Sam, you bring up a good point. Is this measure at all informative by itself? I honestly hadn't considered that too closely. My intial motivation was the desire to run more accurate simulations of 2013 ICT. I realized that before that task could be undertaken, I would have to create a set of statistics to quantify buzzing. When I came up with some measure, I excitedly and impulsively posted it.
So, is the measure useful? I'd actually like the community's help with this. I am a fairly bad quizbowl player, and for this reason I have no frame of reference with which to judge whether this measure is helpful. Translated using the log5 formula, the numbers would indicate that in a game between last year's incarnations of UVA A and Yale, Virginia would be expected to buzz first on 62% of the tossups. Does that seem to jive with what you have seen? In the next sections of the post, I go a bit more in depth into what I created, and then I fleshed out a post spit-balling thoughts on how it could be useful. Most of the remarks are off-the-cuff attempts to support the measure. However, even if this measure fails to be useful on its own, I think it still works as a stepping stone for simulation.
The Probability of First Buzz was calculated using an optimization function. The objective function that was optimized was -Sum(log(P[x=FB_ki, n=FB_ki+FB_kj, p=log5(p_i,p_j)])). In words, the negative sum of the natural log of the binomial pmf for the calculated total and team i "first buzzes" during game k, with probability of success given as p=log5(p_i,p_j) where p_i and p_j are the respective probability that Team i and Team j would buzz first against an "average" team, and log5 is a function that outputs (p_i*(1-p_j))/((p_i*(1-p_j))+(p_j*(1-p_i)). The 32 p_i are the parameters over which the function was optimized. I did transform the parameters so that they optimized over the entire real line, and then could be transformed meaningfully to a (0,1) interval.
I think that this measure tells us something different than points per game, although it can be easily translated to that. It is instead a measure of aggression. This informs our understanding of what "average team" means - it isn't the team with an average amount of knowledge, but instead an average amount of aggression.
While I don't know much about different styles of play among great players, one characteristic that I have heard that Chris Ray is very aggressive. During last year's ICT, despite having only 1.5 PPB less and 2 fewer powers per game than Yale, Maryland had 80 fewer PP20TUH. My measure tells us that Maryland buzzes in first on a question just as often as Yale does. In a 20 tossup game against an average ICT team, both teams would expect to buzz in first on 16 of the 20 tossups. The difference between them is that Yale is only wrong about 9% of the time, while Maryland negs 25% of the time. Yale also has a higher power rate (displayed below). Maryland would be expected to go 4/8/4 on their 16 tossups, while Yale would be expected to go 6/8/2. Using their respective PPB, the expected points per twenty tossups against an average team would be 440 for Yale, and 340 for Maryland - indicating that the simpler PP20TUH from ICT slightly understates how much better Yale is. It may be beneficial for Chris Ray to be a tad less aggressive.
On my end of the tournament, it yields the result that the bottom teams tend to give the game away through negging. While A&M would be expected to buzz first on 4-5 tossups per 20 TUH against the average team, we also expect to neg 2-3 of those. It is likely that when we end up winning at ICT, it is either because the other team negs themself out of the game (like Illinois B did), or because they simply don't know enough to pick up what we've negged (like Guelph and Chicago C). Trevor Davis, on the other hand, greatly over-achieved through sticking with what he knows, and not negging. By points per bonus, he ranked 26th; by aggression, he ranked 28th. He tied for 19th, however, because he was consistent, and negged very little. Looking more closely at these stats, however, it is clear that dead tossups play a much larger role at this end than at the top end.
This exercise is a bit discouraging, since I reluctantly would conclude that this measure is not very useful by itself. Even combined with power rate and neg rate, it doesn't tell us an extraordinary amount of information. I think it is too early, however, to completely dismiss it. It is definitely an improvement for the purpose of running simulations, should that ever happens.
Code: Select all
Team P[Buzz First] P[Neg|Buzz First] P[Correct First Buzz] P[Power|First Buzz]
32 Yale 0.8189777 0.09142857 0.744099716 0.3771429
29 Virginia A 0.8817422 0.15639810 0.743839357 0.4170616
16 Michigan A 0.7965477 0.15469613 0.673324855 0.3480663
27 UC San Diego 0.7891636 0.18644068 0.642031367 0.2316384
13 Illinois A 0.7932358 0.20858896 0.627775571 0.2944785
15 Maryland 0.8041403 0.24705882 0.605470345 0.2705882
12 Harvard 0.7538409 0.20408163 0.599995849 0.3741497
6 Chicago A 0.7906004 0.25170068 0.591605741 0.3537415
23 Penn 0.7764012 0.25465839 0.578684110 0.3478261
19 MIT 0.6186067 0.12380952 0.542017278 0.4380952
18 Minnesota 0.6534550 0.20869565 0.517081802 0.3826087
1 Alabama 0.6359473 0.20689655 0.504371993 0.2241379
3 Brown 0.7054706 0.32061069 0.479289159 0.2977099
9 Columbia 0.5989403 0.20149254 0.478258272 0.1567164
10 Georgia Tech 0.5770207 0.26315789 0.425173136 0.2807018
30 Virginia B 0.5363577 0.27966102 0.386359354 0.2118644
31 WUSTL 0.5628401 0.31868132 0.383473482 0.2197802
21 Ohio St. A 0.5262415 0.28571429 0.375886798 0.2307692
4 Carleton College 0.4967302 0.24509804 0.374982621 0.2843137
28 VCU 0.3666246 0.18556701 0.298591151 0.1649485
7 Chicago B 0.4079407 0.27433628 0.296027760 0.1946903
24 RPI 0.3361205 0.19753086 0.269726295 0.1358025
17 Michigan B 0.3845222 0.35064935 0.249689747 0.1948052
20 Northwestern 0.3745670 0.36363636 0.238360850 0.2500000
5 Carnegie Mellon 0.3114949 0.27777778 0.224968555 0.1944444
14 Illinois B 0.3152851 0.35802469 0.202405259 0.1481481
26 Toronto 0.3497183 0.43023256 0.199258095 0.2325581
22 Ohio St. B 0.3350613 0.40540541 0.199225666 0.2432432
25 Texas A&M 0.2364728 0.50769231 0.116417388 0.2461538
11 Guelph 0.1529954 0.42857143 0.087425962 0.3095238
2 Arizona St. 0.1732829 0.51428571 0.084165957 0.3428571
8 Chicago C 0.0179671 0.83333333 0.002994517 0.1666667