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December 21, 2015

Predicting wild cards: a combinatoric model

In my last two posts, I introduced you to some of the basics of combinatorics: permutations and combinations. Now, I’m going to tie this concept into something that Jeopardy! tournament players might find useful:

How do I calculate the probabilities for wild card contenders to advance?

With the help of several sources – J! Archive, JBoard.tv, Kelly the Wagering Strategist’s notes – I’ve compiled most of the past non-winning scores from quarterfinals. (You can find a table with all historical ToC quarterfinal scores at the bottom of this post.)

For my model, I take those scores as roughly representative of what might happen in a given tournament. Using those numbers, it’s just a matter of calculating the probability that a given score gets bumped off the leaderboard.

In this post, we’ll look at the situation after the second quarterfinal of the most recent Tournament of Champions, won by Alex Jacob. For those who have already played, I’m including the percentage of past non-winning ToC scores that finished below their totals.

toc2015qf2wc

Note that I do not include the winners of future quarterfinals. In any given game, at most two players will have a shot at a wild card; I’m using the faces you see here to make the examples easier to follow.

The Bubble Player

The easiest odds to calculate are those of the player sitting “on the bubble”– in the fourth wild-card slot. If just one non-winner finishes with a higher total, the Bubble Player’s tournament is over.*

After two games, Greg Seroka sat in the fourth position. His total of 11,500 was better than 71% of all past non-winning scores. As I noted at the time, 11,500 is unusually high for that spot with so many games yet to be played; the cut-off in the 2014 ToC, after all, was 9,100.

Using this number as a probability, what are the odds that none of the four remaining non-winners beat Greg? (Remember, when we want to determine the probability that ALL independent events happen, we multiply their probabilities together.)

The odds are 71% x 71% x 71% x 71% x 71% x 71%, or 0.716. That’s about a 12.8% chance of surviving.

*Yes, a fifth wild-card slot will open up if a QF ends with no winner. That possibility has almost no effect on these calculations.

The #3 spot: slightly better

The higher positions are harder to calculate, because there are more ways that can work out in those players’ favor. Let’s consider the third-place position, held by Kristin Sausville. She had 12,800, better than 78% of past non-winning scores.

What is the probability none of the remaining players beats her?

78% x 78% x 78% x 78% x 78% x 78% = 0.786 = 22.5%

Not so great, either. But Kristin has a bit more wiggle room than Greg: it’s fine if one non-winner beats her score. So we need to find a way to calculate that.

Let’s consider the different ways exactly one remaining non-winner could finish with a higher total than Kristin:

  • only John does
  • only Jennifer does
  • only Andrew does
  • only Elliot does
  • only Scott does
  • only Michael does

That’s six different possibilities. What is the probability of each? I’ll make a table to make this more visual.

beats Kristin John Jennifer Andrew Elliot Scott Michael Probability
John only 22% 78% 78% 78% 78% 78% 6.35%
Jennifer only 78% 22% 78% 78% 78% 78% 6.35%
Andrew only 78% 78% 22% 78% 78% 78% 6.35%
Elliot only 78% 78% 78% 22% 78% 78% 6.35%
Scott only 78% 78% 78% 78% 22% 78% 6.35%
Michael only 78% 78% 78% 78% 78% 22% 6.35%
Total 38.1%

Each of these combinations has a 6.35% chance of occurring.

When we want to calculate the probability that ANY combination happens, we add the probabilities together. Thus, using our assumptions, there is a 38.1% chance – six times 6.35% – that one and only one remaining player will pass Kristin’s score.

Combine this with the 22.5% probability that no one beats her and we get odds of around 60% for Kristin to advance. (In my actual analysis, I put her at 62%, because I didn’t round the initial 78% percentage.)

The #2 spot: many more possibilities

Let’s keep rolling. In second place after two quarterfinals was Dan Feitel, whose score of 14,000 was better than 82% of all non-winning scores, historically.

The probability that no one beats him:

82% x 82% x 82% x 82% x 82% x 82% = 0.826 = 30.4%

The probability that exactly one player beats him, using the pattern we identified with Kristin:

82% x 82% x 82% x 82% x 82% x 18% x 6 = 0.825 x 0.181 x 6 = 40.0%

Already, Dan has around a 70% chance of advancing. But he’ll also advance if exactly two players pass him. How do we calculate the odds that this takes place?

Let’s set up another table to find the various possibilities:

Combo # John Jennifer Andrew Elliot Scott Michael Probability
1 18% 18% 82% 82% 82% 82% 1.46%
2 18% 82% 18% 82% 82% 82% 1.46%
3 18% 82% 82% 18% 82% 82% 1.46%
4 18% 82% 82% 82% 18% 82% 1.46%
5 18% 82% 82% 82% 82% 18% 1.46%
6 82% 18% 18% 82% 82% 82% 1.46%
7 82% 18% 82% 18% 82% 82% 1.46%
8 82% 18% 82% 82% 18% 82% 1.46%
9 82% 18% 82% 82% 82% 18% 1.46%
10 82% 82% 18% 18% 82% 82% 1.46%
11 82% 82% 18% 82% 18% 82% 1.46%
12 82% 82% 18% 82% 82% 18% 1.46%
13 82% 82% 82% 18% 18% 82% 1.46%
14 82% 82% 82% 18% 82% 18% 1.46%
15 82% 82% 82% 82% 18% 18% 1.46%
Total 22.0%

I count 15 different combinations of two players. That means the probability that exactly two players beat Dan is

82% x 82% x 82% x 82% x 18% x 18% x 15 = 0.824 x 0.182 x 15 = 22.0%

Let’s line these up and see if there’s a pattern.

