smithlabs
Heisman
Warning, this gets a little geeky.....
Most of all, this year's victory over Michigan restores my confidence that OSU with Tressel is better than scUM with Lllloyd. Some people might been convinced last year but the mathematician in me begs to differ. A football game is similar to a coin flip in that there are now only two possible outcomes - win or loose. Therefor, performance in a game needs to be considered given the constraints of binomial distribution. With this year victory, OSU emerges well beyond the one sigma confidence interval as the better team. The one sigma confidence interval of a binomial distribution is sqrt (p(1-p)/N)) where p is the probability of occurrence and N is the number of trials. When we beat scUM in 2001 we knew we had total confidence in Tressel, after all sqrt(1(1-1)/1) is zero. There was no room for doubt. Likewise for 2002 when we advanced to 2-0. However, 2003 doubt crept in. At 2-1 with only three data points (N=3) there was a lot of uncertainty. The expect outcome was 66.6 for Tressel but the 1 sigma value was sqrt(.66(1-.66)/3) or 27.2 %. We only had a one sigma confidence that Tressel was 66.%-27.2% or 39% the coach that Carr is? In 2004 things got better. Good guys were 3-1 so average was 75% but with only four trials the one sigma value was 21.6%. We could barely say with confidence that Jim would beat Lloyd 75-21.6 or 53.4% of the time but is just beyond the noise. Now a 4-1 we have something going. Our average chance of winning is 80% but what's more we have a confidence interval of sqrt((.8*.2)/5) or 17%. We can now say with 63% confidence that Tressel is the better coach.
Hmm, this was funnier when I first thought it up. It would have been funnier if we weren't over the one sigma value last year. I guess I could delete this post but I have thought about now. Oh well, it's only rep points.
Most of all, this year's victory over Michigan restores my confidence that OSU with Tressel is better than scUM with Lllloyd. Some people might been convinced last year but the mathematician in me begs to differ. A football game is similar to a coin flip in that there are now only two possible outcomes - win or loose. Therefor, performance in a game needs to be considered given the constraints of binomial distribution. With this year victory, OSU emerges well beyond the one sigma confidence interval as the better team. The one sigma confidence interval of a binomial distribution is sqrt (p(1-p)/N)) where p is the probability of occurrence and N is the number of trials. When we beat scUM in 2001 we knew we had total confidence in Tressel, after all sqrt(1(1-1)/1) is zero. There was no room for doubt. Likewise for 2002 when we advanced to 2-0. However, 2003 doubt crept in. At 2-1 with only three data points (N=3) there was a lot of uncertainty. The expect outcome was 66.6 for Tressel but the 1 sigma value was sqrt(.66(1-.66)/3) or 27.2 %. We only had a one sigma confidence that Tressel was 66.%-27.2% or 39% the coach that Carr is? In 2004 things got better. Good guys were 3-1 so average was 75% but with only four trials the one sigma value was 21.6%. We could barely say with confidence that Jim would beat Lloyd 75-21.6 or 53.4% of the time but is just beyond the noise. Now a 4-1 we have something going. Our average chance of winning is 80% but what's more we have a confidence interval of sqrt((.8*.2)/5) or 17%. We can now say with 63% confidence that Tressel is the better coach.
Hmm, this was funnier when I first thought it up. It would have been funnier if we weren't over the one sigma value last year. I guess I could delete this post but I have thought about now. Oh well, it's only rep points.
