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Formula for social purposes needed :D


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Hi guys



First up I'm useless at "complex" mathematical formulae and so would greatly appreciate some help


Secondly this is a totally low brow request for help based upon goofing around so apologies if this is a bit informal.


Right-Me and my housemates have FIFA soccer on Xbox...recently we began debating who is the best player and so I decided to start an excel spread sheet to take down some stats and hopefully work it out, working out win percentages and basic stuff like that is no problem, however let me describe the 2 aspects that are problematic


1) We all play regularly but some people more, some people less so we can't just do a basic league where we all play the same number of games and settle it with points. So for all individuals the number of games played will differ. This scoring system will probably extend for a few months so the differences could be vast



2) We always play with random teams which have star ratings and would like our scoring system to reflect more favourably to those who beat say Real Madrid (5 stars) with Bohemians of the Irish league (1 star)



3) We take drawn games to penalties-once again for a one star team who has taken a 5 star all the way to penalties only to lose we would also like this reflected




So any advice re a forumla I can enter into Excel that will take the overall win percentage of an player coupled with the average rating of his team and give some sort of value that will enable us to say "a ha! Well You might have won a few more but I had a lot of rubbish teams where I won and its reflected right here in this number!!"




Thanks guys


Just in case a little bit of data is needed to illustrate what we're working with here is what we have so far (we only started today you see)




1) 1 (star) vs 5 (star) 2-3


2) 4 vs 4.5 0-1


3) 4 vs 3.5 1-0


4) 4.5 vs 1.5 2-1 (after extra time)


5) 1.5 vs 1 2-1

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If you really wanted you could read up on something like the Elo Rating System, and try and modify this for your use. Another option that is similar to how some high school sports teams are ranked would be that if [latex]x[/latex] and [latex]y[/latex] are players then the players ranking would satisfy:


Where [latex]R_{x}, R_{y}[/latex] are the ratings of their respective teams, and [latex]S_{x}, S_{y}[/latex] are their respective scores. You want to write a program that iteratively finds the players rankings to minimize the error in the above equation for the entire league. This method can be modified to include whether a person beats a really strong player and so on, but again it might be a bit complicated for what you want.


Not sure how it would work, but one simple formula that might give a rough idea of rating would be:


Where [latex]W_{x}[/latex] is the winning perectange of player [latex]x[/latex], [latex]\overline{R_{op}}[/latex] is the average team rating for all of [latex]x[/latex]'s opponents, and [latex]\overline{R_{x}}[/latex] is the average team rating of [latex]x[/latex]. As I said I have no idea if this will give anything resembling decent rankings, but it should be easy to implement in Excel, is normalized, and should at least in theory reward the right things i.e.: the more you win against good teams with bad teams the higher your rating should be.

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Two thoughts.


1) the 'Pythagorean theory' of sports scores is actually fairly amazingly accurate considering that the properties of a right triangle don't have much to do with sports. The Pythagorean theory of sports is:

[math]\frac{\text{points scored by team}^2}{\text{points scored by team}^2 + \text{points scored by opposing team}^2} = \text{projected win percentage}[/math]


That is, if a baseball team has scored 50 runs and allowed 35 to score, this formula predicts that the team should have a 50^2/(50^2+35^2) = 2500/3725 = 0.671141 winning percentage, or in other words, the team should have won about 2/3 of their games. It is a nice measure of how lucky or unlucky a team has been. I.e. if that above team had only won half of its games, it says that it has been very unlucky because it should have won 2/3.


So, an easy way to rank the players of the games are those who have the best W-L percentage AND those whose W-L is above the predicted Pythagorean.


It really is an impressive formula, that seems to work pretty well in most any sport. It is rarely off by more than 10% at the end of the season for every team in most professional sports leagues.


2) Now, if you guys are truly playing random teams, the above should be enough, especially the more games you play. But, in a small sample size, someone could just be unlucky and have gotten rotten teams more often than pure randomness would say. In this case, I would modify the above formula by an inverse weighting of how many stars on the team.


That is, every goal for a 5 star team counts as a single goal. Every goal by a 1 star team counts as 5 goals. And use this weighted goals in the above formula. You may want to tweak the weights some, depending on the relative strengths of the teams. That is, while a 5 star team is clearly superior, is it really 5 times better than a 1 star team? Tough to say. But, in this case, the player with the highest Pythagorean ratio is probably the most skilled. That is, the skill it takes playing a 1 star team to score a goal on a 5 star team helps bump the percentage up a lot more than playing a 5 star team versus a 1 star team.


Again, if you think that you'll be playing a fairly large number of games (I'd say 50+), I wouldn't use the weights, simply because it should all average out after a large number of games. But, if you want to include smaller numbers, that is people who don't play very often, the weighting will help make those stats comparable.

Edited by Bignose
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  • 3 weeks later...

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