What's the length of the average championship reign?

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schoe
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What's the length of the average championship reign?

Post by schoe »

This thread got me thinking... what is the length of the average championship reign on Jeopardy (mean? median? mode? standard deviation?)? I imagine someone knows this or could figure it out from j-archive...? Has anyone ever calculated this?
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Re: What's the length of the average championship reign?

Post by Rafferty Barnes »

I'm pretty sure the average championship jeopardy reign...is one.

From Jared Cohen's book, How I got on Jeopardy!... and Won 75% of contestants lose in their first game, 15% win one, 5% win 2, and the remaining 5% is all the rest.
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Re: What's the length of the average championship reign?

Post by TenPoundHammer »

About 12 feet, or just under 4 metres if you're Canadian.
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Re: What's the length of the average championship reign?

Post by JayK33 »

I'd say the average is 3. We've had plenty of 5+ time champs and of course the constant one and dones. I definitely think the number is higher than 1.
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Re: What's the length of the average championship reign?

Post by BigDaddyMatty »

For the past five seasons (not counting Choyon's in-progress reign), the averages are as follows:
Season 27: 1.85
Season 28: 1.89
Season 29: 2.06
Season 30: 2.01
Season 31: 2.01
Overall: 1.96
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Re: What's the length of the average championship reign?

Post by squizzle »

BigDaddyMatty wrote:For the past five seasons (not counting Choyon's in-progress reign), the averages are as follows:
Season 27: 1.85
Season 28: 1.89
Season 29: 2.06
Season 30: 2.01
Season 31: 2.01
Overall: 1.96
Mind sharing how you got those numbers? Not doubting you or anything, I'm just genuinely curious.
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Re: What's the length of the average championship reign?

Post by triviawayne »

There are also the outliers of Chu and Collins to pump up the number a tiny bit.
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Re: What's the length of the average championship reign?

Post by TheyCallMeMrKid »

schoe wrote:This thread got me thinking... what is the length of the average championship reign on Jeopardy (mean? median? mode? standard deviation?)? I imagine someone knows this or could figure it out from j-archive...? Has anyone ever calculated this?
Is the question meant to include all of the contestants who don't become a champion at all (reign=0), or only the average of those whose reign is >0?
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Re: What's the length of the average championship reign?

Post by schoe »

TheyCallMeMrKid wrote:
schoe wrote:This thread got me thinking... what is the length of the average championship reign on Jeopardy (mean? median? mode? standard deviation?)? I imagine someone knows this or could figure it out from j-archive...? Has anyone ever calculated this?
Is the question meant to include all of the contestants who don't become a champion at all (reign=0), or only the average of those whose reign is >0?
The latter. The former would always approach an average of 0.5 as the number of games increases, no? Because each day you're adding two new players and adding one new victory (barring the former ties and five-day champ rules)?
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Re: What's the length of the average championship reign?

Post by Vermonter »

The data on these three posts (1 2 3) are a few months old but should give you what you need.

Of note: since the last TOC, 7/8 players playing their fifth game have won. Elliot Yates is the only one who didn't.
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Re: What's the length of the average championship reign?

Post by Blue Lion »

triviawayne wrote:There are also the outliers of Chu and Collins to pump up the number a tiny bit.
I wondered about the effect of "super-champs" on the average, and whether they made the average significantly different from the median.
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Re: What's the length of the average championship reign?

Post by mfc248 »

Vermonter wrote:The data on these three posts (1 2 3) are a few months old but should give you what you need.

Of note: since the last TOC, 7/8 players playing their fifth game have won. Elliot Yates is the only one who didn't.
The second of those posts has a link from Robert K S to a script that gives the succession of champions since Ken Jennings, and their games and money won. Throwing that data into Excel yields an average of 1.83 games won for the 1,054 champions post-KJ.

621 (58.9%) were 1x champs; another 235 (22.3%) were 2x.
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Re: What's the length of the average championship reign?

Post by triviawayne »

Blue Lion wrote:
triviawayne wrote:There are also the outliers of Chu and Collins to pump up the number a tiny bit.
I wondered about the effect of "super-champs" on the average, and whether they made the average significantly different from the median.
I'm not much of a math guy, but I doubt it would have much of an effect; I just wanted to throw it out there because it does have some meaning.
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Re: What's the length of the average championship reign?

Post by schoe »

mfc248 wrote:
Vermonter wrote:The data on these three posts (1 2 3) are a few months old but should give you what you need.

