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9.15.2003
Fantasy Football Strategy I'm not a big fantasy football fan, for a number of reasons. Football just doesn't quite do it for me like baseball does, number one. But more than that, the fantasy football format is a little weak. Head to head total points makes the game take a huge amount of luck, and the skill part doesn't involve much game theory or math (which I think some people like, but not me). I have found one application of math, though. And much of the credit should go to Bob Lung over at RotoJunkie who came up with the idea. I just came up with the proof. His theory is basically this: if you're going to win a head to head, 16 game schedule, you need to score an above average number of points for the whole year. Given that fact, you're better off with a consistentscoring team, than a team that scores a wildly fluctuating number of points. Bob calls it his "Consisten Games Theory." Go read his articles if you want applications of it. Or read on, if you want the proof... Take two teams, A and B. A's weekly average is Ma points and B's is Mb. A's standard deviation is Sa, while B's is Sb. We need to find the probability that a random point from distribution A is greater than a point in distribution B. One "easy" way to do this is to create a new distribution, AB. Mean of AB is the difference of the means = MaMb SD of AB is the square root of the sum of the variances = sqrt((Sa)^2+(Sb)^2) So, in the new distribution, A beats B if AB is greater than zero. We need to find the zscore for a random point in AB. The zscore is: (MaMb)/sqrt((Sa)^2+(Sb)^2) What does this mean? Well, assuming team A averages more points than team B, the zscore will be positive, yielding a win probability greater than .500. The greater the differences, the greater the zscore, which makes sense. But also notice that as Sa decrease, the denominator decreases, making the zscore larger. Thus, a lower standard deviation for team A (a team that we're assuming will already be over .500) will raise its expected winning percentage. High scoring teams are good. Consistently high scoring teams are better. How much better? I've done some preliminary research, and so far the results aren't very significant. So, for now, don't worry about it. But, Bob, your theory is sound.
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