Revisiting the 2010 HSNCT Playoffs

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cvdwightw
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Revisiting the 2010 HSNCT Playoffs

Post by cvdwightw »

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%
Dwight Wynne
socalquizbowl.org
UC Irvine 2008-2013; UCLA 2004-2007; Capistrano Valley High School 2000-2003

"It's a competition, but it's not a sport. On a scale, if football is a 10, then rowing would be a two. One would be Quiz Bowl." --Matt Birk on rowing, SI On Campus, 10/21/03

"If you were my teammate, I would have tossed your ass out the door so fast you'd be emitting Cerenkov radiation, but I'm not classy like Dwight." --Jerry

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cvdwightw
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Re: Revisiting the 2010 HSNCT Playoffs

Post by cvdwightw »

[places T-17 through T-43 in this post]

Berkeley
Original Finish: T-17th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0.3%
T-11th place: 2.1%
T-17th place: 12.9%
T-27th place: 53.4%
T-43rd place: 31.3%

Centennial
Original Finish: T-17th

1st place: 0%
2nd place: 0.1%
3rd place: 0.2%
4th place: 0.7%
T-5th place: 2.4%
T-7th place: 9.9%
T-11th place: 14.7%
T-17th place: 24%
T-27th place: 46.2%
T-43rd place: 1.8%

Chattahoochee A
Original Finish: T-17th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0.1%
T-7th place: 1.6%
T-11th place: 8.1%
T-17th place: 42%
T-27th place: 32.3%
T-43rd place: 15.9%

Hume-Fogg
Original Finish: T-17th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0.1%
T-7th place: 0.8%
T-11th place: 8.3%
T-17th place: 59.2%
T-27th place: 17.6%
T-43rd place: 14%

La Jolla A
Original Finish: T-17th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0.3%
T-7th place: 2.4%
T-11th place: 5.3%
T-17th place: 30.4%
T-27th place: 48.3%
T-43rd place: 13.3%

Oak Park-River Forest
Original Finish: T-17th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0.1%
T-7th place: 1.5%
T-11th place: 4.5%
T-17th place: 24.8%
T-27th place: 43.2%
T-43rd place: 25.9%

Auburn A
Original Finish: T-17th

1st place: 0.3%
2nd place: 2.5%
3rd place: 3.5%
4th place: 5.6%
T-5th place: 12.1%
T-7th place: 13.5%
T-11th place: 25.2%
T-17th place: 30%
T-27th place: 7.2%
T-43rd place: 0.1%

Solon
Original Finish: T-17th

1st place: 0%
2nd place: 0.4%
3rd place: 0.8%
4th place: 2.1%
T-5th place: 7.3%
T-7th place: 24%
T-11th place: 33.5%
T-17th place: 23.6%
T-27th place: 8.2%
T-43rd place: 0.1%

St. Mark's
Original Finish: T-17th

1st place: 0%
2nd place: 0.3%
3rd place: 0.2%
4th place: 0.9%
T-5th place: 3.8%
T-7th place: 23.3%
T-11th place: 25.6%
T-17th place: 44.9%
T-27th place: 10.1%
T-43rd place: 0.9%

duPont Manual
Original Finish: T-17th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0.3%
T-5th place: 1.4%
T-7th place: 12.9%
T-11th place: 18.6%
T-17th place: 36.8%
T-27th place: 28.4%
T-43rd place: 1.6%

Bergen A
Original Finish: T-27th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0.5%
T-11th place: 3.5%
T-17th place: 9.4%
T-27th place: 84.5%
T-43rd place: 2.1%

Brophy A
Original Finish: T-27th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0.5%
T-17th place: 7.3%
T-27th place: 58.8%
T-43rd place: 33.4%

Dorman B
Original Finish: T-27th

1st place: 0%
2nd place: 0.1%
3rd place: 0.2%
4th place: 1%
T-5th place: 4%
T-7th place: 24%
T-11th place: 19.5%
T-17th place: 34.3%
T-27th place: 14.5%
T-43rd place: 2.4%

