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February 1, 2016

Wild-card wagering: College edition

2016 College Championship
schools represented wild-card wagering
QF1 QF2 QF3 QF4 QF5 SF1 SF2 SF3 F1 F2

If you can’t get a win in the quarterfinals, it’s not the end of the world – there are those four wild cards for the highest-scoring non-winners.

(Take a drink every time Alex Trebek says that.)

As I do for every tournament, I’ll be using past data to analyze the wild-card race in the upcoming College Championship. I’m using all non-winning quarterfinal scores from Season 13 on, as J! Archive’s Collegiate data is sporadic before then; Season 6 has the only other complete set of scores.

Here is a scatter plot, with lines connecting the fourth wild-card spot (green) and the “first person out”, the fifth-place non-winner (pink).

College QF nonwinning scores

Starting with Season 21, the wild-card cut-off has been fairly consistent, generally falling in the 10k-15k range. The prediction I pulled out on Friday’s video was 14,500, about one standard deviation higher than average. (That was a random number, but I see no compelling reason to disavow it.)

Some stats:

Highest cut-off:

  • Overall, adjusted: 18,600 (Season 13)
  • Doubled clues: 15,800 (Season 27)

Lowest cut-off:

  • Overall, adjusted: 5,600 (Season 15)
  • Doubled clues: 7,999 (Season 20)

Average cut-off:

  • Overall, adjusted: 12,020 (standard deviation: 3,565)
  • Doubled clues: 11,813 (standard deviation: 2,356)

Now, what should you wager if you have $X heading into Final? That depends on a few things.

I don’t have to win. What do I do?

Here are a couple of basic considerations:

One: do you have a chance to win the game? That secure berth might be worth considering. (It might also cap your wager if you’re in first place.)

Two: if you don’t win the game, will you finish in second or third? If the latter, you know you’ve already got someone ahead of you, so your chances of advancing are reduced.

If you’re not sure whether you’ll finish in second or third, you might have to play more aggressively.

I discussed the methodology for these calculations in my introduction to combinatorics. Remember, in the quarterfinals, players are sequestered until their game, so they have no idea what previous scores might have been.

If you are unfamiliar with how Jeopardy! tournaments work, check out the video above or read this post.

Let’s get to the numbers.

Finishing in second place

A few comments:

  • “Odds” indicates the probability that a player will advance with their current score.
  • To make things cleaner, I rounded to zero any wager that was insignificant against the pre-Final score.
  • The quirks in the suggested wagers (e.g., wagering 1,300 with 13,000 at 40% when you’d wager nothing at 11,000) are the result of quirks in the actual data.
Confidence level
Score Odds 20% 30% 40% 50% 60% 70% 80%
1,000 <1% 0 900 900 900 900 900 900
2,000 1% 0 0 2,000 2,000 2,000 2,000 2,000
3,000 2% 0 3,000 3,000 3,000 3,000 3,000 3,000
4,000 2% 4,000 4,000 4,000 4,000 4,000 4,000 4,000
5,000 3% 4,900 4,900 4,900 4,900 4,900 4,900 4,900
6,000 7% 6,000 6,000 6,000 6,000 6,000 6,000 6,000
7,000 11% 7,000 7,000 7,000 7,000 7,000 7,000 7,000
8,000 14% 7,900 7,900 7,900 7,900 7,900 7,900 7,900
9,000 21% 0 8,700 8,700 8,700 8,700 8,700 8,700
10,000 28% 0 7,700 7,700 7,700 8,700 9,100 9,300
11,000 39% 0 0 0 5,500 8,300 8,300 8,300
12,000 57% 0 0 0 0 3,900 5,100 6,700
13,000 64% 0 0 1,300 1,300 1,400 2,900 3,500
14,000 74% 0 0 0 0 1,700 2,300 2,300
15,000 87% 0 0 0 0 0 0 1,300
16,000 95% 0 0 0 0 0 0 0
17,000 98% 0 0 0 0 0 0 0
18,000 99% 0 0 0 0 0 0 0
19,000 99% 0 0 0 0 0 0 0
20,000 99% 0 0 0 0 0 0 0

Finishing in third place

When one spot ahead is already occupied, a player has to be more aggressive.

Confidence level
Score Odds 20% 30% 40% 50% 60% 70% 80%
1,000 <1% 900 900 900 900 900 900 900
2,000 <1% 2,000 2,000 2,000 2,000 2,000 2,000 2,000
3,000 1% 3,000 3,000 3,000 3,000 3,000 3,000 3,000
4,000 1% 4,000 4,000 4,000 4,000 4,000 4,000 4,000
5,000 1% 4,900 4,900 4,900 4,900 4,900 4,900 4,900
6,000 3% 6,000 6,000 6,000 6,000 6,000 6,000 6,000
7,000 5% 7,000 7,000 7,000 7,000 7,000 7,000 7,000
8,000 7% 7,900 7,900 7,900 7,900 7,900 7,900 7,900
9,000 12% 8,700 8,700 8,700 8,700 8,700 8,700 8,700
10,000 16% 9,300 9,300 9,300 9,300 9,300 9,300 9,300
11,000 24% 600 8,300 8,300 9,100 9,100 9,100 9,300
12,000 39% 0 0 6,700 6,700 9,300 9,300 9,300
13,000 45% 0 1,300 1,300 3,500 5,900 6,100 7,100
14,000 57% 0 0 0 2,300 2,300 2,300 4,700
15,000 73% 0 0 0 0 0 2,700 3,400
16,000 85% 0 0 0 0 0 0 1,300
17,000 92% 0 0 0 0 0 0 1,700
18,000 96% 0 0 0 0 0 0 0
19,000 99% 0 0 0 0 0 0 0
20,000 99% 0 0 0 0 0 0 0
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