bt_green_warbler wrote:(Some related stats: 77.3% of 2012 HSNCT games heard at least 20 tossups; 94.9% heard at least 18 tossups; and 98.8% heard at least 17 tossups. So we are talking about a comparatively very small number of tossups here; and the relevant unfairness would be even smaller, given that many, perhaps most, of these games had large enough differences in the score that the extra tossups could not have changed the outcome.)

Really late stats for this topic:

I looked at 1001 of the 1200 HSNCT Prelim Games (2 games had more than 24 tossups heard and thus used more than 1 packet; 3 games had fewer than 16 tossups heard and were not involved in the analysis; 194 had exactly 20 tossups heard and were irrelevant to the analysis).

I calculated the following:

For games with less than 20 TUH: Whether there was a small enough difference in the score that a team getting the maximum score per tossup (45 points) on each remaining tossup up to tossup 20 would have affected the outcome of the game.

For games with more than 20 TUH: Whether there was a small enough difference in the score that randomly removing

*n* tossups from the packet, where

*n* is the number in excess of 20, could have affected the outcome of the game if those

*n* tossups were all scored with a line of 45 points per tossup by the winning team.

In theory, I would think, these two events are equivalent: either adding 45

*n* points to the losing team, or subtracting 45

*n* points from the winning team. For some number

*n*, then, the probability of the first event happening for a 20-

*n* TUH game should equal the probability of the second event happening for a 20+

*n* TUH game.

I looked specifically at odds ratios for each

*n*. Basically, odds ratios are how likely an event is given some categorical description. For instance, an odds ratio of 5 means that the event is 5 times more likely to occur for someone in Category A as opposed to Category B.

Here, the event is that movement to an untimed, 20-tossup game had the possibility of changing who the winner of the game was by adding or subtracting 45 points per tossup. Overall, about 40% of the games fit this description.

For

*n* = 1, the odds ratio was 1.00. In other words, expanding the game by 1 tossup was about as likely to "possibly affect the outcome of the game" as shrinking the game by 1 tossup.

For

*n* = 2, odds ratio = 1.86; for

*n* = 3, odds ratio = 1.90. This means that a 17- or 18-tossup game was a little less than twice as likely to have the outcome possibly affected by moving to an untimed, 20-tossup game than a 22- or 23-tossup game.

For

*n* = 4, odds ratio = 4.05. This means that a 16-tossup game was 4 times as likely to have its outcome possibly affected by moving to an untimed, 20-tossup game than a 24-tossup game was.

Obviously, some comebacks are more likely than others, but I don't know if there is a good or simple way to quantify that. All we can say is that 17- and 18-tossup games are about twice as likely to have a nonzero probability of a different winner with a move to a 20-tossup game than 22- or 23-tossup games, and that 16-tossup games are about 4 times as likely as 24-tossup games to have a nonzero probability of a different winner. I don't know if that's an argument to eliminate the clock, but it pretty well shows that eliminating the clock will likely have a disproportionate effect on low-TUH games compared to "equivalently different from 20 tossups" high-TUH games.