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May 18th, 2009, 09:19 AM  #1 
Newbie Joined: May 2009 Posts: 1 Thanks: 0  How to regress actual data towards projected data.
Hey all, So I am currently working on a system that will predict the outcome of MLB games. I need a method to regress a player's actual stats with his predicted stats. By the end of the season, I want player A's predicted stats for a single game to be 50% projections 50% actual. For example, let's say player A is projected to play 50 games and hit at an average of .300. In actuality, player A has played 25 games and is hitting .200. So what can we predict player A's average to be for his 26th game? Originally I went with a formula like this w = weight = Games played actual/Games played predicted = .5 Average(26th game) = (Projected Average)*(1(w/2)) + (Actual Average)*(w/2) Average(26th game) = (.300)*(.75) + (.200)*(.25) = .275 This looks all well and good, but things start getting messy if we let the actual games played get larger than 2x the predicted. For example... Average(201st game) = (.300)*(1(4/2))+(.200*(4/2)) Average(201st game) = .300 + .400 = .100 Now obviously this result is not correct. In this scenario, a players predicted average for a single game should NEVER drop below his actual average for the entire season. Instead, as the actual games played approaches infinity, the predicted average for a single game should approach the actual average. I'm not sure how to calculate this. 
May 18th, 2009, 10:01 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: How to regress actual data towards projected data.
You're weighting the actual games as ((actual games)/(predicted games))/2 but it seems that you should weight them as (actual games)/(predicted games + actual games). This would probably solve your issue. 

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