Revisiting the 2010 HSNCT Playoffs
Posted: Wed Jan 19, 2011 7:27 pm
If you've been following my wacky Excel sheet posting in the Ongoing Season Rankings thread, you know that I've created a way to Monte Carlo simulate a round-robin tournament on the same packet set for any number of teams at any number of locations. As a test of the model, we ran it on the 2010 HSNCT data.
The Monte Carlo simulation gave me an estimate of the probability that any one team would defeat any other team on a typical 2010 HSNCT packet of 20 tossups, which I took to be roughly equivalent to the probability that any one team would defeat any other team on a typical 2010 HSNCT packet, since I did not want to/know how to deal with moderator speed variability.
Some time ago, Fred gave me the challenge of trying to figure out exactly how "fluky" Adair County's run through the playoffs was. Assuming that this model is at all accurate, I can answer that question and more. I used the diagram of the 2010 HSNCT double-elimination playoff structure and the probabilities from the Monte Carlo simulation results to analytically compute the chances of each playoff team finishing in each playoff position. Because I used Excel and didn't script anything, this took a long time to do, so I don't know how excited I'll be to do it on other data (of course, if someone who likes that stuff wants to spend their time doing it...).
Anyway, without further ado, here are what I believe the chances of each team finishing in each place. Chances are most likely accurate to within 0.2%, owing to roundoff error and my desire to have probabilities add up to 1 (although I think this is mostly an issue with places 1-4).
[top 16 in this post]
Maggie Walker
Original Finish: 1st
1st place: 31.4%
2nd place: 23.8%
3rd place: 18.7%
4th place: 9.8%
T-5th place: 9.7%
T-7th place: 4.4%
T-11th place: 1.1%
T-17th place: 1.1%
State College A
Original Finish: 2nd
1st place: 33.6%
2nd place: 23.9%
3rd place: 19.5%
4th place: 9.1%
T-5th place: 8.8%
T-7th place: 3.9%
T-11th place: 0.6%
T-17th place: 0.3%
T-27th place: 0.3%
LASA A
Original Finish: 3rd
1st place: 0.7%
2nd place: 3.2%
3rd place: 4.9%
4th place: 8.1%
T-5th place: 20.4%
T-7th place: 21%
T-11th place: 22.9%
T-17th place: 10.3%
T-27th place: 8.5%
Bellarmine
Original Finish: 4th
1st place: 0.1%
2nd place: 1.7%
3rd place: 2.9%
4th place: 6.7%
T-5th place: 11.3%
T-7th place: 34.9%
T-11th place: 25.2%
T-17th place: 15%
T-27th place: 2.1%
T-43rd place: 0.1%
Dorman A
Original Finish: T-5th
1st place: 1%
2nd place: 4.1%
3rd place: 5.9%
4th place: 9.1%
T-5th place: 19.7%
T-7th place: 17.2%
T-11th place: 26.5%
T-17th place: 11.5%
T-27th place: 5%
Georgetown Day A
Original Finish: T-5th
1st place: 3.3%
2nd place: 8.9%
3rd place: 10.6%
4th place: 10.8%
T-5th place: 15.9%
T-7th place: 14%
T-11th place: 21.7%
T-17th place: 11.8%
T-27th place: 3%
Adair County
Original Finish: T-7th
1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0.9%
T-11th place: 2.1%
T-17th place: 8.8%
T-27th place: 23.9%
T-43rd place: 44.7%
T-65th place: 19.6%
DCC A
Original Finish: T-7th
1st place: 0%
