# Taking the New Model for a Spin

Yesterday I discussed converting the competition model in the tournament simulator to use Gaussian factors rather than uniform factors. Today I’ll show the results for eight versions of the 16-team double elimination tournament.

As predicted, this has so far yielded results comparable to the old model. And tweaking the new parameters for luck and the elite entry cutoff have yielded results in the expected direction.

bracket
fairness
wins by favorite
duplicates
shifted, blind draw
2.848
43.88%
1.15
shifted, seeded
3.078
45.43
1.16
unshifted, blind draw
2.804
43.60
1.38
unshifted, seeded
3.101
45.51
1.38
unshifted, BD, 0.5 luck
7.363
63.29
1.43
unshifted, BD, 2.0 luck
1.382
24.60
1.40
unshifted, BD, non elite
3.098
48.89
1.40
unshifted, BD, elite 2
2.555
30.43
1.40

The third, highlighted line in the table can be taken as the base case for comparisons. The first line is linked to a new analyzed bracket so you can get more detail.

As before, seeding improves fairness, but it improves it more in a shifted bracket than in an unshifted bracket. Again, the shifted bracket is the best performer for blind draw. The shifted bracket also produces fewer duplicate pairings – nothing else has much of an effect on duplicates.

Decreasing the luck factor by half, which raises the influence of skill from 50% to 66.67%, yields a very strong increase in fairness, which makes sense – the less luck there is in individual matches, the more likely it is that the best player will win, and that’s what the fairness coefficient measures. Similarly, doubling the luck factor, with takes skill from 50% to 33.33%, markedly decreases fairness.

Removing the elite entry cutoff, so that the tournament entries are samples of the full normal distribution, somewhat increases fairness, as it brings in poorer players unlikely to win the tournament. Raising the elite entry cutoff to 2.0, which essentially means that the tournament is open only the the top 2.5% of players, has the opposite effect.

Over time, I expect to use the new model exclusively, and to re-run the experiments reported in previous posts, making the change silently unless there’s some good reason to discuss the differences.