I'm a programmer who also loves playing fantasy football (FF). I want to create a formula for calculating a managers "luck" level over the season. Unfortunately, math is not my strong suit so I'm reaching out here hoping there are some fellow FF enthusiasts who can help out.
I have some ideas for features that can be used in this formula:
1.) Points Against (PA)
This is the simplest feature and only considers the total points scored against you over the season. A high PA is unlucky (the teams you faced each week scored high) and a low PA is lucky.
But this feature alone doesn't capture the essence of "luck." It doesn't matter if teams are constantly scoring high against you if your team is consistently scoring low. You're less unlucky and more just...bad. Enter:
2.) Average Point Differential (APD)
This feature looks at the season long average of your team's point differentials. If your APD is slightly negative (you have on average barely lost each matchup) then you have been super unlucky and if your ADP is slightly positive, then you have been very lucky. Intuitively, a team with high PA and slightly negative APD is much more unlucky than a team with low PA and slightly negative APD because in the first case your team was consistently facing some of the highest weekly scorers and barely losing.
2.5) Modified Average Point Differential (mAPD)
I think there are probably ways of modifying the APD so that it captures additional nuances. For example, you could weigh each matchup by your opponents performance relative to their average performance. For example, if your opponent usually doesn't score many points but scored a ton against you, then that weeks differential is more impactful than a differential where your opponent scored near their expected value.
Maybe there are ways to integrate variance/standard deviation of your scores or your opponents scores. The intuition here being that losing to a less consistent team is more unlucky than losing to a more consistent team.
3.) Ideal Lineup Score (ILS)
This is a fun one. The idea here is that you consider how lucky you have been based on how many lineup permutations of you and your opponent would have won or lost you the week. For example, if you faced the single lineup permutation that your team could have won against (because many players on the opponents bench performed better than their starters), then you are extremely lucky.
Anyways, I'm thinking the final formula would be something simple like:
$$L = a*PA + b*mAPD + c*ILS$$
where a,b,c are coefficients for each feature that modify the contribution of that feature.
Are there better or more sophisticated ways of calculating this "luck" statistic? Are there perhaps other features and aspects of "luck" that I've overlooked or am not capturing?