# Can variance change over time?

I'm working on a toy project that involves fantasy basketball, I know this is the quantitative finance stackexchange, but it seemed like the best place to ask this question.

My goal is to make predictions about fantasy points totals for different NBA players in upcoming games. I'm considering fantasy_points_total a continuous random variable and my goal is to predict both a) an expected mean E(mean) and expected variance E(Var). I then want to use those predicted mean and variance to model and sample a normal distribution N(mean, var) in a monte carlo simulation.

I'm using a gradient boosted random forest to predict E(mean) and I'm satisfied with it's accuracy. I'm running into problems predicting E(Var).

It seems like for a normal random variable with no changes over time one could expect that variance is constant and a decent way to calculate E(Var) would be to look at all past data, calculate it's variance and use that past variance as E(Var).

Is it possible to get a more accurate forecast of E(Var) when variance might change due to other factors? For example in my case, home vs. away, injuries and opponent quality could all effect the variance of a players fantasy points expectations.

• How far down the rabbit hole do you want to go? You could consider the fixtures each player has coming up, you could consider the teammates they have (and how they've changed over the years), you could consider how other players have improved/deteriorated with age, etc. There are many extras you could include in your model, it just depends what you want to do with it. – will Sep 26 '19 at 13:35
• You can think about the Trueskill algorithm from Microsoft which could be useful in your case, with a stochastic variance – DomingoBrown Sep 26 '19 at 13:58
• @will Thanks for the comment-- How far down the rabbit hole do I want to go? How about far enough to give fairly accurate results leaving room to improve on my methods later if I have time :) I understand how different 'extras' could improve prediction of the mean and I include a lot of those things in my model. I'm wondering mostly about the variance though. Is it reasonable to think that my E(Var) changes from game to game? Is there a better way to estimate variance than just looking at historical variations in the response variable? thanks! – George Sep 26 '19 at 14:11
• @DomingoBrown Thanks for the recommendation, I'll check out Trueskill and stochastic variance – George Sep 26 '19 at 14:12
• I'm voting to close this question as off-topic because it belongs on Cross Validated. (Unfortunately, there is no direct migration path to choose as an option.) – Richard Hardy Oct 20 '19 at 10:08