Estimating probability distributions

[Henry Harrison]

So far I've been taking a normality approach. Assume the projections you're using represent the mean. Estimate a variance from historical data. Estimate covariances by positions after. We're not interested in the variance/covariance of the projections, since we can reproduce that in the future, as we'll always have projections. So, I always subtract the projections from the actual results and work with those numbers.

Points for discussion:

• "Predictors" of variance--can we predict variance by position, by player, by performance? Does variance scale with the mean?
• "Predictors" of covariance--e.g., are some QB-WR pairs more highly correlated than others?
• Deviations from norrmality. Skew, other distributions?
  

If anyone knows rigorous techniques for estimating variance and covariance, I'm all ears. Error terms in a regression model perhaps? I'm so used to thinking about means that I'm not sure how to estimate variance, since you can't calculate variance from a single observation.

[Devin McCabe]

I've never calculated correlation/covariance between specific players, but I did recently calculate 2014 regular season correlations for Fanduel player positions. For instance, the correlation in fantasy points between a team's WR2 and their opponent's DST, or between an RB1 and a TE1 on the same team (where rank order within a position is determined by salary).

Here's a spreadsheet of the Fanduel points and the resulting correlation matrix in a list format.

[Henry Harrison]

I should have shared this earlier, I did the same thing.

Here are FanDuel fantasy-point correlations going back to 2009. Asterisks mark significance at the .05 level, Bonferroni corrected:

And these ones are correlations in FanDuel fantasy-point deviation from FantasyPros projections. I.e. what is the correlation beyond the correlation that we already have access to in projections. The dataset is much more limited, only this season. This is same team only, as across team takes twice as much data.

I have a bit more data now, I'll regenerate that last one when I have a chance.