Hmm, how about this continuous tournament style: You have
- a number q between .5 and 1
- N teams.
Every team has a history of match wins and losses. The history is recorded in a sequence w_i of numbers. w_i is 0 if the game i rounds ago was lost by the team, it is 2 if the game was won, and 1 if it was a draw (although currently, no game mode allows that result for a game). w_0 always is the result of the very last round, w_1 is the result of the round before that, and so on.
From that, the Win Metric is calculated. It is given by
Code: Select all
W := sum( i from 0 to infinity ) of w_i * q^i
Edit: Rico's plan is also fine. Make w_i the number of won rounds in the corresponding engagement. This would make games get played properly to the end.
Initially, everyone's win history is all zeroes. The initial team list is randomized. A round of the tournament works as this:
1. The two topmost teams on the team list battle each other, the third and fourth topmost teams battle each other, and so on. Results are stored in both teams' win history.
2. The Win Metrics are updated from the changed history. The team list is sorted according to the Win Metric, higher metrics go to the top. The team on top is declared this round's champion if it has a different Win Metric than the second team. This is bound to happen sometime. Even if draws are a legal result, sooner or later, the two Win Metrics will differ.
Performance optimization: you don't have to calculate the whole Win Metric anew every round or store the whole win history. It is perfectly sufficient to record the result w of the last game (0 for loss, 2 for win, 1 for draw) and update the Win Metric according to
The result is the same.
Example with q=3/4 and four teams labeled A,B,C and
In round 1, everyone starts off with Win Metric 0. The list is sorted arbitrarily (that is only required in the first N rounds), let's assume it is A 0, B 0, C 0, D 0. Now A and B compete, as well as C and D. Assume A and D win. The Win Metrics are now 2 for A and D, and still 0 for B and D. The list is sorted, yielding A 2, D 2, B 0, C 0. A and D have the same Metric, so no champion is declared yet.
Round 2: A and D have to battle it out, B and C too. Assume D and C win. Now the Metrics are A 1.5, B 0, C 2, D 3.5 or sorted: D 3.5, C 2, A 1.5, B 0. D is declared champion of the second round. That's the same result as a knockout tournament would have given.
Round 3: It's D vs C and A vs B. Let's say B manages to improve drastically: B and D win. The sorted list is D 7.625, B 2, C 1.5, A 1.125. D stays champion. Still, the same result as a knockout tournament staring with the setup of round 2.
Round 4: D vs B and C vs A again, B and A win. Sorted list: D 5.71875, B 3.5, A 2.84375, C 1.125. D stays champion. This time, a knockout tournament starting from round 3's setup would have declared B the champion, but D's persistent history of won games saved it it's title for now. Only if B beats D again in the next round, B will become champion. By tuning q, you can determine the number of rounds a team can stay champion even though it gets beaten consistently.
Analysis: With a number q between .5 and 1. q = .5 gives the same result as knockout tournaments and quickly changing champions, q=1 gives the other end: the old champion with a long history of won games will take very long to replace. The number of rounds required to replace a previously undefeated, but now completely harmless champion is -1/log_2(q), rounded down. In the example above, that's 2. Err. Sorry for the math, I can't help it
I'd probably organize this with one game played per week, so each round is spread over 2^N weeks. Or maybe, for starters, roughly every two weeks to avoid collisions with the ladle. Each game would look like a ladle final, essentially. I'd be willing to give it a try, taking a bit of care over the ladle matches was sort of fun so far. I'd make the minor modification that the default player count per team is 5, no 8, and that it can be increased only on request from both teams. I'd pick the second rating model with q=3/4 and maybe seed the win history from past ladles. The seed gets irrelevant after some rounds. What do you think?
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