Tuesday, October 28, 2008

Mock Trial Scoring and Ties

I've developed a strong preference for quoting mock trial scores and results in terms of total ballots (equivalently, total wins) over in terms of win-loss record. A win is worth one win, naturally; a loss is worth zero wins. But the tie ends up adding a ternary complexity to the otherwise binary system, being worth half a win. Some systems (for example, Georgia high school mock trial) address this problem by eliminating the possibility of a tie altogether by means of a "team score" that's specifically designed to break a tie. College mock trial, though, gives a total score that's the sum of the individual performances, and nothing more. This can range from 14 to 140, although scores typically find themselves in the range of 80-120.

The combinatorically savvy will note that out of 127 possible scores, or even 40 or so likely scores, the tie should not happen very often. It does, more than it really has any right to. One Georgia Tech team had three of them in one weekend, out of eight total ballots. Therefore, you get monstrosities like a record of 3-3-2, which is far from self-explanatory at first glance. Decoded, it's three wins, three losses, and two ties, and if you know the tie-win conversion factor, it's easy to see that this team has four win equivalents... but how much better or worse is that than a team with plain old four wins?

Here's the key: in college mock trial, it's not necessarily either. A team that goes 3-3-2 is not necessarily going to be ranked higher or lower than a team that goes 4-4. No, that comes down to a construct called CS, which stands for combined strength, and is actually the least arcane of all the tiebreaker formulae. A quick rundown: CS is like strength of schedule in football; higher CS means you played tougher teams and ranks higher in the tiebreaker.

So consider the following (admittedly contrived, but mathematically possible) scenario. At a particularly tough tournament, the best teams only get six wins or the equivalent. Team A has a record of 6-2, CS 15. Team B has a record of 5-1-2, CS 16. Team C has a record of 4-0-4, CS 14. To someone who knows 1) tie equivalencies, and 2) what CS means, it's obvious that the top three teams in order are B, then A, then C.

Plenty of tournaments would choose to report the standings with win-loss record, so we'd see a convoluted mess of wins and losses and ties that make you do the tie conversions yourself. Why not just report each team as having six wins?

Currently listening: "One By One All Day", the Shins

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