Moving players into teams - equal as possible random

hello all , i am a beginner at matlab , i have 33 players in my league , every player has an avg score ,

players_AVG=[166.29,156.57,155.72,171.29,156.76,155.67,168.36,161.77,155.65,173.92,162.06,149.21,177.44,161.79,148.64,177.25,162.15,146.02,175.28,162.72,142.59,174.21,164.88,141.91,180.69,168.75,127.06,184.18,165.39,133.26,191.41,185.23,90];

i want to insert the 33 players into 11 teams of 3 players each , i want the team_AVG to be as equal as possible . example output:

TEAM1=[player1(166.29),player5(156.57),player7(155.72)] --> TEAM1_AVG=159.53

TEAM2=[player2(171.29),player3(156.76),player4(155.67)] --> TEAM2_AVG=161.24

etc...

At the end of the year we want to reshuffle the teams.

i dont know where to start , how can i achieve this ??

thanks lampel.

Answer 1

[Walter Roberson]

Repeat several times: randperm(33), group by 3, use that to index averages, sum by team, std(), if lower than any found so far then remember the permutation

[eyal lampel]

wow thanks walter!

such an easy / elegant solution !

if someone is interested this is how i implemented it :

players_AVG=[166.29,156.57,155.72,171.29,156.76,155.67,168.36,161.77,155.65,173.92,162.06,149.21,177.44,161.79,148.64,177.25,162.15,146.02,175.28,162.72,142.59,174.21,164.88,141.91,180.69,168.75,127.06,184.18,165.39,133.26,191.41,185.23,90];
teams_avg=ones(1,11)*9;
teams_player_candidate=ones(11,3)*9;
a=ones(1,10000)*9;
bestCombination=9;
index=1;
for i=1:5000

    rand_position=randperm(33);  
      for j=0:10
          index=index+1;
          teams_avg(j+1)=(players_AVG(rand_position(1+3*j))+players_AVG(rand_position(2+3*j))+players_AVG(rand_position(3+3*j)))/3;
          teams_player_candidate(j+1,1)=players_AVG(rand_position(1+3*j));
          teams_player_candidate(j+1,2)=players_AVG(rand_position(2+3*j));
          teams_player_candidate(j+1,3)=players_AVG(rand_position(3+3*j));
      end

      if bestCombination>std(teams_avg)
      bestCombination=std(teams_avg);
      optimalteams=teams_player_candidate;
      optimal_teams_avg=teams_avg;
      end

end

optimal_teams_avg

This is a great community thanks all.

[Walter Roberson]

You can simplify a lot:

idx = reshape(randperm(33), 11, 3);
this_std = std(sum(players_AVG(idx), 2));
if this_std < bestCombination
  bestCombination = this_std;
  optimalteams = idx;
end

[eyal lampel]

Even better :)

THANKS!

randperm is a very powerful function , its nice to know it.

Answer 2

[John D'Errico]

There are lots of similar problems out there that can be formulated as an integer programming problem of some sort. In this case though, I'd be lazy, and just use a greedy method.

Start out with a random permutation of the integers 1:33. Then reshape those integers into an 11x3 array. So each row of the array indicates one team.

You know the overall sum of the players. So

target_average = mean(scores);

is the target average for each team.

Choose a tolerance, for how close to the goal you need to get all teams. Now pick one player from a team that is under the target average, and swap them for a player from a team with a average above the target average. Repeat this process until you can do no better, or you are within the goal tolerance for all teams.

Answer 3

[Cory Johnson]

What a great question!

Try matching the highest and lowest scores, then filling in the middle with the average score that would round out the team the best. This technique would work well for teams of two, but teams of three get more complex.

• Sort the player average scores
• Assign team(n).players, one from the high end, and one from the low end for as many teams as desired
• Sort the created teams based on the sum of player scores
• Add the third player using the same method, adding the lowest scoring player to the highest summing team

As an example:

scores 1 3 4 5 6 7

would go into two teams as follows:

1-7, 3-6

the sum of these teams:

8, 9

Add the remaining scores to balance the teams based on these sums:

(8)-5, (9)-4

So the final teams would be:

1-7-5, 3-6-4

Both teams have a total score of 13!

Hope that helps!

[eyal lampel]

Thanks Cory ,

If it helps its a bowling game (highest score=300, lowest=0).

i am trying to implement your algorithm , i am stuck at the:

"Add the remaining scores to balance the teams based on these sums:"

here's what i've got so far:

players_AVG=[166.29,156.57,155.72,171.29,156.76,155.67,168.36,161.77,155.65,173.92,162.06,149.21,177.44,161.79,148.64,177.25,162.15,146.02,175.28,162.72,142.59,174.21,164.88,141.91,180.69,168.75,127.06,184.18,165.39,133.26,191.41,185.23,90];
players_AVG_sorted=sort(players_AVG);
Two_Player_sum=0;
for i=1:17
Two_Player_sum=[Two_Player_sum,players_AVG_sorted(34-i)+players_AVG_sorted(i)];
end

Two_Player_sum=Two_Player_sum(2:end)

i am not sure how to manipulate the Two_Player_sum ??

thanks lampel

[Cory Johnson]

It is not as elegant as the solution above, but here is an attempt:

players_AVG=[166.29,156.57,155.72,171.29,156.76,155.67,168.36,161.77,155.65,173.92,162.06,149.21,177.44,161.79,148.64,177.25,162.15,146.02,175.28,162.72,142.59,174.21,164.88,141.91,180.69,168.75,127.06,184.18,165.39,133.26,191.41,185.23,90];
players_AVG_sorted=sort(players_AVG);

% divide into sections, high, med, and low
set1 = players_AVG_sorted(1:11);
set2 = players_AVG_sorted(12:22);
set3 = players_AVG_sorted(23:33);

% match high values to low values. Teams are by column
teams = [set1; flip(set3)];
% sort by the sum of each team, get index value
[~,b] = sort(sum(teams));
% Use index value to sort remaining set, make sure to flip so high/low are
% matched
set3_sort = flip(set3(b));
% add sorted set to teams
teams = [teams;set3_sort];
% Verify results

The numbers I get with this method are as follows:

465.5900 497.5200 508.8500 500.0400 500.7200 500.5200 498.1300 498.7000 503.4900 498.2500 493.2200

Not bad!