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November 9, 2015

Monday, November 9, 2015 – ToC2015 QF #1

2015 Tournament of Champions
Pre-tourney stats: Pre-Final position Forrest Bouncing
Coryat scores
QF preview SF preview
QF1 QF2 QF3 QF4 QF5 SF1 SF2 SF3 F1 F2

We’re off and running in the 2015 Tournament of Champions! Will Dan, Vaughn, or Catherine earn the first semifinal berth?

Are you in the #Vaughntourage!?…

vaughntourage

…or are you a #FanofDan?

fanofdan

What a rush this episode was! My model had Catherine in the lead heading into Final – but not with scores like this.

Dan

Feitel

Vaughn

Winchell

Catherine

Hardee

7,800 17,200 17,800

Everyone’s in decent position with this Final Jeopardy! category:

AMERICAN AUTHORS

I built a calculator to derive optimal wagers depending on a player’s confidence level in the category. It uses all past non-winning scores from ToCs.

I’ll write about it in more depth later this week, but here’s what it says:

Dan Vaughn Catherine
7,800 17,200 17,800
Current percentile 54% 95% 96%
20% confidence 0 400 0
30% confidence 0 400 0
40% confidence 5,300 400 0
50% confidence 5,300 400 0
60% confidence 5,300 400 800
70% confidence 7,300 400 800
80% confidence 7,300 2,900 2,300

Now, one thing the calculator does not take into account is winning outright – to see what everyone should do there, we’ll do some old-school math.

First-order calculations

My first assumption is that Vaughn will wager Shoretegically – that is, he’ll keep Dan locked out no matter what. He can max out at 1,600, and Catherine can cover him with a wager of 1,000.

Dan
Vaughn
Catherine
7,800 17,200 17,800
FIRST-ORDER SECOND-ORDER COVER ZERO
min max min max min max
1,600 1,000

Second-order calculations

Now, as you’ll see in my video, I think maybe Vaughn will take Catherine’s potential 1,000 wager into account and cap his bet at 399, but that’s probably going too far, right?

Right?

What actually happened

Dan Vaughn Catherine
7,800 17,200 17,800
6,200 601 200
14,000 16,599 17,600
min max min max
601 1,599 1,001 1,199
399 199

…and then Catherine comes out of nowhere with a fourth-level wager of 200. Note that if Vaughn had indeed wagered 399 and gotten it right, Catherine would have won by a dollar!

Seriously – someone’s been doing her homework when it comes to wagering! Huge gold star for Catherine, and my sincere gratitude to all three players for a spectacular start to the tournament.

Quarterfinal winners:

  1. Catherine Hardee

Wild-card race:

  1. Vaughn Winchell – 16,599 (98%)
  2. Dan Feitel – 14,000 (84%)

Percentage represents probability of advancing based on past ToC data. Although it’s not a Gaussian distribution, the average non-winning score is 8,290 with standard deviation 6,306.

The Final Jeopardy! clue

AMERICAN AUTHORS
HE WAS THE FIRST TO HAVE BOTH FICTION AND NONFICTION NUMBER ONE NEW YORK TIMES BEST SELLERS; THE LATTER FEATURED HIS BELOVED POODLE

Correct response: Show

The Final Wager – November 9, 2015
2015 Tournament of Champions
Pre-tourney stats: Pre-Final position Forrest Bouncing
Coryat scores
QF preview SF preview
QF1 QF2 QF3 QF4 QF5 SF1 SF2 SF3 F1 F2

5 Comments
  1. bill permalink

    you don’t think Dan should have gone all in for the wild card chances to increase because if he misses the question he’s out.

  2. I thought there were a lot of category four questions in this episode. By that I mean: category ones are the ones you think you know (whether or not you actually do) within the time allotted and answer; category twos are the ones you think you could have gotten if only you had more time (“Oh, that’s right!”); and category threes are the ones that you would never have gotten even if you had all the time in the world. And some of the category threes are those that make you say, “How could they possibly even know that?” Those are category four.

What do you think?