Dunbar A
Original Finish: T-27th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0.2%
T-5th place: 0.6%
T-7th place: 3.9%
T-11th place: 8.4%
T-17th place: 23.3%
T-27th place: 60.4%
T-43rd place: 3.2%

Hoover
Original Finish: T-27th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0.4%
T-7th place: 7.6%
T-11th place: 11.1%
T-17th place: 30.5%
T-27th place: 39.7%
T-43rd place: 10.7%

Kellenberg A
Original Finish: T-27th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0.1%
T-7th place: 0.3%
T-11th place: 1.7%
T-17th place: 12.9%
T-27th place: 75.9%
T-43rd place: 9.1%

Olmstead Falls A
Original Finish: T-27th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0.3%
T-7th place: 2.9%
T-11th place: 11.%
T-17th place: 30.6%
T-27th place: 38.4%
T-43rd place: 16.7%

Pensacola
Original Finish: T-27th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0.4%
T-11th place: 3%
T-17th place: 7.7%
T-27th place: 77.1%
T-43rd place: 11.8%

Quince Orchard
Original Finish: T-27th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0.6%
T-7th place: 0.5%
T-11th place: 3.7%
T-17th place: 15.4%
T-27th place: 42.6%
T-43rd place: 37.7%

Raleigh Charter A
Original Finish: T-27th

1st place: 0%
2nd place: 0.2%
3rd place: 0.3%
4th place: 1.2%
T-5th place: 5.1%
T-7th place: 17%
T-11th place: 20.7%
T-17th place: 23.6%
T-27th place: 31.5%
T-43rd place: 0.4%

Rancho Bernardo
Original Finish: T-27th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0.2%
T-11th place: 1.9%
T-17th place: 25.8%
T-27th place: 47.1%
T-43rd place: 25%

Santa Monica
Original Finish: T-27th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0.1%
T-7th place: 0.4%
T-11th place: 3.3%
T-17th place: 6.7%
T-27th place: 67.2%
T-43rd place: 22.3%

St. Joseph (NJ)
Original Finish: T-27th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0.4%
T-7th place: 10.3%
T-11th place: 19.2%
T-17th place: 39.4%
T-27th place: 22.4%
T-43rd place: 8.3%

St. Thomas
Original Finish: T-27th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0.3%
T-17th place: 11.9%
T-27th place: 49.8%
T-43rd place: 38%

Thomas Jefferson
Original Finish: T-27th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0.2%
T-5th place: 0.9%
T-7th place: 4.5%
T-11th place: 6.1%
T-17th place: 22.9%
T-27th place: 63.3%
T-43rd place: 2.1%

Walnut Hills
Original Finish: T-27th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0.1%
T-7th place: 2.5%
T-11th place: 5.1%
T-17th place: 8%
T-27th place: 16.8%
T-43rd place: 67.5%

Arcadia
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0%
T-17th place: 0.2%
T-27th place: 8.9%
T-43rd place: 90.9%

Caesar Rodney
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0.2%
T-17th place: 7.2%
T-27th place: 6.6%
T-43rd place: 74.2%
T-65th place: 11.8%

Chaska
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0.2%
T-17th place: 2%
T-27th place: 3.6%
T-43rd place: 52%
T-65th place: 42.2%

Chatham Glenwood
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0%
T-17th place: 0%
T-27th place: 2.1%
T-43rd place: 97.9%

Cheshire
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0.1%
T-17th place: 3.1%
T-27th place: 31.9%
T-43rd place: 64.9%

Cistercian A
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0.3%
T-17th place: 4.8%
T-27th place: 9.9%
T-43rd place: 67.8%
T-65th place: 17.2%

Culver
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0.1%
T-17th place: 5.8%
T-27th place: 29%
T-43rd place: 45%
T-65th place: 20.1%

DeLaSalle A
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0%
T-17th place: 0.3%
T-27th place: 11.6%
T-43rd place: 88.1%

