Periplus of the Erythraean Sea wrote:These stats are pretty interesting, Andrew - I'd be interested to see the methodology, particularly for generating the expected game stats? I figure if I did this it'd be using something along the lines of "log5-generated chance of getting tossup x (10 + PPB)" but I'm not precisely sure about the specifics.

One thing - I think that Ohio State-Chicago game is from 2012, not 2014, i.e. before the John Lawrence era.

Thanks for catching the transcription error on the Chicago/OSU game; I just fixed it.

As for methodology, here's basically what I did:

1. I calculated a z-score for each team's tossup conversion rate (tossups answered / tossups heard) relative to that year's Nationals field. I did the same with points per bonus, again relative to that year's field.

2. I ran some regressions in Excel until I found the mix of tossup/bonus z-scores that had the highest r^2 to winning percentage (13-to-1 tossup-to-bonus). I'll call that the "measure of strength" or MoS.

3. I copied all of the individual game scores from 2012-2016 Nationals into Excel and did some data entry to get them matched up with each team's tossup/bonus z-scores and MoS.

4. At this point, I wanted to calculate the expected points, but Excel was struggling to find a good line of fit. So I put the matchups into the eight bins shown in the above-linked table and made a scatterplot of average MoS vs. average margin of victory for each eight points. The result was almost exactly linear (r^2 f 0.98 or so), and very nearly passed through the origin, so it was on the right track. I used Excel's option of having the regression line run through the origin so that it wouldn't give the favored team a negative expected margin of victory in the very closest matchups, which lowered the r^2 to about 0.95. This is kind of a quick-and-dirty way to do it, but I think it's good enough for these purposes.

5. Based on the above, you can find a team's estimated margin of victory in a given matchup by taking the absolute value of the difference in the two teams' MoS and multiplying the result by 16.95.