Outcome Worse Better Combinations Total
Zero players better 0.826 x 0.180 x 1 30.4%
One player better 0.825 x 0.181 x 6 40.0%
Two players better 0.824 x 0.182 x 15 22.0%
Odds of advancing 92.4%

This looks promising: the exponents for the “worse” and “better” probabilities always add up to six, because all future players must finish either worse or better than our chosen player.

Have you figured out how we populate the “combinations” column? That’s right: in every case, we’re finding a “combination of n choose k” possibilities, where n is the total number of players remaining (six), and k is the number of players who finish higher than Dan in that particular scenario.

Recall that the number of combinations when you choose k objects from a population of n is

nCk = n!
k! x (nk)!

Therefore:

6C0 = 6! = 6! = 1
0! x (6-0)! 1 x 6!
6C1 = 6! = 6! = 6 x 5! = 6
1! x (6-1)! 1 x 5! 5!
6C2 = 6! = 6! = 6 x 5 x 4! = 30 = 15
2! x (6-2)! 2 x 4! 2 x 4! 2

One of the neat things about combinations is it actually doesn’t matter whether I’m looking at the number of players who finish better than Dan, or the number of players who finish worse than Dan. If I were to instead find the number of combinations in which exactly five players finish with a lower total – 6 choose 5, in other words – I’ll get:

6C5 = 6! = 6! = 6 x 5! = 6
5! x (6-5)! 5! x 1 5!

…which is exactly the same as 6C1 (six choose one), the number of combinations in which exactly one player finishes higher.

The #1 seed: an exercise

Time to put to work what you’ve learned so far.

After QF #2, Vaughn Winchell led the wild card pack with 16,599, a total higher than 95% of past non-winning scores.

Compared with Dan, Vaughn has one additional fallback to still qualify for the next round: if exactly three of the remaining non-winning players finish with a higher score.

Even without this option, Vaughn already has a 99.8% chance of moving on. But what should I put in the green cells to make this complete?

Outcome Worse Better Combinations Total
Zero players better 0.956 x 0.050 x 1 73.5%
One player better 0.955 x 0.051 x 6 23.2%
Two players better 0.954 x 0.052 x 15 3.1%
Three players better x x
Odds of advancing

Here’s what this should look like:

Correct response: Show

If you’re interested in another, try this: in the 2004 Tournament of Champions, I sat in third place on the wild-card standings after 3 quarterfinal matches (meaning there were four players remaining who could beat me).

Assuming a player has a 40% chance of finishing below my score of 3,500, what were the odds that I’d advance?

Correct response: Show

Potential issues

This model comes with some issues, of course.

Non-winning scores are not consistent from tournament to tournament; the strength of competitors and the difficulty of material vary widely.

Second, as I’ve pointed out in the past, Final Jeopardy! plays an outsized factor in determining wild cards, and there is probably an underlying correlation missing from the math above. The Final clue in this year’s QF #4 played much, much easier than the others, for example; Elliot Yates, however, didn’t have enough money to make anything of it.

Because the assignment of FJ! clues is random, I feel safe in ignoring any effects from the vagaries of their difficulty.

What’s next?

In my concluding post in this series – which I’ll certainly publish before the College Championship tapes in the new year – I’ll share the model behind my Wild Card Wagering Calculator (WC2), which takes into account your confidence level in the category.

For example, if you’ve got 8,000 heading into Final Jeopardy! in a ToC quarterfinal, and you’ll probably finish second in the game, you should wager as follows:

wcwcpreview

Stay tuned!

