We are now ready to implement a points based ratings system! This will enable you to gauge how well you are playing compared to others and should prove to be more accurate than averages (which we will still be running) as the rating points will be carried on to each season. Basically, each player has a certain amount of rating points and after each fixture you will either gain or lose points based on how well you play against your opponents. If you beat a player with a high rating, you will gain more points than beating a player with a low rating and conversely you will lose fewer points if you lose to a player with a high rating as opposed to a lower rating.
There are quite a few variables to the system and therefore the rest of the current season will be used to test the variables and adjustments may be necessary before next season. I am basing everyone's initial rating on their averages at the end of 2008 so that players in the Premier Division have ratings ranging from 2000 to 2500, Division One 1500 to 2000 and Division Two 1000 to 1500. Another variable is the maximum amount of points that you could win or lose in a single match which will be set at 32 points. The last variable is the points difference between two players which would mean the full 32 points are won or lost which is set to a 720 point difference.
How it's calculated
How many points are won or lost are calculated using the difference between the two player's ratings applied to a logarithmic scale, with the result being probability of winning the match. The formula is as follows:
Where Pa is the probability of player 'a' winning, Rb is player 'b's rating and Ra is player 'a's rating. This probability is then applied to the second formula to calculate the number of points won or lost:
Where R'a is player 'a's new rating, Ra is their previous rating, K is the maximum points availble (32), Wa is 1 for a win or 0 for a loss and Pa is the previously calculated probability of winnning.
Example
Let's say we have a rating of 1627 and our three oponents have ratings of 1594, 1864 and 1902. Plugging these values into the first formula give us probabilities of 0.55, 0.2 and 0.17 for winning each match. Supposing we won the first match and lost the other two, we would win 14 points for the first match, lose 7 points for the second and lose 5 points for the third match. So overall we would gain 2 points giving us a new rating of 1629 points.
