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 You may be wondering why the score ("T SCORE") used to decide the team order is not just the simple average of each team member's score as it used to be in the AM.com v BT.net 2-team contests. Don't worry if you don't understand all of what follows, you can rest assured that there are enough statisticians on these boards to shoot these adjustments down if they are not valid! The reason is that the larger the sample you base an average on, the less variable that average is likely to be. In simpler terms, if we just used the unadjusted average for each team, most of the bigger teams would end the competition clumped together in the middle of the table with the very small teams filling most of the places at the top and bottom. This would make the competition very unexciting for the teams that together comprise most of the people taking part. How exactly do we adjust for this? To compensate for this, if a team has more than 20 entrants and an average score that is higher than the average of all entrants, its score is adjusted up further away from the overall average ... conversely, if its average score is lower than the overall average, its score will be adjusted down. Meanwhile, the scores of teams with less than 20 entrants (15 for 2007 Wimb.) will have their scores adjusted back the other way towards the average, whether that be up or down, instead. What is the actual formula? For the statisticians among you, the formula used for a team of N entrants is: TS = OA + (TA - OA) * ( SQRT (N) / SQRT (M) ) where TS is the adjusted "T score" being calculated, TA is the simple team average (also shown on the teams table), OA is the overall average score of all entrants in all teams, M was 15 for Wimby 2007, 20 after that, and N is the number of entrants in the team. If N = M, this becomes TS = OA + (TA - OA) * 1 = TA, of course. Why not do it a simpler way? We could have dealt with this by setting a much higher threshold for the minimum size of a team and/or forcing really big teams to split up into two or more smaller teams, but it was felt that both of these options could spoil some people's fun. The method used is the theoretically fairest method available for teams of very different sizes, and it's a lot less complicated to do than to explain. If this adjustment is important, why is it not used when there are only two teams? When there are only two teams and one team's average score is above the average of all players in both teams, the other team's average score must automatically be below that average. So this adjustment cannot affect who finishes 1st or 2nd. Hence in the case of just two teams, including matches in the team knockout competition, it is simpler not to bother with the adjustment in the first place. |