2nd place: 0%
3rd place: 0.1%
4th place: 0.2%
T-5th place: 1.5%
T-7th place: 8.7%
T-11th place: 24.3%
T-17th place: 41.4%
T-27th place: 22.1%
T-43rd place: 1.7%
Detroit Country Day
Original Finish: T-7th
1st place: 27.9%
2nd place: 23.1%
3rd place: 19.9%
4th place: 10.2%
T-5th place: 7.3%
T-7th place: 6.1%
T-11th place: 5%
T-17th place: 0.5%
Torrey Pines
Original Finish: T-7th
1st place: 0.2%
2nd place: 0.8%
3rd place: 1.5%
4th place: 4.1%
T-5th place: 11.5%
T-7th place: 28.4%
T-11th place: 30.9%
T-17th place: 30%
T-27th place: 2.6%
Stevenson
Original Finish: T-11th
1st place: 0.1%
2nd place: 0.7%
3rd place: 1.3%
4th place: 3.3%
T-5th place: 8%
T-7th place: 21.6%
T-11th place: 30.1%
T-17th place: 20.5%
T-27th place: 13.9%
T-43rd place: 0.5%
Eden Prairie A
Original Finish: T-11th
1st place: 1.2%
2nd place: 4.1%
3rd place: 6.2%
4th place: 9.1%
T-5th place: 20.3%
T-7th place: 17.6%
T-11th place: 26%
T-17th place: 11.2%
T-27th place: 4.4%
T-43rd place: 0.5%
LASA B
Original Finish: T-11th
1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0.1%
T-7th place: 2.8%
T-11th place: 7.5%
T-17th place: 19.3%
T-27th place: 47.7%
T-43rd place: 22.6%
Mission San Jose A
Original Finish: T-11th
1st place: 0%
2nd place: 0%
3rd place: 0.1%
4th place: 0.9%
T-5th place: 3.2%
T-7th place: 12.8%
T-11th place: 27.8%
T-17th place: 42%
T-27th place: 12.2%
T-43rd place: 1%
Seven Lakes A
Original Finish: T-11th
1st place: 0.1%
2nd place: 1.3%
3rd place: 1.9%
4th place: 3.0%
T-5th place: 13.1%
T-7th place: 10.3%
T-11th place: 19.8%
T-17th place: 35.6%
T-27th place: 14%
T-43rd place: 0.9%
Wilmington Charter A
Original Finish: T-11th
1st place: 0.1%
2nd place: 0.8%
3rd place: 1.3%
4th place: 3.3%
T-5th place: 8.7%
T-7th place: 23.5%
T-11th place: 34%
T-17th place: 14%
T-27th place: 14.3%
The Monte Carlo simulation gave me an estimate of the probability that any one team would defeat any other team on a typical 2010 HSNCT packet of 20 tossups, which I took to be roughly equivalent to the probability that any one team would defeat any other team on a typical 2010 HSNCT packet, since I did not want to/know how to deal with moderator speed variability.
Some time ago, Fred gave me the challenge of trying to figure out exactly how "fluky" Adair County's run through the playoffs was. Assuming that this model is at all accurate, I can answer that question and more. I used the diagram of the 2010 HSNCT double-elimination playoff structure and the probabilities from the Monte Carlo simulation results to analytically compute the chances of each playoff team finishing in each playoff position. Because I used Excel and didn't script anything, this took a long time to do, so I don't know how excited I'll be to do it on other data (of course, if someone who likes that stuff wants to spend their time doing it...).
Anyway, without further ado, here are what I believe the chances of each team finishing in each place. Chances are most likely accurate to within 0.2%, owing to roundoff error and my desire to have probabilities add up to 1 (although I think this is mostly an issue with places 1-4).