Past ToC wild card data

#PlayerQFScoreFinishRankPre-FJ!FJ!Adj
S02John Genova1QF10third9eliminated1,800WFJW0
S02Elise Beraru1QF10second7eliminated6,400WFJW0
S02Ric Moser1QF13,599firstwinner8,200WFJW7,198
S02Liz Caccese2QF24,100second34,100RFJR8,200
S02Jerry Frankel2QF23,300third4cut-off wild card bubble5,800WFJW6,600
S02Larry Floyd2QF28,600firstwinner6,500RFJR17,200
S02Paul Croshier3QF3-800third10eliminated-800--FJE-1,600
S02Paul Boymel3QF37,601firstwinner6,000RFJR15,202
S02John Hnat3QF34,800second23,800RFJR9,600
S02Bruce Fauman4QF410,100firstwinner9,100RFJR20,200
S02Paula Tupper4QF42,100third5alternate eliminated bubble3,100WFJW4,200
S02Steve Rogitz4QF47,000second14,000RFJR14,000
S02Michael Day5QF50third8eliminated2,400WFJW0
S02Nathan Walpow5QF53second6eliminated2,600WFJW6
S02Ron Black5QF512,000firstwinner8,700RFJR24,000
S03Jay Rosenberg1QF17,600firstwinner9,400WFJW15,200
S03Lionel Goldbart1QF15,000second4cut-off wild card bubble5,695WFJW10,000
S03Danny Green1QF10third9eliminated3,300WFJW0
S03Paul Rouffa2QF27,801firstwinner5,800RFJR15,602
S03Marvin Shinkman2QF27,800second17,800WFJW15,600
S03Jared Eisenstat2QF22,400third6eliminated1,200RFJR4,800
S03Donald Burgo3QF310,100firstwinner8,100RFJR20,200
S03Mark Leinwand3QF31,000third8eliminated1,600WFJW2,000
S03Beryl Arbit3QF37,600second28,300WFJW15,200
S03Gary Giardina4QF44,400firstwinner2,200RFJR8,800
S03Harvey Becker4QF41,900third7eliminated3,200WFJW3,800
S03Eric Schoeck4QF43,900second5alternate eliminated bubble2,000RFJR7,800
S03Chuck Forrest5QF510,000firstwinner11,000WFJW20,000
S03Guy Tonti5QF50third10eliminated2,600WFJW0
S03Gary Palmer5QF56,000second33,000RFJR12,000
S04Dave Traini1QF18,402firstwinner8,400RFJR16,804
S04John Podhoretz1QF11,599third9eliminated800RFJR3,198
S04Eric Berman1QF18,401second35,000RFJR16,802
S04Richard Cordray2QF29,900firstwinner8,000RFJR19,800
S04Frank Hughes2QF24,900third6eliminated4,900WFJW9,800
S04Michael Galvin2QF28,600second27,800RFJR17,200
S04Eugene Finerman3QF33,900firstwinner5,900WFJW7,800
S04Keith Bell3QF30third10eliminated1,200WFJW0
S04Jonathan Fellows3QF33,399second8eliminated7,600WFJW6,798
S04Bob Verini4QF49,400firstwinner5,200RFJR18,800
S04Keith Walker4QF43,500third7eliminated6,800WFJW7,000
S04Zeke Sevilla, Jr.4QF46,000second5alternate eliminated bubble6,700WFJW12,000
S04John Ryan5QF512,200firstwinner6,100RFJR24,400
S04Doug Molitor5QF510,000second110,000WFJW20,000
S04Roger Storm5QF58,100third4cut-off wild card bubble4,100RFJR16,200
S05Bruce Naegeli1QF113,801firstwinner13,600RFJR27,602
S05Kate Waits1QF110,400third4cut-off wild card bubble5,200RFJR20,800
S05Richard Perez-Pena1QF113,800second16,900RFJR27,600
S05Roy Holliday2QF2500firstwinner5,600WFJW1,000
S05Barbara-Anne Eddy2QF2399second8eliminated5,800WFJW798
S05Stephen Lebowitz2QF20third10eliminated3,000WFJW0
S05Steven Popper3QF310,800third35,400RFJR21,600
S05Michael Rankins3QF313,801firstwinner7,000RFJR27,602
S05Peggy Kennedy3QF313,800second26,900RFJR27,600
S05Sandra Gore4QF48,600firstwinner9,300WFJW17,200
S05Bruce Seymour4QF46,500second7eliminated7,700WFJW13,000
S05Michael Block4QF41third9eliminated2,900WFJW2
S05Mark Lowenthal5QF58,800firstwinner6,400RFJR17,600
S05Leah Greenwald5QF58,000second5alternate eliminated bubble4,000RFJR16,000
S05Ron Trigueiro5QF57,000third6eliminated9,500WFJW14,000
S06Mark McDermott1QF13,800firstwinner8,000WFJW7,600
S06Jim Tompkins-MacLaine1QF11third7eliminated1,600WFJW2
S06Peggi Malys1QF13,600second26,100WFJW7,200
S06Cigus Vanni2QF27,000firstwinner3,600RFJR14,000
S06Bruce Cox2QF22,400second34,700WFJW4,800
S06Ouida Rellstab2QF21,399third4cut-off wild card bubble5,400WFJW2,798
S06Jeff Richmond3QF31,000second5alternate eliminated bubble8,900WFJW2,000