DCC B
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0.1%
T-11th place: 0.5%
T-17th place: 6.4%
T-27th place: 19.5%
T-43rd place: 55.1%
T-65th place: 18.4%

Lisgar A
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0.1%
T-11th place: 0.5%
T-17th place: 4%
T-27th place: 27.1%
T-43rd place: 54.4%
T-65th place: 13.9%

Livingston A
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 1%
T-17th place: 3.1%
T-27th place: 19.3%
T-43rd place: 58.8%
T-65th place: 17.8%

Loyola
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0%
T-17th place: 0.5%
T-27th place: 2.5%
T-43rd place: 37.2%
T-65th place: 59.8%

New Trier
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0%
T-17th place: 0.1%
T-27th place: 1.7%
T-43rd place: 98.2%

Parkview
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0.1%
T-17th place: 0.8%
T-27th place: 21.4%
T-43rd place: 77.7%

Ransom Everglades
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0%
T-17th place: 0.3%
T-27th place: 1.2%
T-43rd place: 61.2%
T-65th place: 37.3%

Seton Hall
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0.2%
T-17th place: 6%
T-27th place: 9.4%
T-43rd place: 66.8%
T-65th place: 17.6%

South Range
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0%
T-17th place: 0.1%
T-27th place: 3.1%
T-43rd place: 96.8%

St. Ignatius
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0.1%
T-11th place: 1.1%
T-17th place: 7.4%
T-27th place: 29.1%
T-43rd place: 62.3%

St. Paul Central
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0%
T-17th place: 0.1%
T-27th place: 0.8%
T-43rd place: 99.1%

University
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0.3%
T-17th place: 3.4%
T-27th place: 13%
T-43rd place: 83.3%

Walter Johnson
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0.2%
T-7th place: 5.2%
T-11th place: 10.9%
T-17th place: 22.8%
T-27th place: 44.7%
T-43rd place: 16.2%

Walton
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0.1%
T-5th place: 0.7%
T-7th place: 11.1%
T-11th place: 13.6%
T-17th place: 16.8%
T-27th place: 25.2%
T-43rd place: 32.5%
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Re: Revisiting the 2010 HSNCT Playoffs

Post by cvdwightw »

[T-65 and brief comments in this post]

Carbondale
Original Finish: T-65th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0.3%
T-17th place: 1.8%
T-27th place: 6%
T-43rd place: 51.7%
T-65th place: 40.2%

Eden Prairie B
Original Finish: T-65th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0%
T-17th place: 0%
T-27th place: 0.1%
T-43rd place: 11.7%
T-65th place: 88.2%

Edmond Santa Fe
Original Finish: T-65th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0%
T-17th place: 0.1%
T-27th place: 0.3%
T-43rd place: 36.9%
T-65th place: 62.7%

Grand Junction
Original Finish: T-65th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0%
T-17th place: 0.1%
T-27th place: 3%
T-43rd place: 17%
T-65th place: 79.9%

Grosse Pointe North
Original Finish: T-65th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0.1%
T-17th place: 0.7%
T-27th place: 1.8%
T-43rd place: 39.6%
T-65th place: 57.8%

Livonia Churchill
Original Finish: T-65th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0%
T-17th place: 0.1%
T-27th place: 1.5%
T-43rd place: 16.2%
T-65th place: 82.2%

MLK Magnet
Original Finish: T-65th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0%
T-17th place: 0.3%
T-27th place: 2.8%
T-43rd place: 16.5%
T-65th place: 80.4%

Novi A
Original Finish: T-65th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0%
T-17th place: 0%
T-27th place: 0.4%
T-43rd place: 16.8%
T-65th place: 82.8%

Rocky Grove
Original Finish: T-65th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0%
T-17th place: 0%
T-27th place: 1.2%
T-43rd place: 12.7%
T-65th place: 86.1%

Tippecanoe
Original Finish: T-65th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0%
T-17th place: 0.1%
T-27th place: 0.7%
T-43rd place: 16.8%
T-65th place: 82.4%

