Thread: Fantasy Sports Algorithm

Hi,

I was wondering if forum members could help me with this:

I’ve been writing a computer program for fun for Yahoo! fantasy hockey this year. It will read in the player’s stats from a file and give each player a rating out of 10 (like 7.8/10) for each of: Goals, Assists, Plus Minus Rating, Penality Minutes, Power Play Points, and Shots on Goal (all 6 stat categories have equal weight). It would then total up the ranks into an Overall Rank category, and print out the player names, from highest to lowest, perfect for draft day.

As I have it programmed now, the ranking algorithm is based on percentile (eg. top Goal Scorer gets 10 rating, median gets a 5, and bottom gets 0). This seems to be OK at first, but now in hindsight, I think it’s wrong:

Say for example, the sample size was 4, and players one through four had a Goals total of 11,11,11,12 respectively. In this case, the player with 12 goals would get a rating of 10. To me this seems too much, and I think in terms of the player rankings, this category should almost be a tie, with everyone getting the same rating (say around 5 or something), with the overall player ranking being left to the other 5 categories instead. I hope I’ve explained myself well...

So my question(s) is/are: What topic in math/stats should I read up on? What subject am I talking about? Do you see any problems with my formula?

Thanks in advance,
Wesley

There is not really a specific branch of stats I can think of but I have a suggestion.

Rank = Individual Score / Average Score * Middle Rank

Using your example:

Average(mean) = 11.25
If score is 11 then give a rank of 11/11.25 * 5 = 5 (to 1 significant figure)
If score is 11 then give a rank of 12/11.25 * 5 = 5 (to 1 significant figure)

If for example the score of 12 was instead 14 you would get a rank of 6.

The only problem is if one of the scores is very high you could get a rank of greater than 10. But perhaps in this case you could just impose a maximum of 10.

Well, I'm open to being flexable with the ranking method, just as long as it gives me a good ranking where I would be able to compare forwards and goalies together.
ESPN has the following player ratings:
ESPN Fantasy Hockey: FHL 2007 Playerrater

Player Rater Explained: In each of the scoring categories, a number is calculated that represents the average stat total in that category. If a player has that average exactly, his rating for that category is 0.00. The numbers then represent how much a player is above or below that average. If the rating is positive, then that player is an above average fantasy player in that category. If it is negative, the player is below average in that category. All ratings are then added together to get a grand total player rating, and they are ranked accordingly.

I guess the part that confuses me is the

The numbers then represent how much a player is above or below that average.

part. This doesn't seem to be 1 to 1. For example if the average goals was 10, then a player with 50 would be +40, but this isn't the case... can anyone guess as to what sort of scaling or whatever you'd call it?

They may be standardising the scores. To do this they would do the following:

(Individual score - mean average score) / standard deviation of scores

As a further point this statistic could be used to calculate the corresponding percentile for example assuming a normal distribution - e.g. use the normsdist function in excel.