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Simulation

Posted By: Tom Keith
Date: Friday, 17 May 2013, at 8:34 p.m.

In Response To: The good and the bad and the only fix needed (Tom Keith)

I simulated a tournament with 63 players in it (an odd number so as to create more byes.) Players were paired at random and eliminated when they received three losses. Play continued until only one player was left, and that player was declared the winner of the tournament.

I set up a range of abilities among the players. Player #1 was the strongest and was favored over all others, Player #2 was second and favored over all players except #1, etc. I ran the simulation 10 million times and kept track of how often each player won. As expected, Player #1 won most often (about 4.14% of the time) and Player #63 won least often (about 0.31% of the time).

What I wanted to find out is if the method of assigning byes would affect these numbers. So I created two flavors of the simulation.

Format A: When byes were needed they were assigned as follows:

  1. First priority was to pick a player who had received the fewest byes so far.
  2. If there was a tie, next priority was to pick the player who had the most losses so far.
  3. If there was still a tie, a player was chosen at random among the remaining players.

Format B: The only difference from Format A was step b:

  1. If there was a tie, next priority was to pick the player who had the fewest losses so far.

Other than that, the two Formats were identical.

So what were the results? They were a little bit surprising, at least to me.

(1) For performance (ability of the format to choose the strongest player), there was no measurable difference. Both formats performed equally well. From that point of view, it doesn't matter which method of selecting byes is used.

(2) For duration (number of rounds required), Format A had an advantage:

Format A used 12.82 rounds on average.
Format B used 13.25 rounds on average.

Not a big difference, but it's not what I would have guessed (and it's not what Chiva expected either).

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