Wilmington Charter B
Original Finish: T-65th

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0%
T-17th place: 0.1%
T-27th place: 1.7%
T-43rd place: 16.6%
T-65th place: 81.6%

Brief comments: what this has done is completely remove all upsets from the equation - if an upset had a 5% chance of happening, then with 5% probability the lower-seeded team took the winner card and the next match was calculated for all involved teams accordingly. Therefore, the "Adair County got through because of upsets" theory doesn't hold that much water - every other team in that part of the bracket had a higher chance of getting farther than I initially expected. What this likely means is that teams on that side of the bracket were probably more even in terms of who was winning the game, as opposed to some other brackets in which the loser of the winner's bracket game or the winner of the loser's bracket game game had a much greater chance of winning the next loser's bracket game. We can also see this in the bottom part of the losers' bracket, where Stevenson, Raleigh Charter, Dunbar, and Centennial all seemed to have greater chances to advance than their counterparts in other brackets (either crushing their opponents in R17 or losing convincingly in R17).

Another wacky thing that happened was how the bracketing worked out in the TJ - La Jolla A game. The winner of the game immediately faced State College (almost certain loss) and then Seven Lakes (slightly less certain loss), while the loser faced a relatively mediocre 6-4 team and then, theoretically, a relatively mediocre 7-3 team. Indeed, despite being the theoretically better team and having a 70.7% chance of winning their Round 16 game, TJ had a 65.4% chance of being eliminated in Round 17 or 18 as compared to La Jolla's 61.6% chance. Similarly, seeds 51-53 took advantage of a first round bye and a second round game against a comparatively weak 7-3 team, while similar teams with higher seeds (St. Ignatius, Parkview, Walton/Walnut Hills) faced games against a much better opponent.

Based on my analysis, I can pretty conclusively claim that some teams had legitimate beefs with the way their schedule was set up (they would have had problems even if upsets hadn't happened), but I'm not at all sure how to correct this problem.
Dwight Wynne
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"It's a competition, but it's not a sport. On a scale, if football is a 10, then rowing would be a two. One would be Quiz Bowl." --Matt Birk on rowing, SI On Campus, 10/21/03

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Re: Revisiting the 2010 HSNCT Playoffs

Post by jonpin »

Interesting. To summarize the data in a different concise way, here are the top three places:

1st: SC 33.6, MW 31.4, DCD 27.9, GDS 3.3, Eden 1.2, Dorman 1.0, (LASA, Auburn, Torrey, 4 others) <1%
2nd: SC 23.9, MW 23.8, DCD 23.1, GDS 8.9, Dorman 4.1, Eden 4.1, LASA 3.2, others 8.9
3rd: DCD(!) 19.9, SC 19.5, MW 18.7, GDS 10.6, Eden 6.2, Dorman 5.9, LASA 4.9, others 14.3

Based on what actually wound up happening, perhaps the most meaningful "upset" of the bracket was Bellarmine beating DCD in the third playoff round. That put Bellarmine one win away from a guaranteed spot in the Final Four, while pushing DCD down into a game with 4th-seed LASA for a spot in the Super Six.
Similarly, seeds 51-53 took advantage of a first round bye and a second round game against a comparatively weak 7-3 team, while similar teams with higher seeds (St. Ignatius, Parkview, Walton/Walnut Hills) faced games against a much better opponent.
As the now-coach of the team seeded 51, I was selfishly very happy about that. The team with the next-highest PPT among 6-4 teams had to face Seven Lakes, the best 6-4 team, in the second playoff round. We got to face the lowest-rated 7-3 team in that same round, and due to the Swiss system set-up the day before, that 7-3 team is almost always going to be somewhat weaker than the best 6-4 team.

Again, not sure how to practically fix it.
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Re: Revisiting the 2010 HSNCT Playoffs

Post by AKKOLADE »

I'll just say real quick that DCD should definitely not have been surprising as the team most likely to finish third per the Monte Carlo sim. They had a fantastic tournament and, statistically, were on par with every team in the field.

