topic Re: Program an Elo rating for sports teams in Mathematical Optimization, Discrete-Event Simulation, and OR

Program an Elo rating for sports teams

cxkev182 — Thu, 15 Jan 2015 19:42:34 GMT

Hi,

I would like to program an "Elo" rating in SAS to rate sports teams. The Elo rating was originally developed to rate chess players. I would like this one to work as follows:

Each team starts off with an initial rating of 1,000 points.
For each match, each team contributes 5% of their current rating to the "Pot"
The winning team collects the pot and that amount is added to the it's new (post match) rating
The losing team does not take anything from the pot and their rating will decrease by how much they contributed
If there is a tie, the pot will be split equally between to the two teams.

Example

Lets say we have 3 teams, Team A, B and C
First match is A v B. Each team's initial rating is 1,000 and they contribute 5% of that (50 points) each to the pot
Team A wins and collects the pot. Their new rating is 1,050. Team B lose so take nothing, just lose the 50 points they contributed so their new rating is 950.
Next match is B v C. B's pre match rating is 950 and they contribute 5% of that to the pot (48). It's team C's first match so their pre match rating is 1,000 and they contribute 5% (50) to the pot.
Team B win and collect the pot so their new rating is 1,048. Team C lose so their rating decreases by the 50 they contributed. Their post match rating is 950.
So at this point the team rating would read as follows:

Team A 1,050

Team B 1,048

Team C 950

See below the variables in my dataset (along with first few lines of sample data)

Date Team 1 Team 2 Winner

01jan2014 Team A Team B Team A

05jan2014 Team B Team C Team B

Thanks

cxkev182

Re: Program an Elo rating for sports teams

Ksharp — Fri, 16 Jan 2015 09:24:42 GMT

I don't understand.

"The first match is A v B. Both of their pre match rating is 1,000 so they each contribute 5% of their rating to the pot (50 points each.)

Team A wins so their rating increases to 1,050. Team B loses so their rating decreases to 950."

TeamA would be 1,050( take 50 from TeamB). TeamB would be 950(lost 50).

"The next match is B v C. B's current rating is 950 and they contribute 5% of that (48 points) to the point. This is C's first match so their rating is 1,000. They contribute 5% (50 points) to the pot."

TeamB would be 950+50(take 50 from TeamC) ?? TeamC would be 950(lost 50). ??

Why TeamB would be Team B 950+50+48= 1,048 ? That is right ?

Assuming the first scenario is right .

data have;

input Date : date9. ( Team1 Team2 Winner ) (& $);

format date date9.;

cards;

01jan2014 Team A Team B Team A

05jan2014 Team B Team C Team B

;

run;

data _null_;

if _n_ eq 1 then do;

length team $ 80;

declare hash h();

h.definekey('team');

h.definedata('team','score');

h.definedone();

end;

set have end=last;

retain score 1000;

team=team1;h.replace();

team=team2;h.replace();

if last then h.output(dataset:'team');

run;

data _null_;

if _n_ eq 1 then do;

if 0 then set team;

declare hash h(dataset:'team');

h.definekey('team');

h.definedata('team','score');

h.definedone();

end;

set have end=last;

if winner=team1 then do;

h.find(key:team2);get=score*0.05;score=score-get; h.replace();

h.find(key:team1);score=score+get;h.replace();

end;

else if winner=team2 then do;

h.find(key:team1);get=score*0.05;score=score-get; h.replace();

h.find(key:team2);score=score+get;h.replace();

end;

if last then h.output(dataset:'want');

run;

Xia Keshan

Re: Program an Elo rating for sports teams

CTorres — Fri, 16 Jan 2015 21:01:47 GMT

I developed other solution and I got the same result gotten by Xia-Keshan:

It can be easily generalized includying more teams in the Array and updating the do's. I assume a null value of winner when the result is a draw:

data games;

infile cards truncover;

input date date9. team1 $ team2 $ winner $ ;

format date date9.;

cards;

01jan2014 Team_A Team_B Team_A

05jan2014 Team_B Team_C Team_B

06jan2014 Team_C Team_A

;

run;

data winn_loss(drop=team:);

set games;

if winner = ' ' then do;

winner=team1;

losser=team1;

end;

else if winner = team1 then do;

losser=team2;

end;

else do;

winner=team2;

losser=team1;

end;

run;

data want(drop=i: pot:);

set winn_loss;

array team[3] Team_A Team_B Team_C (3*1000);

i_winn=0;

i_loss=0;

do i=1 to 3 while (i_winn=0);

if vinarrayx(winner) and vname(team)=winner then i_winn=i;

end;

do i=1 to 3 while (i_loss=0);

if vinarrayx(losser) and vname(team)=losser then i_loss=i;

end;

pot_win=round(team[i_winn]*0.05);

pot_los=round(team[i_loss]*0.05);

team[i_winn]=team[i_winn]+pot_los;

team[i_loss]=team[i_loss]-pot_los;

run;

CTorres

Re: Program an Elo rating for sports teams

cxkev182 — Sat, 17 Jan 2015 09:54:09 GMT

That's great thanks for your help and apologies for my typo in the original question. I wish I could mark both as correct answer.