# Best Way to Calculate “Luck” as a Fantasy Football Statistic

I have an array of point differences from each matchup over 13 weeks from fantasy football. I would like to know how "lucky" or "unlucky" a player was over the course of 13 weeks using how close their win or loss was per week(how close their point difference was to zero). Any insights on the best way to do this? Right now I'm using the absolute average difference from zero, but that feels a bit clunky.

More elaboration: I've inserted some data from our competition with the difference in score. The rows are the players and the columns are the week. FF Week 1-10 point difference

The idea is that a win only a few points over zero should increase the luck score, and a loss with a few points below zero. Now I'm thinking I can take the average point difference of a win and a loss and use that as some sort of baseline.

An alternative idea I actually have now is to compare weekly scores and see how many players he or she would have beaten, and a win when that person would have beaten less than half of the other players should increase the luck score. Either way, any insight on both of these would be great!

• I'd be more understandable if you were to conclude an example and what you wanted to calculate. – Bobson Dugnutt Feb 21 '16 at 22:26
• My first thought would be to use a standard normal distribution, and then vary the sigma to see how much it affects the ranking of the results (if it affects them a lot, you'll have to find a sigma that best reflects your estimation of "luck"). – barrycarter Feb 21 '16 at 23:50
• @Lovsovs I've added more information – L. Chu Feb 23 '16 at 0:55
• Would you be able to elaborate on that @barrycarter ? – L. Chu Feb 23 '16 at 0:55

This only provides an example, not a methodology, but is too long for a comment.

As a note, you're defining 'luck' the opposite way most people define it.

If someone scores well above the average, we normally say they are "lucky".

In your case, you are saying they must be skillful (not lucky) to score that high.

Let sigma be the standard deviation of everyone's scores (for whatever scoreset you're looking at), and compute everyone's deviations above/below the mean (if the mean should always be 0, use the square of the scoreset).

Suppose Bob scores 0.25 deviations above the mean. The probability of scoring 0.25+ deviations above the mean is about 40.13%

Suppose Alice scores 3 deviations above the mean. That probability is 0.135%.

So, you could assign Bob a "luck score" of 40.13 and Alice a luck score of 0.135. Bob is much more lucky because there's a 40% chance he would've won at random, whereas Alice is more skillful since there's only a 0.135% chance she would have won at random.

• I see what you mean. It is a fault of syntax though; you are right about luck being usually so (in this case I meant luck as beating a player despite scoring low, or losing despite scoring high, i.e. matchup dependent) However, what you mentioned is also something I would like to pursue. I'd like to pose a follow-up question: Can we make this matchup dependent? I.e. if Bob scores high and plays against someone who scores low, or if Bob score highs and plays against someone who scores high --- can we make a statistic out of that? – L. Chu Feb 25 '16 at 20:18