Thanks a lot for looking at this, Dwight. I hope to have time in the near future to sit down and look at this more.
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Re: Revisiting the 2010 HSNCT Playoffs

Post by Papa's in the House »

cvdwightw wrote: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...).
If you have access to it, I would use Crystal Ball to run further Monte Carlo simulations in Excel. It reduces the time necessary pretty drastically.

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Re: Revisiting the 2010 HSNCT Playoffs

Post by Frater Taciturnus »

Papa's in the House wrote:
cvdwightw wrote: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...).
If you have access to it, I would use Crystal Ball to run further Monte Carlo simulations in Excel. It reduces the time necessary pretty drastically.

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Re: Revisiting the 2010 HSNCT Playoffs

Post by cvdwightw »

Fred wrote:I'll just say real quick that DCD should definitely not have been surprising as the team most likely to finish third per the Monte Carlo sim. They had a fantastic tournament and, statistically, were on par with every team in the field.

Thanks a lot for looking at this, Dwight. I hope to have time in the near future to sit down and look at this more.
I just want to note briefly that this wasn't exactly a Monte Carlo simulation. The Monte Carlo simulation was to figure out the probabilities of each team beating each other team if the HSNCT was some kind of gigantic 200-team round robin tournament. In turn, those probabilities were taken to be roughly "the probability that Team A would beat Team B if they played each other in a single HSNCT match" and used to derive the chances of each team winning each game. Detroit Country Day did not win 27.9% of the Monte Carlo simulations; instead, they had a 27.9% chance of winning based on analytically computing their chances to win given probabilities derived from Monte Carlo simulation.

As an example, Auburn A had a 90% chance of beating Hume-Fogg in R16 according to a Monte Carlo simulation of 1000 games between Auburn A and Hume-Fogg, given statistics elucidated in the Season Rankings thread. Instead of calculating the chances of GDS A beating Hume-Fogg in R17, like actually happened, I instead computed GDS's chance of beating a team that had a 90% chance of being Auburn (GDS's chances: 63.8%) and a 10% chance of being Hume-Fogg (94.1%). Therefore, at the end of that game, the 5 card was 66.8% GDS, 32.6% Auburn A, and 0.6% Hume-Fogg, while the 16 card was 57.4% Auburn A, 33.2% GDS, and 9.4% Hume-Fogg. Similarly, for the Round 22 4 vs 5 match, I had 17 teams that could have held the 4 card entering the match and 21 teams that could have held the 5 card entering the match, and computed the probability of all 26 distinct teams exiting the match with the 4 card (12 teams showed up as possibly holding either the 4 or 5 card).
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Re: Revisiting the 2010 HSNCT Playoffs

Post by cchiego »

So to be clear, this is all data from the Saturday portion, correct? What elements went into your model exactly? I'd be cautious about things that varied based on SOS, but I know just PPB is not very useful.

Is there any way to modify your model so that instead of predicting the RR outcomes by itself, you can plug in the results you generate into the actual elimination brackets and see how that's gamed out? It might be tricky (read: very difficult) to do, but then could produce a more real-world outcome. The end goal of having some way to predict outcomes of Sundays' playoffs on Saturday night seems rather insignificant, but would be very cool to see.

If you send me the data file and a description of what you did, I'll see if I can't write something in R (Gordon might be better at this) that would be more universally usable (at the reseeding part of every tournament, you can run a model and see how the tournament should turn out :shock: ).

Also, have you considered trying to write something using in-match Bayesian updating? That would be an even neater way of seeing just how probable or improbable comebacks might be.
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Re: Revisiting the 2010 HSNCT Playoffs

Post by Mechanical Beasts »

Swank diet wrote: Is there any way to modify your model so that instead of predicting the RR outcomes by itself, you can plug in the results you generate into the actual elimination brackets and see how that's gamed out? It might be tricky (read: very difficult) to do, but then could produce a more real-world outcome. The end goal of having some way to predict outcomes of Sundays' playoffs on Saturday night seems rather insignificant, but would be very cool to see.
I'm almost sure he's doing that already, unless I misunderstand you.
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Re: Revisiting the 2010 HSNCT Playoffs

