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May 18th, 2009, 09:19 AM   #1
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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.
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May 18th, 2009, 10:01 AM   #2
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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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