[top 16 in this post]
Maggie Walker
Original Finish: 1st
1st place: 31.4%
2nd place: 23.8%
3rd place: 18.7%
4th place: 9.8%
T-5th place: 9.7%
T-7th place: 4.4%
T-11th place: 1.1%
T-17th place: 1.1%
State College A
Original Finish: 2nd
1st place: 33.6%
2nd place: 23.9%
3rd place: 19.5%
4th place: 9.1%
T-5th place: 8.8%
T-7th place: 3.9%
T-11th place: 0.6%
T-17th place: 0.3%
T-27th place: 0.3%
LASA A
Original Finish: 3rd
1st place: 0.7%
2nd place: 3.2%
3rd place: 4.9%
4th place: 8.1%
T-5th place: 20.4%
T-7th place: 21%
T-11th place: 22.9%
T-17th place: 10.3%
T-27th place: 8.5%
Bellarmine
Original Finish: 4th
1st place: 0.1%
2nd place: 1.7%
3rd place: 2.9%
4th place: 6.7%
T-5th place: 11.3%
T-7th place: 34.9%
T-11th place: 25.2%
T-17th place: 15%
T-27th place: 2.1%
T-43rd place: 0.1%
Dorman A
Original Finish: T-5th
1st place: 1%
2nd place: 4.1%
3rd place: 5.9%
4th place: 9.1%
T-5th place: 19.7%
T-7th place: 17.2%
T-11th place: 26.5%
T-17th place: 11.5%
T-27th place: 5%
Georgetown Day A
Original Finish: T-5th
1st place: 3.3%
2nd place: 8.9%
3rd place: 10.6%
4th place: 10.8%
T-5th place: 15.9%
T-7th place: 14%
T-11th place: 21.7%
T-17th place: 11.8%
T-27th place: 3%
Adair County
Original Finish: T-7th
1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0.9%
T-11th place: 2.1%
T-17th place: 8.8%
T-27th place: 23.9%
T-43rd place: 44.7%
T-65th place: 19.6%
DCC A
Original Finish: T-7th
1st place: 0%
2nd place: 0%
3rd place: 0.1%
4th place: 0.2%
T-5th place: 1.5%
T-7th place: 8.7%
T-11th place: 24.3%
T-17th place: 41.4%
T-27th place: 22.1%
T-43rd place: 1.7%
Detroit Country Day
Original Finish: T-7th
1st place: 27.9%
2nd place: 23.1%
3rd place: 19.9%
4th place: 10.2%
T-5th place: 7.3%
T-7th place: 6.1%
T-11th place: 5%
T-17th place: 0.5%
Torrey Pines
Original Finish: T-7th
1st place: 0.2%
2nd place: 0.8%
3rd place: 1.5%
4th place: 4.1%
T-5th place: 11.5%
T-7th place: 28.4%
T-11th place: 30.9%
T-17th place: 30%
T-27th place: 2.6%
Stevenson
Original Finish: T-11th
1st place: 0.1%
2nd place: 0.7%
3rd place: 1.3%
4th place: 3.3%
T-5th place: 8%
T-7th place: 21.6%
T-11th place: 30.1%
T-17th place: 20.5%
T-27th place: 13.9%
T-43rd place: 0.5%
Eden Prairie A
Original Finish: T-11th
1st place: 1.2%
2nd place: 4.1%
3rd place: 6.2%
4th place: 9.1%
T-5th place: 20.3%
T-7th place: 17.6%
T-11th place: 26%
T-17th place: 11.2%
T-27th place: 4.4%
T-43rd place: 0.5%
LASA B
Original Finish: T-11th
1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0.1%
T-7th place: 2.8%
T-11th place: 7.5%
T-17th place: 19.3%
T-27th place: 47.7%
T-43rd place: 22.6%
Mission San Jose A
Original Finish: T-11th
1st place: 0%
2nd place: 0%
3rd place: 0.1%
4th place: 0.9%
T-5th place: 3.2%
T-7th place: 12.8%
T-11th place: 27.8%
T-17th place: 42%
T-27th place: 12.2%
T-43rd place: 1%
Seven Lakes A
Original Finish: T-11th
1st place: 0.1%
2nd place: 1.3%
3rd place: 1.9%
4th place: 3.0%
T-5th place: 13.1%
T-7th place: 10.3%
T-11th place: 19.8%
T-17th place: 35.6%
T-27th place: 14%
T-43rd place: 0.9%
Wilmington Charter A
Original Finish: T-11th
1st place: 0.1%
2nd place: 0.8%
3rd place: 1.3%
4th place: 3.3%
T-5th place: 8.7%
T-7th place: 23.5%
T-11th place: 34%
T-17th place: 14%
T-27th place: 14.3%