Post by Down and out in Quintana Roo »

cvdwightw wrote: Caesar Rodney
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0.2%
T-17th place: 7.2%
T-27th place: 6.6%

T-43rd place: 74.2%
T-65th place: 11.8%
How is it possible that we were more likely to finish 17th than 27th? Does it have anything to do with the incredibly close game we played against Rockford Auburn in that playoff round?
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Re: Revisiting the 2010 HSNCT Playoffs

Post by Whiter Hydra »

Carangoides ciliarius wrote:
cvdwightw wrote: Caesar Rodney
Original Finish: T-43rd

1st place: 0%
2nd place: 0%
3rd place: 0%
4th place: 0%
T-5th place: 0%
T-7th place: 0%
T-11th place: 0.2%
T-17th place: 7.2%
T-27th place: 6.6%

T-43rd place: 74.2%
T-65th place: 11.8%
How is it possible that we were more likely to finish 17th than 27th? Does it have anything to do with the incredibly close game we played against Rockford Auburn in that playoff round?
My guess is that the team you would face in the Round of 27 would be fairly weak, while the team you would face in the Round of 17 would be very strong.
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Re: Revisiting the 2010 HSNCT Playoffs

Post by Stained Diviner »

It's a little bit more complicated than this, but if you would have beaten Auburn, then you would have played the winner of St. Thomas vs Culver, and you would have had a slightly better than 50/50 chance. If you had won that game, your next match would have been against Dorman A, and you would have had about a 3% chance.
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Re: Revisiting the 2010 HSNCT Playoffs

Post by cvdwightw »

Swank diet wrote:So to be clear, this is all data from the Saturday portion, correct? What elements went into your model exactly? I'd be cautious about things that varied based on SOS, but I know just PPB is not very useful.
I used the data directly available from NAQT's statistics page, which includes the 10 Saturday games as well as all Sunday games (both regular and small-school playoffs). I used PPB as well as powers/tens/negs by both each team and each team's opponents.

The basic methodology can be found in the second post in this thread. For each pair of teams (a,b), we calculate the probability that a has a 15/10/-5 on any given question, and that b has a 15/10/-5 on any question, based essentially on a variant on PATH.

For the Monte Carlo simulation, we take those probabilities and assume that bonus conversion is normally distributed with mean probability (BC/30) and standard deviation = sqrt((BC/30)(1-BC/30)/(number of answered tossups)). This is used to create a set of 20 random numbers on the interval [0,3], which is then multiplied by 10 to give each team's hypothetical score on an unknown bonus.
Swank diet wrote:Is there any way to modify your model so that instead of predicting the RR outcomes by itself, you can plug in the results you generate into the actual elimination brackets and see how that's gamed out? It might be tricky (read: very difficult) to do, but then could produce a more real-world outcome. The end goal of having some way to predict outcomes of Sundays' playoffs on Saturday night seems rather insignificant, but would be very cool to see.
This is exactly what I did, with the caveat that I didn't bother subtracting out the Sunday data, so I'm using the combined Saturday-Sunday data to see what the chances of each team were to advance given the elimination brackets and the Monte Carlo RR simulation probabilities of a team beating another team. It did take a long time in Excel.
Swank diet wrote:If you send me the data file and a description of what you did, I'll see if I can't write something in R (Gordon might be better at this) that would be more universally usable (at the reseeding part of every tournament, you can run a model and see how the tournament should turn out :shock: ).
This would be very cool to see; my problem right now is getting the brackets to come out right (i.e. sending the loser to the correct place) - which, I mean, shouldn't be an issue, given that I've written a card-system simulation, so I'll see if I can't do something like that. In the meantime, I will send you:

