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We play football/soccer between our group of friends, but often some of them can't play, so the teams vary every week. My teammate this week can be my opponent next week.

We're starting a sort of championship, trying to rank players individuadilly, and we want a system that makes it so that the actual best players are expected to end at the top. Something simple would be to just award 3 points to a player for a win, 1 point for a draw and 0 points to a loss. While this would work if teams were choosen randomly, we also would like to keep the games balanced, and random teams aren't good to fulfill that requirement.

To choose each week's team in a balanced manner, two opposite players take turns picking the best next player that is not yet picked. But this makes a system like the above a bit weird, in the sense that the best players aren't more likely to make more points than the worst. Probabilly this system now favors the most underrated player, which is interesting but not quite what we're looking for.

Is there any combination of scoring system/picking strategy that would allow us to keep games balanced, yet making it so that the score table will represent absolute individual skill in the end (disregarding luck, for simplicity)?

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You could start with random teams (or any team composition you would consider fair) and start keeping track of points by simply awarding 3 points for a victory and 1 for a draw.

Then, from next match on, you create teams whose combined total score are equal. That way, you slowly create a ranking by which the better players have better scores.

Example

Match 1: ABCD* - EFGH 
Match 2: ABEF* - CDGH
Match 3: ACEG* - BDFH

Asterix (*) indicates winning team

Standings:

A        - 9 points
B, C, E  - 6 points
D, F, G  - 3 points
H        - 0 points

Next match could be: ADFG - BCEH.

Refinements

Of course, this is very simple and requires every player to be present every time. However, some adjustments can be made to create a more flexible statistic.

  • Divide a player's score over the number of participations (or maximum points or so).
  • Use goaldifference (or percentage of goals) instead of the 3-1-0 point system. That way, a very big victory shifts the ranking more than a narrow one. This way, you will get the ranking to adapt faster to the "real world values".
  • 1
    You can still use goal average AND the point system, which is useful to tell which player is decisive in complicated games too and has the thing to make his team win. For example and as we say in France, better are seven 1-0 wins than one 7-0 win ;) (and better is one 0-7 loss than seven 1-0 losses !) – LeReferee May 27 '15 at 15:09
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Well, it completely depends on what the purpose of your ranking system is. Building evenly competitive teams, or simply providing a list of the best players for personal satisfaction.

Case 1: Optimally Balancing Teams

It is worth noting that a good team isn't necessarily the team of the most skilled players but rather the most balanced team offensively and defensively. Your question reads like you play more of a small-sided game or park football, which is more suited to unstructured play with utility-style (no fixed position) players but even so a well structured team would comfortably beat a park team.

I have coached low-grade football for many years, and an important skill is dividing the playing squad into fair teams at training to maximise the benefit of drills and scratch matches. There is no way to do this mathematically; you have to observe your players and note their individual strengths and weaknesses, try them in different roles and mess with the formula until you get it right. Players aren't robots, they will perform differently on different days- the right squad on a Tuesday may be completely off on a Thursday.

For the purposes of your situation, my recommendation would be to assign two people (possibly including yourself, or whoever the group feel is the most knowledgeable, reliable and balanced) to have the responsibility of picking the teams. These people should then confer after matches about who was good and where, who was out of their depth and where, and use this to create a "fuzzy" ranking system (ideally, impart some structure and rate players defensively, offensively, or even in finer detail such as passing, tackling, dribbling etc). This can then be used to pick the next two teams, ensuring an even balance of playing style and ability. The two who pick the teams then are separated into a team each (for further impartiality, one is nominated to flip a coin - heads they are team one, tails team two).

Case 2: Individual Ranking For Personal Glory

OK, cautionary warning here, nobody likes being told they are the worst (or amongst the worst) at something. Especially when they are with friends. Letting team-mates down is bad enough, letting friends down is even worse. Having a public leader-board of player rankings may encourage middle and upper level players to push higher, but you do so at the risk that you will lose your players propping up the table. You've already said you have trouble with consistent attendance week-to-week, implicitly shaming players could very well make that worse.

If you are ranking players purely to find the best, as some sort of reward mechanism, many clubs run a voting system amongst players to determine this for end of year awards. Have your players submit 3-2-1 votes (3pts = best, 2pts = second best, 1pt = third best) for their team-mates for the match, average them over the number of players (this prevents a player from having a blinder that puts them way in front, but being mediocre afterwards and still winning it) then tally them up in a private leader-board. Publicly make available the top subset of this list if your players want it (say top 5) so Fred can say "I'm fourth, I'm going to try even harder and get ahead of Bob in third", whilst sparing the less skilled players from the public humiliation of being last. Having the players do it for their own team means that good players in a losing team are still acknowledged.