S06Joel Sacks3QF30third10eliminated1,900WFJW0
S06Eric Newhouse3QF310,000firstwinner8,400RFJR20,000
S06Brian Wangsgard4QF49,800firstwinner4,900RFJR19,600
S06Yael Sofaer4QF4989third6eliminated5,395WFJW1,978
S06Tom Cubbage4QF48,199second14,100RFJR16,398
S06Rich Lerner5QF510,500firstwinner8,700RFJR21,000
S06Cathy Boggs5QF50third9eliminated3,000WFJW0
S06Chris Shea5QF50second8eliminated3,400WFJW0
S07Bob Blake1QF16,399firstwinner7,400WFJW12,798
S07Dan Katz1QF13,000second5alternate eliminated bubble4,200WFJW6,000
S07Michael Thayer1QF11third7eliminated2,100WFJW2
S07Jeff Bandman2QF28,002firstwinner9,900WFJW16,004
S07Larry McKnight2QF27,400second28,700WFJW14,800
S07Jamie Weiss2QF24,600third34,800WFJW9,200
S07Eric Terzuolo3QF39,601firstwinner8,800RFJR19,202
S07Elaine Zollner3QF30third9eliminated3,200WFJW0
S07George Soule3QF30second8eliminated4,800WFJW0
S07Richard Neale4QF42,900second6eliminated9,900WFJW5,800
S07Erik Larsen4QF47,600firstwinner8,300WFJW15,200
S07Lisa Guay4QF40third10eliminated2,500WFJW0
S07Frank Spangenberg5QF510,100firstwinner8,800RFJR20,200
S07Steve Berman5QF57,601second17,600RFJR15,202
S07Andrew Bernknopf5QF54,200third4cut-off wild card bubble2,100RFJR8,400
S08Leslie Frates1QF113,000firstwinner11,700RFJR26,000
S08John LeDonne1QF16,000third8eliminated3,000RFJR12,000
S08Lou Pryor1QF110,001second38,300RFJR20,002
S08Mark Pestronk2QF210,801firstwinner8,000RFJR21,602
S08Lynne Wexler2QF27,700second7eliminated3,900RFJR15,400
S08Andy Westney2QF20third10eliminated5,400WFJW0
S08Bruce Ikawa3QF38,800third6eliminated7,000RFJR17,600
S08Jonathan Jacobs3QF310,001second28,800RFJR20,002
S08Lois Kurowski3QF312,000firstwinner7,000RFJR24,000
S08Sara Cox4QF49,200second5alternate eliminated bubble7,200RFJR18,400
S08Tom Halpern4QF42,800third9eliminated1,400RFJR5,600
S08Scott Gillispie4QF414,500firstwinner12,900RFJR29,000
S08Mark Born5QF516,601firstwinner8,600RFJR33,202
S08Steve Robin5QF514,300second18,300RFJR28,600
S08Jim Scott5QF59,550third4cut-off wild card bubble4,800RFJR19,100
S09India Cooper1QF19,100firstwinner9,700WFJW18,200
S09Dave Willis1QF11,300third8eliminated6,300WFJW2,600
S09Leonard Schmidt1QF17,600second4cut-off wild card bubble7,600WFJW15,200
S09Jerome Vered2QF212,500firstwinner12,400RFJR25,000
S09Steve Newman2QF20third9eliminated3,000WFJW0
S09Bruce Simmons2QF212,200second16,100RFJR24,400
S09Phil Yellman3QF34,799third5alternate eliminated bubble7,600WFJW9,598
S09Kirk Ditzler3QF310,200firstwinner5,200RFJR20,400
S09April McManus3QF39,997second35,000RFJR19,994
S09Richard Kaplan4QF410,700second25,700RFJR21,400
S09John Kelly4QF41,799third7eliminated6,600WFJW3,598
S09Robert Slaven4QF411,000firstwinner5,500RFJR22,000
S09Leszek Pawlowicz5QF516,800firstwinner15,900RFJR33,600
S09Frank Epstein5QF50third10eliminated2,700WFJW0
S09Billy Baxter5QF53,000second6eliminated7,000WFJW6,000
S10Bev Schwartzberg1QF110,900third35,500RFJR21,800
S10Dennis Donohue1QF115,001firstwinner8,600RFJR30,002
S10Marilyn Kneeland1QF112,200second27,500RFJR24,400
S10Ed Schiffer2QF216,601firstwinner8,500RFJR33,202
S10Linda Sheppard2QF20third9eliminated6,400WFJW0
S10Phoebe Juel2QF213,300second18,300RFJR26,600
S10Leslie Miller3QF310,400second4cut-off wild card bubble5,200RFJR20,800
S10Walt Senterfitt3QF315,600firstwinner13,100RFJR31,200
S10David Tiemann3QF38,800third5alternate eliminated bubble4,400RFJR17,600
S10Tom Nosek4QF413,100firstwinner13,100RFJR26,200
S10Debby Arnold4QF40third10eliminated2,700WFJW0
S10Fraser Woodford4QF47,500second6eliminated9,500WFJW15,000
S10Diane Siegel5QF52third8eliminated3,700WFJW4
S10Al Lin5QF5599second7eliminated6,300WFJW1,198
S10Jack Mahoney5QF512,613firstwinner7,700RFJR25,226