1) a .xls file of the "Raw Stats" used
2) a .m file of the MATLAB code used for the Monte Carlo simulation (I'll comment it so you can see what each step does - you can open this in a text editor)
3) a .xls file of the actual work done computing each team's chances (warning: this is kind of unwieldy and not well cleaned-up)
Swank diet wrote:Also, have you considered trying to write something using in-match Bayesian updating? That would be an even neater way of seeing just how probable or improbable comebacks might be.
I haven't done this. From a quick off-the-cuff reaction, this might be hard to do for the first couple of rounds because very poor teams are likely to (a) not get very many, if any, tossups (thus p(get a tossup) = 0 and our posterior probability of them getting a tossup is 0) or (b) not get very many, if any, bonuses (thus p(get more than 0 on the bonus) = 0). It's certainly an interesting idea to work with, though.
Carangoides ciliarius wrote:How is it possible that we were more likely to finish 17th than 27th? Does it have anything to do with the incredibly close game we played against Rockford Auburn in that playoff round?
Reinstein and Harry are more-or-less both right. Had you gotten past the Auburn-Hume-Fogg loser in R17 (probability of that: 14%), you would have played one of {Culver, Torrey Pines, Grand Junction, St. Thomas} - you had a > 50% probability of beating Culver, around a 50% probability of beating St. Thomas, and the other two were in that particular game with total probability 5.1%. So you had a 7.4% chance of advancing past that round and a 6.6% chance of being eliminated. In Round 19, though, you would have faced with about 40% chance LASA A, 20% Eden Prairie A, 20% Dorman A, and 18% Raleigh Charter, all of which you had less than a 6.5% chance of beating; so though you had a 7.4% chance of making it to Round 19, you had a 7.2% chance of being eliminated in that round. As it was, your part of the bracket ended up harder-than-expected due to either upsets (Hume-Fogg over Auburn) or statistically worse higher seeds winning (LASA over Dorman).
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Re: Revisiting the 2010 HSNCT Playoffs

Post by Down and out in Quintana Roo »

cvdwightw wrote:
Carangoides ciliarius wrote:How is it possible that we were more likely to finish 17th than 27th? Does it have anything to do with the incredibly close game we played against Rockford Auburn in that playoff round?
Reinstein and Harry are more-or-less both right. Had you gotten past the Auburn-Hume-Fogg loser in R17 (probability of that: 14%), you would have played one of {Culver, Torrey Pines, Grand Junction, St. Thomas} - you had a > 50% probability of beating Culver, around a 50% probability of beating St. Thomas, and the other two were in that particular game with total probability 5.1%. So you had a 7.4% chance of advancing past that round and a 6.6% chance of being eliminated. In Round 19, though, you would have faced with about 40% chance LASA A, 20% Eden Prairie A, 20% Dorman A, and 18% Raleigh Charter, all of which you had less than a 6.5% chance of beating; so though you had a 7.4% chance of making it to Round 19, you had a 7.2% chance of being eliminated in that round. As it was, your part of the bracket ended up harder-than-expected due to either upsets (Hume-Fogg over Auburn) or statistically worse higher seeds winning (LASA over Dorman).
That's really fascinating. I love numbers and stats like this. Interesting stuff. Man, that 5-point loss to such an awesome team still really hurts...
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Re: Revisiting the 2010 HSNCT Playoffs

Post by Stained Diviner »

cvdwightw wrote:
Swank diet wrote:Also, have you considered trying to write something using in-match Bayesian updating? That would be an even neater way of seeing just how probable or improbable comebacks might be.
I haven't done this. From a quick off-the-cuff reaction, this might be hard to do for the first couple of rounds because very poor teams are likely to (a) not get very many, if any, tossups (thus p(get a tossup) = 0 and our posterior probability of them getting a tossup is 0) or (b) not get very many, if any, bonuses (thus p(get more than 0 on the bonus) = 0). It's certainly an interesting idea to work with, though.
This would be pretty cool, but HSNCT would be a particularly difficult place to do it. The timed matches make it difficult to know how many questions are left, which could significantly affect the probability of a comeback--to get a meaningful result, especially later in the match, you would have to keep track of time on the clock and use it to figure out how many questions are likely to be left. Also, the size and complexity of the tournament make it difficult to get and calculate all the statistics you need going into the match.
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