Important Side Note

It is for a similar reason to the above private leader-board that I would stop using the "captains pick" team selection method. You are telling the last people picked that they aren't wanted, which is awful for morale, enjoying the game, and will only lead to worse performance. Good examples of fair team selection include:

  • Line up players by height, or
  • Line up players by age/date of birth, or
  • Line up players alphabetically by first/last name, and then go along the line labelling them alternately "team 1" or "team 2"

Pick characteristics that are completely not skill related. If one method unbalances the sides, choose another the next week. At no point is anyone being given the impression that they are the last choice, or only being picked because the team needs another player.

If you get a good combination going, try to stick with it. It is always better to have a group that plays together every week with minimal changes to the team. If a team is missing a player, ask for a volunteer to go across from the other team rather than dictating. Should no-one volunteer, draw straws or equivalent. Keep it as random as possible.

  • When we ranked players, we formed a committee of former players, coaches, and refs, people everyone trusted to do it fairly. They explained what would be important in the ranking, but the end result was secret. Each player was put into one of four buckets: Awesome to Working-on-it. Teams were created by randomly selecting players from the buckets. Nobody had to be told you are the most rubbish player or even you are in the "Working-on-it" bucket. – Val May 28 '15 at 14:20
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Okay, if you are asking this question, then you probably haven't heard of Jogabo. It lets you track number of goals and many more for pickup matches, it also allows you to see pickup games around you. This tracks performance and statistics. The best app out there, my friends and I use it and it is world wide, anywhere you find yourself, you might find people around you.

Once you are tracking your goals and performance with Jogabo, you are halfway done with the job. You can use the statistics to separate your team to balance things out.

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It seems that rankade, our ranking system for sports, games, and more, fits your needs.

It's free to use and it's designed to manage rankings (and stats, including matchup stats, and more) for small or large groups of players. It can manage any kind of match: one-on-one, faction vs. faction (two teams, which may be asymmetrical), and more.

Here are some examples for soccer and foosball (and table tennis, and more) public group. We have many groups that use ranking to build teams (and/or brackets) for next match/tournament.

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The best thing would be planning the teams in a way that everyone plays with every other player in the end, or you can draw lots for the teams, while keeping your scoring system, and this would bring equity (and not equality, which is an important distinction) to the rankings.

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Record an individual score for each player as $(f,a)$ where $f$ is the number of goals scored by that player's team when that player was actively playing, and $a$ similarly the goals against their team. This means a sub, or someone who left early or arrived late or left the field or switched teams partway through, doesn't get credit for a goal scored by their team if they couldn't possibly have contributed to the goalscoring situation, and similarly don't get marked against if they couldn't have done anything to prevent the goal. You could add a third component $p$, which is how many goals a player personally scores, if there are individuals who often get the decisive strike or final touch. Having established this system, future teams are picked such that the 2-norm of differences of sums is minimised. For example, a team has $(F,A)=(17,10)$ and their opponents have $(14,8)$. The differences are 3 and 2; the squares are 9 and 4; the sum is 13; the 2-norm is therefore $√13=3.6$. If there is no way to trade exactly one player from each team and lower that value, then this is the "fairest" way to pick two teams from that group of players. If you have a $p$-score as well, the difference between $P$-scores must be as small as possible (this balances the amazing strikers separately from picking teams). This is a simple system to score for: either they were on the field or they weren't, and either their team scored or was scored against, each time a goal happens. It gives some measure of attacking and defending ability, especially after several games or when several players are added together. It can be modified for creating three fair teams from a group of players (this requires more math than needed here). It can even be applied after every single goal, especially if a computer spreadsheets is being used to record scores and calculate teams. If you don't like the 2-norm team calculation, the $(p,f,a)$ system gives you something to start with, anyway.

  • Further, if you also track attendance by $g$ (games played), you can adjust these scores by a factor of the maximum g divided by their own g. Say Joe plays 5 games with 6 goals and Owen plays 2 with 3, then Owen adjusts to $3×5/2=3×2.5=7.5$ for the next calculation. – Nij May 31 '16 at 21:44

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