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February 9, 2015

Wild cards: underperformers in the later rounds

Over the months, I’ve developed a nice color scheme for Jeopardy! tournaments. As with regular winners, quarterfinal winners are marked with green, like an optimal wager; wild cards get orange, usually reserved for acceptable alternative wagers.

In my mind, an orange wager is as good as a green wager. Is the same true for the strengths of the two flavors of semifinalists?

The short answer: no.

Jeopardy tournament champions

Significant at p < .10. Z-score: -1.76 (p = 0.294; π = 0.444; n = 34)

Assuming each semifinalist is evenly matched, we should expect wild cards to win 4 out of every 9 tournaments, or around 15 of the 34 that have taken place since Season 21. They’ve won only 10.

Perhaps even more surprising is the rate at which wild cards make the Finals. Even when spotted a 2-1 advantage against a lone quarterfinal winner, they bat only around 27%.

Jeopardy semifinal results

Significant at p < .05, disregarding 0 or 3 WCs. Z-score: -2.03 (p = 0.392; π = 0.503; n = 84)

(That red bar, as you likely recall, is from the Season 29 Teen Tournament triple-zero debacle. The third finalist spot was taken by Leonard Cooper, a QF winner.)

When I ran these stats, I was surprised to see any games pitting three wild cards. I figured the contestant coordinators would even things out in most tournaments, sticking at least one wild card in each match.

Turns out they do that over half of the time.

Jeopardy tournament champs by semifinal distribution

This chart certainly caught my eye. When the wild cards are spread out, one has taken down the whole thing 7/19 times. When three are in a single game – which guarantees at least one wild card and one QF champ in the Finals – they’re 2/3.

But look at that middle bar. When the producers put three QF winners in one match and put two wild cards in each of the others, the wild cards are a dismal 1/12 as champions.

It’s not as if they don’t have a chance. Thrice have 2 wild cards met in the Finals after facing this distribution, but even then only once has one reigned supreme (Michael Falk in the S22 TOC).

Jeopardy wild cards in finals

2-2-0 is significant at p < .05 (Z-score: -2.60)

So we have some statistically significant evidence that wild cards are, on average, weaker than quarterfinal winners, particularly when it comes to advancing to the Finals. Why might this be?

A few possible explanations:

Steamrollers. Players who are strong in the first round, perhaps sewing up a victory before Final, are more likely to be strong in subsequent rounds.

Less incentive to wager big in the quarterfinals. A player with the lead, who might have lost a game with ‘normal’ wagering, might have been up against someone willing to play for the wild card rather than the outright win. It’s also possible the leader wagered small in order to preserve her own position. Which leads to…

Confidence keeps rolling. Someone who’s already won a game knows the feeling, and has some built-in confidence heading into Week Two. Some or all of the wild cards might feel like they’re lucky to be there – or even worse, that they don’t deserve their semifinal slot, and that might come through in their play.

Back-door semifinalists. As I suggested last week, sometimes Final Jeopardy! is a crapshoot that rewards players who are lucky.

I’m sure I’ll run the stats on all of these eventually, but for now: What do you think? I’d love to hear your thoughts in the comments below.

This Teachers Tournament has a 2-1-1 format, which suggests the wild cards have a fighting shot.

In case you’re interested in running the data yourself, here are summaries of the 34 tournaments used in this study.

Wild Cards in…
Tournament Champ SF Distribution Finals Champ’s SF
S21 TOC Wild Card 2-1-1 1 2
S21 College QF Winner 2-1-1 1 1
S21 Teen QF Winner 2-2-0 1 0
S22 College QF Winner 2-2-0 0 2
S22 Teen QF Winner 2-1-1 0 1
S22 TOC Wild Card 2-2-0 1 2
S23 Teen Wild Card 2-1-1 2 2
S23 College Wild Card 3-1-0 1 3
S23 Teen Summer Wild Card 2-1-1 2 2
S24 TOC Wild Card 2-1-1 2 2
S24 Teen QF Winner 2-1-1 0 1
S24 College QF Winner 2-2-0 1 2
S25 Teen QF Winner 3-1-0 1 1
S25 TOC QF Winner 2-2-0 0 2
S25 College QF Winner 2-1-1 1 1
S26 Teen Wild Card 3-1-0 1 3
S26 College QF Winner 2-1-1 1 1
S26 TOC QF Winner 2-2-0 2 0
S27 College QF Winner 2-1-1 1 1
S27 Teen Wild Card 2-1-1 2 2
S27 Teachers QF Winner 2-1-1 0 1
S28 TOC QF Winner 2-2-0 0 0
S28 College Wild Card 2-1-1 3 1
S28 Teachers QF Winner 2-2-0 0 0
S28 Teen QF Winner 2-1-1 2 1
S29 Teachers QF Winner 2-2-0 2 0
S29 Teen QF Winner 2-1-1 0 1
S29 TOC QF Winner 2-2-0 1 2
S29 College QF Winner 2-1-1 1 1
S30 Teachers QF Winner 2-1-1 2 1
S30 College QF Winner 2-2-0 2 0
BOTD QF Winner 2-2-0 0 2
S30 Teen Wild Card 2-1-1 1 1
S31 TOC QF Winner 2-1-1 1 1

 

3 Comments
  1. Ben Wiles permalink

    I think the steamroller effect may be the strongest here. I’d be interested in seeing how far above average the pre-FJ QF scores of eventual tournament winners are, and whether they won their QF in a lock. I’d also be interested in knowing how often steamrollers crash out in the semis.

What do you think?