Ranking explained

A player's ranking is always between 0 and 1000.

In each acknowledged tournament a player can obtain a base rank between 0 and 1000. The player's total ranking is an average (a weighted average) of his obtained base ranks from the tournaments he has participated in.

A player who wins all his tournaments, will have a total ranking of 1000.

A player who loses all this tournaments, will have a total ranking of 0.

Results from certain tournaments, like the OEMC, count more towards a player's ranking, than results from local tournaments do.

A player's older results count less towards his ranking, than his more recent results do.

Minimum number of tournaments

A player who has participated in only one tournament, will not have a representative ranking. Consider a player who won his first tournament and never participated in another. He would have a ranking of 1000, and is likely to stay on top of the ranking list forever. Therefore a player's ranking should not count, until he has played a certain number of tournaments, so that there are a number of results to average over.

Therefore a player with less than 5 tournaments is given a result of 0 (weight 1) for each missing tournament.

The base rank

A player's base rank in a tournament is based on his place in the tournament compared to the other participants. If you win you get a base rank of 1000. If you are in the middle of the field you get a base rank close to 500. If you are number 75 out of 100 you get a base rank of 252. If you are last of 100 players, you get a base rank of 0.

Calculation of the base rank: Find the number of player's you have beaten by taking the number of players and subtract your position. Divide by (number of players minus 1). Then multiply by 1000 to avoid small numbers.

Example 1: There are 100 players. Consider the last player: His position is 100, he beat 0 players and will get a base rank of 0: (100-100)/99 = 0. Multiply by 1000, you still get 0.

Example 2: There are 100 players. Consider the winner: He beat the remaining 99 players, his position is 1: base rank = (100-1)/99 = 1. Multiply by 1000 = 1000.

Example 3: There are 100 players. Consider the player who got the 25th place. Base rank: (100 - 25)/99 * 1000 = 757

Example 4: There are 100 players. Consider the player who got the 75th place. Base rank: (100 - 75)/99 * 1000 = 252

Picture lining up all the players in one long line with the winner at one end and the loser at the other end. Now take a very long and very elastic rubber band with numbers from 0 to 1000 (0,1,2,3,4 and so on up to 1000) painted with even distance along the rubber band. Now whether there are 20 or 100 player, you stretch the elastic band so that the number 0 is in front of the loser and, at the other end of the line of people, the number 1000 is in front of the winner. In front of each player will be a number corresponding to his base rank.

Averaging

Let's first consider a basic system. Forget anything about weights. This is the general principle: When a player has participated in several tournaments, you take the average of all the base ranks he has obtained and this is his total ranking. So a player who got base ranks 200, 500 and 1000 in the 3 tournaments he has participated in, would have a total ranking of (200 + 500 + 1000)/3 = 567.

The idea of weights

Now, if you think all tournaments are equally important, you should look no further. You should calculate the total ranking as it was done just above: Just average all the obtained base ranks. But please read on.

Now consider that you don't think all tournaments are equally important. Maybe you think winning the OEMC is more important than winning the Danish Championship?

Consider a player, A. This player has won an OEMC (100 players) and he became number 25 out of 50 players in DK. The base ranks for these tournaments are 1000 and 510. If we take the average, he would get a total ranking of 755. If we think the OEMC is 2.5 times more important than the Champ DK we can introduce weights so that the weight for OEMC is 5 and for DK is 2, then the OEMC weight is 2.5 times the DK weight. Now instead of a normal average, we make a so-called weighted average:
(5*1000 + 2*755)/(5+2) = 930
Before adding the base ranks, we multiply them by their weights. We now need to divide by the sum of weights in stead of by the number of tournaments. So instead of 755 (normal average), he got a total ranking of 930.

The weighted average is identical to letting the OEMC result count five times and the national championship count two times: calculate a normal average, but instead of two results, you average over seven results: five times you add the result from OEMC and two times the national championship result, then divide by seven, as if the player had participated in seven tournaments.

Now consider a player, B, who was 50 out of 100 in an OEMC and won in DK. His base ranks: 505 and 1000. Almost the same as A. When we do the normal average, his total ranking is 752, almost the same as the normal average for A. Let's do the weighted average:
(5*505 + 2*1000)/(5+2) = 646
So instead of 752 (normal average), he got a total ranking of 646.