is about 40[=(20*20 +109.82*20+104.82*20)/(106.12) for the offense, = (20*20 +104.22*20+107.72*20)/(106.12) for the defense]. In general, ratings fluctuate from game to game with a standard deviation of 12 (or a variance of 150) . Hence, the Kalman weight is 0.2145 [=41/(41+150)]. The updated road offensive rating for the Bulls is then 107.9 [=109.8+0.2145*(99.8-108.5)]. The variance on this new estimate is 15.7 [=(1-0.2145)*20], only a slight drop from before. For the defense, the updated rating is 104.8 [=105.2+0.2145*(105.0-105.2)], a slight improvement. The variance decreased to 15.8."

For example, if team A has an OR of 100 and DR of 95, and team B has a OR of 102 and DR of 100, with a league average rating of 100, how will team A OR change if they win by 99-90 with 95 possessions (assuming neutral court)?
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Mark



Joined: 20 Aug 2005
Posts: 807

PostPosted: Fri May 25, 2007 12:13 pm    Post subject: Reply with quote

This may not help much and I havent done this...
but it looks like you need to know the past variance for this particular team at that moment (Use past season or season to date for this? If you are doing it for WNBA right now it would probably be past season at least for awhile but maybe season to date later). If you had the game to game points scored and allowed data and possessions for computing the ratings for team A (should be able to get that from internet for those teams) and find the variance by software function- variance function is in Excel (see help section or from menu click insert/function/statistical/VAR)- or manual calculation using formula from a statistical reference. Then just follow the Kalman formula given.
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