S11Jean Grewe1QF13,200firstwinner7,200WFJW6,400
S11Tom Nichols1QF11,900second7eliminated8,200WFJW3,800
S11Matt Morris1QF10third9eliminated3,600WFJW0
S11Bill Pitassy2QF217,200firstwinner8,600RFJR34,400
S11Fred Frank2QF24,000third5alternate eliminated bubble7,500WFJW8,000
S11Jeff Stewart2QF28,100second4cut-off wild card bubble9,300WFJW16,200
S11Amy Fine3QF33,599second6eliminated5,200WFJW7,198
S11Kurt Bray3QF35,350firstwinner2,700RFJR10,700
S11Bart Thomas3QF30third10eliminated3,400WFJW0
S11John Cuthbertson4QF410,401firstwinner5,300RFJR20,802
S11David Hillinck4QF410,400second25,200RFJR20,800
S11Rachael Schwartz4QF49,300third36,200RFJR18,600
S11Steve Chernicoff5QF510,801firstwinner9,800RFJR21,602
S11Brian Moore5QF510,800second15,400RFJR21,600
S11David Venderbush5QF51third8eliminated500WFJW2
S12Bruce Borchardt1QF112,201firstwinner7,100RFJR24,402
S12Gordon Wean1QF17,750second4cut-off wild card bubble3,900RFJR15,500
S12Ben Lyon1QF13,100third6eliminated6,100WFJW6,200
S12Paul Thompson2QF211,001firstwinner6,000RFJR22,002
S12Isaac Segal2QF211,000second15,500RFJR22,000
S12Jim Vercolen2QF210,000third25,500RFJR20,000
S12Jonathan Groff3QF37,700firstwinner7,000RFJR15,400
S12Linda Roberts3QF31second8eliminated3,300WFJW2
S12Aaron Klein3QF30third10eliminated3,800WFJW0
S12David Siegel4QF413,000firstwinner12,000RFJR26,000
S12Ryan Holznagel4QF48,621second37,400RFJR17,242
S12John McKeon4QF40third9eliminated4,300WFJW0
S12Len Krisak5QF52,199third7eliminated1,100RFJR4,398
S12Matt Zielenski5QF511,601firstwinner9,100RFJR23,202
S12Jim Morgan5QF56,800second5alternate eliminated bubble5,800RFJR13,600
S13Brad Plovan1QF11,800third5alternate eliminated bubble5,900WFJW3,600
S13Mary Hirschfeld1QF117,000firstwinner11,200RFJR34,000
S13Shane Whitlock1QF110,100second18,400RFJR20,200
S13Bernie Cullen2QF2799second7eliminated5,800WFJW1,598
S13Beverly Spurs2QF211,700firstwinner6,600RFJR23,400
S13David Cuneo2QF20third8eliminated5,400WFJW0
S13Mike Dup_e3QF313,601firstwinner8,800RFJR27,202
S13Bill Sloan3QF310,100second26,800RFJR20,200
S13Amanda Goad3QF39,600third34,800RFJR19,200
S13David Sampugnaro4QF40third9eliminated4,100WFJW0
S13Bill Dickenson4QF411,601firstwinner9,600RFJR23,202
S13Lucien Schmit4QF41,800second6eliminated5,800WFJW3,600
S13Michael Daunt5QF510,300firstwinner7,900RFJR20,600
S13Barbara Walker5QF50third10eliminated3,400WFJW0
S13Bob Scarpone5QF57,901second4cut-off wild card bubble6,900RFJR15,802
S14Kim Worth1QF18,200third24,100RFJR16,400
S14Fred Ramen1QF110,000second17,500RFJR20,000
S14Lyn Payne1QF115,001firstwinner8,700RFJR30,002
S14Paul Gutowski2QF22third10eliminated1,800WFJW4
S14Claudia Perry2QF27,500firstwinner8,000WFJW15,000
S14Josh Den Hartog2QF214second9eliminated6,400WFJW28
S14Dan Melia3QF38,100second39,100WFJW16,200
S14Peter Scott3QF310,599firstwinner5,300RFJR21,198
S14Craig Barker3QF32,300third5alternate eliminated bubble5,800WFJW4,600
S14Arthur Phillips4QF42,201second6eliminated6,100WFJW4,402
S14Pam Mifflin4QF4100third8eliminated1,100WFJW200
S14Sahir Islam4QF47,787firstwinner7,800WFJW15,574
S14Wes Ulm5QF5600third7eliminated5,700WFJW1,200
S14Bob Harris5QF53,200second4cut-off wild card bubble1,600RFJR6,400
S14Grace Veach5QF510,500firstwinner9,500RFJR21,000
S15James Arey1QF10second9eliminated3,400WFJW0
S15Dan Girard1QF115,000firstwinner12,800RFJR30,000
S15Melizza Zygmunt1QF10third10eliminated2,300WFJW0
S15Dave Abbott2QF210,200firstwinner9,200RFJR20,400
S15Lara Robillard2QF21,600second7eliminated3,700WFJW3,200
S15Andrew Hutchings2QF20third8eliminated5,700WFJW0
S15Pat Healy3QF315,801firstwinner9,800RFJR31,602
S15David Bagley3QF312,400second17,900RFJR24,800
S15Juliet Wiley3QF36,000third33,000RFJR12,000
