Do you want to see more analysis like what's in these posts? Do you have any particular questions you'd like to see us dive into?

Thanks!

Dr. Noah Prince

Normal Community High School (2002)
University of Illinois at Urbana-Champaign (2004, 2007, 2008)

Illinois Mathematics and Science Academy - Scholastic Bowl coach (2009-2014), assistant coach (2014-2015), well wisher (2015-2016)
guy in San Diego (2016-present)
President of Qblitz (2018-present)

The game theory post is interesting. I don't know how applicable it is because there is a major lack of information during a tossup because you don't know how close the other team is to getting it and you don't know what is going on in your teammates' minds. Also, the probability of getting a question correct is very jumpy rather than linear, and you don't know whether the next clue or two is going to be useless or is going to significantly change your probability of getting the answer correct--it is not unusual for a player to go from no clue to absolutely knowing the answer based on one clue. Also, different questions play differently--at low levels a question about an architect is going to have a decent probability of correctness for somebody who guesses, but other questions might have 100 or more possible answers without any of them sticking out as particularly probable. An underdog probably wants to pick their spots rather than playing every question the same--take your chances on the fraudable questions, and play some of the others based on whether or not you know the answer.

I decided to play with this anyways, because why not? I'm assuming negs but no powers.

If you are a favorite team that gets 95% of tossups by the giveaway and has 20 PPB, and your opponent gets 80% by the giveaway and has 15 PPB, then buzzing in when your probability of being correct is p gives 30p+(1-p)(-5-.8*25)=55p-25 expected net points. The underdog, on the other hand, if they buzz in when their probability is p, has 25p+(1-p)(-5-.95*30)=58.5p-33.5 expected net points.

Extending that, let's assume that if the favorite waits until their probability is p, then the probability is p that the other team buzzed in, and the probability the underdog is correct is .84p. Then the expected number of net points is (1-p)(55p-25)-p(25*.84p+(1-.84p)(-5-.95*30))=-104.14p^2+113.5p-25. That function peaks at p=.54 with 5.9 net points.

Similarly, with the underdog and using 1.19p instead of .84p, you get (1-p)(58.5p-33.5)-p(30*1.19p+(1-1.19p)(-5-.8*25))=-123.95p^2+117p-33.5. This function peaks at p=.47 with -5.9 net points. It sucks to have negative net points, but -5.9 net points is better than -10 net points, which is what happens if the underdog waits until their probability is 2/3.

The fact that the underdog should buzz sooner measured by their own probability of knowing the answer matches both intuition and Noah's analysis. Keep in mind that p=.54 and p=.47 is actually pretty much the same time, because the favorite having a .54 probability of guessing the answer is about the same time as the underdog having a .47 probability of guessing the answer under the assumptions I have made. Also, keep in mind that as I said at the beginning this is all based on a whole lot of simplifying assumptions that would be difficult to implement in an actual game.

David Reinstein
PACE VP of Outreach, Head Writer and Editor for Scobol Solo and Masonics (Illinois), TD for New Trier Scobol Solo and New Trier Varsity, Writer for NAQT (2011-2017), IHSSBCA Board Member, IHSSBCA Chair (2004-2014), PACE Member, PACE President (2016-2018), New Trier Coach (1994-2011)