*Weighting tournaments by the number of players*

A player's Overall (Log32) score is the sum of their best tournament scores. For 2009 onwards the best 4 tournament scores are used. This is a change from 2007 - 2008 where it was the sum of their 3 best tournament scores. The points scored for each tournament is based on the size of the tournament, with larger events worth more, and where the player came in the event.

The average size for tournaments varies from year to year, between about 30
and 35. In the Log32 scoring system an event with 32 players is worth 100 points, and the maximum
points you can get from a single tournament is 120 points (for events with 64
or more players). Each position in the tournament below first place
is then awarded points down to last place based on the position incremental
value (for example last place in a 64 player tournament would receive 1.875 points).

The increment value is calculated the following way:

(tournament weighting)/(# of players)

The best 4 tournament ranking points a player receives in a calendar year are
added together to form their ranking points total for the year.

Since 2003, the scoring system for tournament rankings has been the one that Geoff Tewierik (GT) introduced. The GT Scoring system weights tournaments by their size compared to the average size, capped at a maximum weighting of 125%. The average size of tournaments in Australia/NZ has varied between 30 and 35 since records have been kept. If we take the average size of a tournament as 32, then a tournament with 40 or more players would get the maximum weighting. This is fairly equitable, as most regions will have events that qualify for maximum points (in 2007 only South Australia didn't have an event large enough to get the maximum weighting). However, under the GT system coming 8th in the 40 player event would be worth about as much as winning the 32 player event.

Because of this limitation of the GT system, I considered alternatives. For some time during 2007 I trialled the scoring system that Irresistible Force was using at the time (Irresistible Force modified their system for 2008). However, the IF scoring system used in 2007 had coming 32nd in a 64 player event worth more than winning a 20 player event. This means that players who have attended 64 player events dominated the rankings. There were only 3 such events in 2007, with one each in Melbourne, Canberra and Brisbane, and the system disadvantaged players who couldn't get to one of these but who still won the largest events in their region. Because of the limitations of the GT and IF 2007 scoring systems, I introduced the Log32 scoring system in 2007.

If you have two players, a single game will determine a winner. In an elimination tournament with 3 or 4 players you need two rounds, with up to 8 players you need three rounds, with up to 16 players you need 4 rounds, up to 32 players you need 5 rounds and with up to 64 players you need 6 rounds. This suggests to me that the difficulty of winning a tournament increases by one step each time the number of players is doubled. This is what is known as a logarithmic function.

Number | Log2 | Log32 |

2 | 1 | 20% |

4 | 2 | 40% |

8 | 3 | 60% |

16 | 4 | 80% |

32 | 5 | 100% |

64 | 6 | 120% |

To work out the weighting of any tournament with a size of 1 - 64 players, you can use your scientific calculator to determine log(N)/log(32)*100%where N is the number of players. In Microsoft Excel you can use the the formula =log(N,32).

The maximum value for any tournament is 120, even if more than 64 players
attend. This is because you an elimination tournament with 6 rounds can
determine the best player out of a pool of up to 64 players. Once you get
more than 64 players, you really need 7 rounds to determine a winner in an
elimination tournament. Most tournaments have 5 or 6 rounds. The only
event that has more than 64 players *and* more than 6 rounds is Cancon.
In order to provide a level of consistency, I consider any event with 64 or more
players to be equally prestigious to win.

Given that 32 players is approximately the average size of a tournament, the
Log32 function looks like a worthy candidate. The following graph compares the Log32 weighting
with the GT weighting (assuming an average size of 32 players) and a
"normalised" IF 2007 weighting (which has been scaled to give a result of 50 - 125
rather than 40 - 100).

Suppose a player came 1st in a 20 player event.
How do the different weighting systems compare this to a result in a 40 player
event. Under the GT system 1st in a 20 player event is equivalent to about 20th
in the 40 player event. Under the IF 2007 system
1st on the 20 player event is equivalent to about 13th in a 40 player event. Under the Log2 system
1st in a 20 player event is equivalent to
about 8th in a 40 player event.

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