S15Andrew Maly4QF410,800firstwinner5,400RFJR21,600
S15Carolyn White4QF45,400third5alternate eliminated bubble2,700RFJR10,800
S15J.J. Todor4QF45,599second4cut-off wild card bubble8,200WFJW11,198
S15Chris Ward5QF53,400third6eliminated1,700RFJR6,800
S15John Skelton5QF57,499second23,800RFJR14,998
S15Lance Johnson5QF57,601firstwinner7,400RFJR15,202
S16Jeremy Bate1QF15,900second26,700WFJW11,800
S16Mike Blumenfeld1QF17,200firstwinner3,700RFJR14,400
S16Melissa Sexstone1QF1400third7eliminated2,700WFJW800
S16Steve Fried2QF27,499second18,000WFJW14,998
S16Helen Petroff2QF20third9eliminated2,400WFJW0
S16Chacko George2QF210,000firstwinner8,500RFJR20,000
S16Eddie Timanus3QF34,399firstwinner7,000WFJW8,798
S16Jack Archey3QF30third8eliminated3,800WFJW0
S16Janet Wong3QF31,600second6eliminated4,800WFJW3,200
S16Robin Carroll4QF44,800second4cut-off wild card bubble6,400WFJW9,600
S16Lee Lassiter4QF40third10eliminated900WFJW0
S16Michael Rooney4QF415,500firstwinner15,500RFJR31,000
S16Terry Currin5QF510,000firstwinner9,900RFJR20,000
S16Darlene Lieblich5QF52,400third5alternate eliminated bubble1,200RFJR4,800
S16Carolyn Cracraft5QF55,500second34,300RFJR11,000
S18Babu Srinivasan1QF111,500second15,800RFJR23,000
S18Mark Eckard1QF112,900firstwinner11,400RFJR25,800
S18Rick Knutsen1QF17,599third29,600WFJW15,198
S18Larry Cloud2QF22,000second4cut-off wild card bubble7,000WFJW4,000
S18Andrew Garen2QF2900third6eliminated4,900WFJW1,800
S18Pam Mueller2QF26,399firstwinner6,700WFJW12,798
S18Michael Arnone3QF30third10eliminated2,400WFJW0
S18Michelle Clum3QF31,599second5alternate eliminated bubble7,800WFJW3,198
S18Ryan Moore3QF36,000firstwinner7,000WFJW12,000
S18Doug Lach4QF40third8eliminated5,300WFJW0
S18Bob Fleenor4QF42second7eliminated2,500WFJW4
S18Brad Rutter4QF418,000firstwinner18,000WFJW36,000
S18Tad Carithers5QF54,900firstwinner7,200WFJW9,800
S18Lan Djang5QF52,400second31,200RFJR4,800
S18Kevin Keach5QF50third9eliminated4,700WFJW0
MDMBob Harris1QF120,000firstwinner15,800RFJR20,000
MDMRachael Schwartz1QF112,401second5alternate eliminated bubble10,100RFJR12,401
MDMFrank Spangenberg1QF16,799third7eliminated19,200WFJW6,799
MDMClaudia Perry2QF217,400second4cut-off wild card bubble12,400RFJR17,400
MDMBrad Rutter2QF224,801firstwinner17,800RFJR24,801
MDMKate Waits2QF20third9eliminated4,200WFJW0
MDMChuck Forrest3QF332,000firstwinner16,000RFJR32,000
MDMLeslie Frates3QF322,000second121,700RFJR22,000
MDMEric Newhouse3QF320,000third210,000RFJR20,000
MDMLeslie Shannon4QF420,000second310,000RFJR20,000
MDMEddie Timanus4QF40third10eliminated800WFJW0
MDMBob Verini4QF421,000firstwinner21,000RFJR21,000
MDMRobin Carroll5QF55,600third8eliminated8,800WFJW5,600
MDMIndia Cooper5QF518,100firstwinner18,200WFJW18,100
MDMBabu Srinivasan5QF512,000second6eliminated6,000RFJR12,000
S19Brian Weikle1QF122,200firstwinner22,200RFJR22,200
S19Ben Tritle1QF10second6eliminated6,400WFJW0
S19Kathy Cassity1QF1-3,000third10eliminated-3,000--FJE-3,000
S19Max Levaren2QF20third4cut-off wild card bubble7,600WFJW0
S19Trevor Norris2QF218,000firstwinner15,000RFJR18,000
S19Mark Dawson2QF216,799second116,000RFJR16,799
S19Jill Bunzendahl Chimka3QF314,400firstwinner7,400RFJR14,400
S19Travis Troyer3QF32,599second25,000WFJW2,599
S19Mark Lee3QF30third5alternate eliminated bubble7,400WFJW0
S19Jason McCune4QF4-2,000third9eliminated-2,000--FJE-2,000
S19Mark Brown4QF419,205firstwinner19,200RFJR19,205
S19Jackie Harrison4QF40second8eliminated2,600WFJW0
S19Eric Floyd5QF50second39,000WFJW0
S19Alan Bailey5QF520,400firstwinner20,400WFJW20,400
S19Kyle Hale5QF50third7eliminated5,300WFJW0
S21Arthur Gandolfi1QF116,200firstwinner16,200WFJW16,200
S21Sam Ott1QF10third10eliminated1,700WFJW0
