04a – Mathematics

Welcome, brave adventurers, into the world of statistics. This is going to be a semi mathematical text about my computer ratings system.

Why computer ratings? Because people go about having ‘opinions’ and other such things that cloud their judgement when asked questions like “Who’s better – Diamonds or Bulls?”, rather than just look at the numbers. I actually use four different systems and combine the results, actually only one of them is truly mine, the rest are all ‘borrowed’ from better mathematicians and thinkers than I am. So now I’m going to describe all four systems.

10+

I stumbled across this system while reading a writers college football power rankings – he mentioned it while justifying his ranking of Boise State at #1 (at the time). At any rate this is a simple one.

Each team gets 10 points for a win, plus 1 point for each time any of their previous opponents win, plus 0.1 points for every point they have outscored their opponents by over the course of the season. Still with me? Then you divide by the number of games played and voila, there’s your rating.

Conserve

This one is almost exactly the same as the one used by the International Rugby Board to rate their teams. I used this last year on the BFL forum.

All teams start with 5000 points. Every game, each team puts some of their points ‘on the line’, equal to   :  100-(opponent points-team points)/10. The winner of the game takes all points and the rankings are adjusted accordingly. From the formula, you can see that higher ranked teams have to put in more than lower ranked teams. Teams also get a 50% bonus for winning by 17 or more points (you may ask how I came up with 17 as the bonus threshold – that’s the point at which you must score more than 2 times to make a comeback, ie, coaches don’t have to worry at the end of the game).

TrueSkill

X-Box gamers amongst you might recognise that name. It’s the system that Microsoft use to rank their gamers online. This is a really complicated one and uses lots of fancy techincal words like ‘variance’ and ‘standard deviation’ and I’d love to explain it all but the truth is I don’t have the time, space, or mathematical knowledge to do so. The short version is it’s actually similar to the Conserve system in that as one team goes up in points, the other must go down. TrueSkill does not care by how many points a team won, only that they won.

OriginalX

Short for ‘Original – eXtended’, this one is my baby. For every team against every opponent it does  :  (ave points scored – ave opponent points conceeded) – (ave points conceeded – ave opponent points scored). Adding all those scores gives the final value which will be positive for good teams and negative for weaker teams.

3000

Once all that’s done, all four ratings systems are standardised so that the top ranked team in each system scores 750, therefore the maximum score is 3000, hence the name. Why 3000? Well, it’s made up but it tends to give logical answers when I do this : (team 3000points)² / (team 3000points)²+(opponent 3000points)². Why would I want to do that? It gives a probability of winning the game. Well, that’s my story and I’m sticking to it!

Conclusion

No, actually I use the system on Australian Football and it does pretty well. It may turn out not to be so useful with the FFL because the season is very short (or more likely because my logic is faulty). At any rate, once each team has played at least one game, I’ll be including a section called “Man vs Machine” in which I will take on the computer in “guessing” which team is going to win each game.

I hope at least a couple of people made it to the end without giving up! Thanks for reading

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