Calculating expected point spread between two opponents based on past results

[Glen Hertz]

Hi,

Out of personal interest I wanted to come up with a better way to schedule match-ups between sports teams so that you play teams that are close to the same strength.  This should take into account the results of the games and the strength of a team's schedule.  It would be good if each team didn't have to play every other to determine their ranking as that would create a lot of blow-outs which wouldn't be fun. 

After a bit of research some people use a linear regression where rating_team1 - rating_team2 = expected_point_spread.   A paper written about it is here:

http://masseyratings.com/theory/massey97.pdf

The paper gives an example set of games:



The ratings can be calculated as X * r = y or r = X \ y:

# 1=Beast Squares, 2=Gaussian Eliminators, 3=Likelyhood Loggers, 4=Linear Aggressors:
julia> X = [1 -1 0 0; 0 0 1 -1; 0 -1 0 1; 1 0 0 -1; 0 1 -1 0]
5x4 Array{Int64,2}:
 1  -1   0   0
 0   0   1  -1
 0  -1   0   1
 1   0   0  -1
 0   1  -1   0

# Point spreads:
julia> y = [4, 0, 7, 2, 1]
5-element Array{Int64,1}:
 4
 0
 7
 2
 1

julia> X \ y
4-element Array{Float64,1}:
  2.375
 -2.5  
 -1.125
  1.25

(It is amazing what Julia can do in 1 line of code!)  So if 1 plays 2 the expected point spread is 4.875.   But when I use my own dataset and code posted in this gist:

https://gist.github.com/GlenHertz/6360352

I get:

julia> reload("calc_spreads.jl")

julia> standings_by_points
6x11 DataFrame:
        Team GP  W  L T PTS GF GA DIFF       PCT    Rating
[1,]     "F" 15  0 14 1   1 27 77  -50 0.0333333  -1.48166
[2,]     "E" 14  5  9 0  10 42 58  -16  0.357143  0.456697
[3,]     "D" 16  6  9 1  13 44 69  -25   0.40625 -0.239425
[4,]     "C" 15  9  5 1  19 52 34   18  0.633333  0.377248
[5,]     "B" 17 11  5 1  23 73 45   28  0.676471  0.309839
[6,]     "A" 17 14  3 0  28 85 40   45  0.823529    0.5773

The PTS are 2 points for a win, 1 for a tie, 0 for a loss.  GF and GA are goals for and against.  Diff = GF - GA.  PCT is winning percentage (ties count as half a win).

julia> standings_by_rating
6x12 DataFrame:
        Team GP  W  L T OT PTS GF GA DIFF       PCT    Rating
[1,]     "F" 15  0 14 1  0   1 27 77  -50 0.0333333  -1.48166
[2,]     "D" 16  6  9 1  0  13 44 69  -25   0.40625 -0.239425
[3,]     "B" 17 11  5 1  0  23 73 45   28  0.676471  0.309839
[4,]     "C" 15  9  5 1  0  19 52 34   18  0.633333  0.377248
[5,]     "E" 14  5  9 0  0  10 42 58  -16  0.357143  0.456697
[6,]     "A" 17 14  3 0  0  28 85 40   45  0.823529    0.5773

(On an aside, I feel a bit stupid that I couldn't figure out how to sort the dataframe in reverse order...the Julia way isn't followed and it wasn't obvious to me.  Is it planned to catch up to Julia?  I also found the API hard to pick up again after being away from DF for a while.  I was looking for "append!" instead of "rbind")

The ratings seem hard to believe.  For example, how can team E have a higher rating than team B?

Aside from explaining the odd results with the regression, what technique do people recommend for this?  It looks like the GLM package would be helpful and some researchers use a Bayes approach.  I'm not sure how to structure this so it is usable in the GLM package.  The true dataset is probably not going to be larger than 15 teams and 250 games.  Any recommendations for a model and the packages to use would be greatly appreciated! 

Thanks again!

Glen

[John Myles White]

Hi Glen,

I'll try to look through your code to find what's going wrong a little later, but for now I might suggest that you read Sean Taylor's slides on ranking methods: http://seanjtaylor.github.io/NFLRanking/web/slides/

If you were interested in implementing something that will perform really well, you might try to implement Sean's optimal ranking algorithm. Otherwise, using something like Bradley-Terry will probably work well.

 -- John

[Edmund Jackson]

Glen,

  A nice Bayesian approach to ranking is the Microsoft TrueSkill algorithm (http://en.wikipedia.org/wiki/TrueSkill).  Its benefits from have MATLAB code available from Kevin Murphy's terrific book at http://code.google.com/p/pmtk3/source/browse/trunk/demos/trueskillDemo.m?spec=svn2839&r=2839

 Edmund

[John Myles White]

Having TrueSkill implemented in Julia would be great. This thread makes me think that we might want to have a Ranking.jl package.

 -- John

[John Myles White]

I started a package with draft implementations of Elo and TrueSkill:

https://github.com/johnmyleswhite/Ranking.jl

 -- John

[Edmund Jackson]

I was going to volunteer to help out, and its done !  Have mercy :)

[John Myles White]

Well, it's really just started, so any contributions you have to make would be great. Making that code more rigorous (convergence, in-place computation) would be great.

 -- John