S21Keith Williams1QF13,500second5alternate eliminated bubble7,200WFJW3,500
S21Tom Walsh2QF212,401firstwinner11,600RFJR12,401
S21Seth Alcorn2QF210,600third35,300RFJR10,600
S21Steve Reynolds2QF210,900second26,200RFJR10,900
S21John Beck3QF3599third9eliminated5,600WFJW599
S21Scott Renzoni3QF32,000second8eliminated11,000WFJW2,000
S21Vinita Kailasanath3QF310,200firstwinner10,600WFJW10,200
S21Chris Miller4QF44,000third4cut-off wild card bubble2,000RFJR4,000
S21Tom Baker4QF420,100firstwinner20,000RFJR20,100
S21Russ Schumacher4QF412,400second16,400RFJR12,400
S21Sean Ryan5QF52,600second6eliminated5,200WFJW2,600
S21Anne Boyd5QF57,599firstwinner9,000WFJW7,599
S21Jim Stalley5QF52,400third7eliminated2,400WFJW2,400
S22Doug Dorst1QF15,999second8eliminated9,000WFJW5,999
S22Kermin Fleming1QF199third9eliminated4,200WFJW99
S22Maria Wenglinsky1QF16,400firstwinner13,200WFJW6,400
S22Kevin Marshall2QF216,402firstwinner16,400RFJR16,402
S22David Rozenson2QF26,399third7eliminated3,200RFJR6,399
S22Aaron Thompson2QF216,401second113,000RFJR16,401
S22Kerry Breitenbach3QF310,799third5alternate eliminated bubble10,400RFJR10,799
S22Jason Richards3QF311,000second4cut-off wild card bubble13,000WFJW11,000
S22Vik Vaz3QF326,001firstwinner23,200RFJR26,001
S22Michael Falk4QF414,000third314,000WFJW14,000
S22David Madden4QF428,001firstwinner23,000RFJR28,001
S22Bob Mesko4QF414,400second210,400RFJR14,400
S22Tom Kavanaugh5QF510,000second6eliminated6,000RFJR10,000
S22Bill MacDonald5QF518,733firstwinner15,400RFJR18,733
S22Nico Martinez5QF50third10eliminated0--FJE0
S24Mehrun Etebari1QF1700third9eliminated9,400WFJW700
S24Cathy Lanctot1QF14,400second7eliminated10,400WFJW4,400
S24Chris Mazurek1QF117,999firstwinner19,400WFJW17,999
S24Celeste DiNucci2QF221,800second115,800RFJR21,800
S24Nick Swezey2QF210,600third5alternate eliminated bubble6,600RFJR10,600
S24Craig Westphal2QF226,600firstwinner21,600RFJR26,600
S24Paul Glaser3QF319,599firstwinner24,800WFJW19,599
S24Susan Mitchell3QF312,200second215,000WFJW12,200
S24Jeff Spoeri3QF312,000third37,800RFJR12,000
S24Christian Haines4QF424,001firstwinner18,800RFJR24,001
S24Sara Terrell4QF4-1,000third10eliminated-1,000--FJE-1,000
S24Steve Unite4QF410,000second6eliminated12,000WFJW10,000
S24Cliff Galiher5QF511,400second4cut-off wild card bubble14,200WFJW11,400
S24Doug Hicton5QF516,400firstwinner8,200RFJR16,400
S24Andrew Rostan5QF53,400third8eliminated16,400WFJW3,400
S25Carl Brandt1QF14,800third6eliminated12,400WFJW4,800
S25Dan Pawson1QF116,599firstwinner16,800WFJW16,599
S25Cora Peck1QF115,500second18,500RFJR15,500
S25Larissa Kelly2QF226,400firstwinner23,400RFJR26,400
S25Matt Kohlstedt2QF210,600second313,800WFJW10,600
S25Tom Morris2QF29,600third5alternate eliminated bubble9,600WFJW9,600
S25Ben Bishop3QF315,004firstwinner14,000RFJR15,004
S25Lisa Klink3QF31,000third7eliminated4,000WFJW1,000
S25Dave Simpson3QF313,000second211,800RFJR13,000
S25Aaron Schroeder4QF418,200firstwinner18,200RFJR18,200
S25Jim Stevens4QF41,000third8eliminated1,000WFJW1,000
S25Donna Vogel4QF49,900second4cut-off wild card bubble11,600WFJW9,900
S25Deborah Fitzgerald5QF51third10eliminated3,400WFJW1
S25Erik Nelson5QF53second9eliminated4,800WFJW3
S25Mark Wales5QF519,400firstwinner19,400RFJR19,400
S26Ryan Chaffee1QF11,800third8eliminated7,800WFJW1,800
S26Liz Murphy1QF117,400firstwinner17,400WFJW17,400
S26Patrick Tucker1QF14,700second5alternate eliminated bubble2,400RFJR4,700
S26Terry Linwood2QF221,950firstwinner22,200WFJW21,950
S26Stephen Weingarten2QF250third9eliminated16,400WFJW50
S26Nick Yozamp2QF216,400second116,400WFJW16,400
S26Dave Belote3QF34,999second4cut-off wild card bubble9,600WFJW4,999
S26Regina Robbins3QF34,600third6eliminated12,600WFJW4,600