Of note: since the last TOC, 7/8 players playing their fifth game have won. Elliot Yates is the only one who didn't.
The second of those posts has a link from Robert K S to a script that gives the succession of champions since Ken Jennings, and their games and money won. Throwing that data into Excel yields an average of 1.83 games won for the 1,054 champions post-KJ.

621 (58.9%) were 1x champs; another 235 (22.3%) were 2x.
Safe to say that the median and mode are both 1 then.
TheyCallMeMrKid wrote:
schoe wrote:This thread got me thinking... what is the length of the average championship reign on Jeopardy (mean? median? mode? standard deviation?)? I imagine someone knows this or could figure it out from j-archive...? Has anyone ever calculated this?
Is the question meant to include all of the contestants who don't become a champion at all (reign=0), or only the average of those whose reign is >0?
I guess a converse question to my original post is, what percentage of contestants do not become champions (i.e., do not win one game)? I imagine that could be derived from the championship averages and the total number of games played, but I don't feel like doing the math now, so I just throw that out there if anyone else wants to derive. :D
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Re: What's the length of the average championship reign?

Post by BigDaddyMatty »

schoe wrote:I guess a converse question to my original post is, what percentage of contestants do not become champions (i.e., do not win one game)? I imagine that could be derived from the championship averages and the total number of games played, but I don't feel like doing the math now, so I just throw that out there if anyone else wants to derive. :D
Assuming that
mfc248 wrote:The second of those posts has a link from Robert K S to a script that gives the succession of champions since Ken Jennings, and their games and money won. Throwing that data into Excel yields an average of 1.83 games won for the 1,054 champions post-KJ.
is correct, there have been approximately 1,929 regular games from Ken's loss to Andrew Haringer's last win. Each game has two new contestants, so there have been 3,858 new contestants over that span. That means that 72.7% of contestants (2,804/3,858) never won a game.
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Re: What's the length of the average championship reign?

Post by BigDaddyMatty »

squizzle wrote:
BigDaddyMatty wrote:For the past five seasons (not counting Choyon's in-progress reign), the averages are as follows:
Season 27: 1.85
Season 28: 1.89
Season 29: 2.06
Season 30: 2.01
Season 31: 2.01
Overall: 1.96
Mind sharing how you got those numbers? Not doubting you or anything, I'm just genuinely curious.
I manually entered data from the archive into Excel. I'm sure there's a better way, but it was the best tool I had at my disposal.
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Re: What's the length of the average championship reign?

Post by goatman »

I think the figure you're looking for is not the mean, but either the median or even the mode, which for the subset of players who win at least one game, are both near one (75% of winners win just one, so the mode (def: most common occurring value) = one; remember, 67% of all contestants come in 2nd or 3rd!); for the subset of players who win at least two games, it seems the median = mode = 2, from above discussion thread. So getting 3 or more wins is definitely an outlier!
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Re: What's the length of the average championship reign?

Post by squizzle »

BigDaddyMatty wrote: That means that 72.7% of contestants (2,804/3,858) never won a game.
That corresponds nicely with The Final Wager's model from his 1st link simulating a 27.8% probability of a new contestant winning his/her game.
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Re: What's the length of the average championship reign?

Post by DadofTwins »

BigDaddyMatty wrote:
schoe wrote:I guess a converse question to my original post is, what percentage of contestants do not become champions (i.e., do not win one game)? I imagine that could be derived from the championship averages and the total number of games played, but I don't feel like doing the math now, so I just throw that out there if anyone else wants to derive. :D
Assuming that
mfc248 wrote:The second of those posts has a link from Robert K S to a script that gives the succession of champions since Ken Jennings, and their games and money won. Throwing that data into Excel yields an average of 1.83 games won for the 1,054 champions post-KJ.
is correct, there have been approximately 1,929 regular games from Ken's loss to Andrew Haringer's last win. Each game has two new contestants, so there have been 3,858 new contestants over that span. That means that 72.7% of contestants (2,804/3,858) never won a game.
The 3,858 number should be a handful lower, as it doesn't account for ties, but it's probably close enough.
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Re: What's the length of the average championship reign?

Post by BobF »

Rafferty Barnes wrote:I'm pretty sure the average championship jeopardy reign...is one.

From Jared Cohen's book, How I got on Jeopardy!... and Won 75% of contestants lose in their first game, 15% win one, 5% win 2, and the remaining 5% is all the rest.
The mode at least has to be one.
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