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April 8, 2015

Kerry Greene’s run is statistically improbable

When Kerry Greene won her fifth Jeopardy! match last night, it was the third consecutive game in which she’d won from behind. I thought that feat was relatively rare – maybe once or twice a season, tops. Turns out I was overestimating.

According to J! Archive data, Kerry is just the fourth player in Jeopardy! history* to win three straight games when trailing before Final – and the first five-timer to do so.

Why is this so rare? Let’s start with some basic statistics.

If you can’t get a lock, get the lead

This one is simple: if possible, you want to be in the lead heading into Final Jeopardy!.

Pre-Final position of winners solid

It should come as no surprise that the player in the lead heading into Final wins most frequently: about 71.7% of the time since Ken Jennings lost.

Here’s that same chart showing only players who have won 5 or more games.

Pre-Final position of winners 5x plus solid

Be in first heading into Final, and you’re much more likely to win.

This is particularly true if you have a lock, of course. In fact, 5xers have a much higher lock rate than the population as a whole: 35.0% against 23.2%. (In non-lock situations, first wins a little under half the time in both cases.)

In any position, it also helps to get Final correct, as Kerry has done all five times.

A simulation: flipping coins

Another way to demonstrate the statistical improbability of what Kerry has done is by simulating the Final Jeopardy! outcomes of these three games.

Let’s assume, as I often do, that every player has a 50% chance of getting Final right, and there is no correlation between players’ responses. (In other words, every player is flipping a coin.)

Game 3: Kerry, in second, could win only if she got it right and Tom got it wrong.
Probability: 1/2 * 1/2 = 1/4

Game 4: Kerry, in third, could win only if she were the only player to respond correctly.
Probability: 1/2 * 1/2 * 1/2 = 1/8

Game 5: Kerry, in second, could win only if she got it right and Evan missed.
Probability: 1/2 * 1/2 = 1/4

The probability that all of these things work out is 1/128, or 0.78%. (Kerry could have improved her odds by wagering more conservatively.)

Kerry’s company

As I mentioned, Kerry is not alone in winning three in a row from behind. 4xer and eventual TOCer Carolyn White won her first three games in this fashion in 1998. More recently, two 3xers have pulled off the feat: Kristina Caffrey (2008) and Jessamine Price (2012).

(Some good news for Kerry, perhaps: two of those players took the lead into Final in their next game.)

Nor is Kerry the first 5xer to come from behind thrice overall. J.J. Todor, Paul Nelson, and Joel Pool all faced deficits three times in their first five games, with Joel even winning his sixth game from second.

But to make a longer run, a player needs to be in first more consistently. Ken Jennings never trailed in regular play. Neither did Julia Collins or Arthur Chu – until the games they lost. Of all champions with 7 wins or more, only 19-game-winner David Madden won from behind three times.

*EDIT: As expected, the fine historians over at JBoard knew of some examples not in the J! Archive. Sara Cox‘s first three games were come-from-behind victories, but as the first two were ties that wouldn’t happen in today’s environment (the leader withheld the dollar), I’m loathe to add it. Frank Epstein‘s five wins featured three second-place Finals.

Player Wins Lock First Second Third
Ken Jennings 74 65 9
Julia Collins 20 12 8
David Madden 19 11 5 3
Arthur Chu 11 7 4
Dan Pawson 9 3 5 1
Jason Keller 9 3 4 2
Ben Ingram 8 2 5 1
Drew Horwood 8 1 5 1 1
Tom Kavanaugh 8 3 3 1 1
Tom Nissley 8 1 6 1
Joon Pahk 7 4 2 1
Justin Bernbach 7 2 5
Keith Whitener 7 3 2 2
Stephanie Jass 7 5 2
Tom Walsh 7 1 6
Andrew Moore 6 2 4
Christopher Short 6 1 3 1 1
Dave Leach 6 3 1 2
Jared Hall 6 3 1 2
Jason Zollinger 6 1 5
Jim Stevens 6 2 4
Joel Pool 6 2 4
Justin Sausville 6 1 4 1
Kevin Marshall 6 2 1 3
Larissa Kelly 6 2 2 2
Roger Craig 6 4 2
Sandie Baker 6 3 2 1
Sean Ryan 6 1 5

Jeopardy! is a tough game to win – and it’s even tougher to win when you’re trailing.

  1. Joel Poole won all 6 of his games without a lock and Drew Horwood 8 of 9. Both probably ran on the high end of variance of getting FJ correct. Joel seems to hold the record for most come from behind wins with 4?

    • That’s right – looks like Joel is the only one to hit that number. And Drew didn’t have his lock until his 8th game, which is incredible.

  2. Mark Barrett permalink

    The 1990 player is Sara Cox, not Sara Pool.

  3. Shane permalink

    Looks like Andrew Haringer joins the list of players to come from behind three games in a row, and the first male ever to do so!

  4. Cerulean permalink

    Brad Plovan also apparently had three wins from behind (not necessarily in a row though).

What do you think?