S26Andy Srinivasan3QF318,200firstwinner14,200RFJR18,200
S26Joey Beachum4QF40third10eliminated4,600WFJW0
S26Justin Bernbach4QF425,836firstwinner25,800RFJR25,836
S26Christine Valada4QF42,400second7eliminated10,200WFJW2,400
S26Vijay Balse5QF515,100firstwinner15,600WFJW15,100
S26Stefan Goodreau5QF513,575second214,800WFJW13,575
S26Jason Zollinger5QF511,500third39,200RFJR11,500
S28Tom Nissley1QF116,403firstwinner16,400RFJR16,403
S28Jay Rhee1QF116,401second212,000RFJR16,401
S28Charles Temple1QF1285third6eliminated400WFJW285
S28Roger Craig2QF219,600firstwinner39,800WFJW19,600
S28Brian Meacham2QF20third8eliminated8,800WFJW0
S28Kara Spak2QF26,012second4cut-off wild card bubble6,000RFJR6,012
S28John Krizel3QF314second7eliminated2,000WFJW14
S28Tom Kunzen3QF30third10eliminated4,200WFJW0
S28Joon Pahk3QF330,800firstwinner20,800RFJR30,800
S28Paul Kursky4QF42,400third5alternate eliminated bubble1,200RFJR2,400
S28Erin McLean4QF416,003second38,600RFJR16,003
S28Buddy Wright4QF417,201firstwinner16,800RFJR17,201
S28Mark Runsvold5QF524,000firstwinner12,200RFJR24,000
S28Justin Sausville5QF518,599second115,200RFJR18,599
S28Christopher Short5QF50third9eliminated5,900WFJW0
S29Jason Shore1QF114,000second313,000RFJR14,000
S29Stephanie Jass1QF113,000third4cut-off wild card bubble13,000RFJR13,000
S29Paul Nelson1QF115,800firstwinner15,800RFJR15,800
S29Joel Pool2QF20third10eliminated5,800WFJW0
S29David Menchaca2QF211,600second6eliminated11,600WFJW11,600
S29Colby Burnett2QF216,400firstwinner15,200RFJR16,400
S29Jason Keller3QF328,200firstwinner28,200RFJR28,200
S29Monica Thieu3QF311,000second7eliminated9,800RFJR11,000
S29David Gard3QF3100third9eliminated2,400WFJW100
S29Keith Whitener4QF426,601firstwinner16,000RFJR26,601
S29Kristin Morgan4QF417,500third213,300RFJR17,500
S29Dan McShane4QF420,000second112,400RFJR20,000
S29Dave Leach5QF515,100firstwinner12,600RFJR15,100
S29Patrick Quinn5QF5989third8eliminated5,000WFJW989
S29Ashok Poozhikunnel5QF512,000second5alternate eliminated bubble12,400WFJW12,000
BOTDLeszek Pawlowicz1QF115,000second215,000WFJW15,000
BOTDRobin Carroll1QF10third10eliminated5,200WFJW0
BOTDRoger Craig1QF122,078firstwinner21,000RFJR22,078
BOTDTom Nosek2QF22,400third7eliminated11,200WFJW2,400
BOTDPam Mueller2QF214,798second317,400WFJW14,798
BOTDRuss Schumacher2QF216,700firstwinner15,400RFJR16,700
BOTDMark Lowenthal3QF3300third9eliminated1,800WFJW300
BOTDBrad Rutter3QF332,400firstwinner32,400WFJW32,400
BOTDDan Pawson3QF3399second8eliminated10,200WFJW399
BOTDTom Cubbage4QF419,500second19,800RFJR19,500
BOTDRachael Schwartz4QF47,600third6eliminated3,800RFJR7,600
BOTDKen Jennings4QF440,000firstwinner30,200RFJR40,000
BOTDChuck Forrest5QF511,900firstwinner14,400WFJW11,900
BOTDMark Dawson5QF58,600third5alternate eliminated bubble10,600WFJW8,600
BOTDColby Burnett5QF511,000second4cut-off wild card bubble11,800WFJW11,000
S31Ben Ingram1QF116,801firstwinner16,100RFJR16,801
S31Rebecca Rider1QF111,600second36,600RFJR11,600
S31John Pearson1QF10third9eliminated8,400WFJW0
S31Arthur Chu2QF221,000firstwinner21,000RFJR21,000
S31Andrew Moore2QF21third8eliminated5,200WFJW1
S31Rani Peffer2QF27,599second5alternate eliminated bubble3,800RFJR7,599
S31Julia Collins3QF39,100second4cut-off wild card bubble16,200WFJW9,100
S31Joshua Brakhage3QF316,206firstwinner11,600RFJR16,206
S31Jim Coury3QF35,600third6eliminated2,800RFJR5,600
S31Drew Horwood4QF4-800third10eliminated-800--FJE-800
S31Terry O'Shea4QF417,200firstwinner8,800RFJR17,200
S31Sarah McNitt4QF4500second7eliminated8,600WFJW500
S31Jared Hall5QF516,800firstwinner9,800RFJR16,800
S31Sandie Baker5QF515,500second19,000RFJR15,500
S31Mark Japinga5QF515,003third213,900RFJR15,003
S32Dan Feitel1QF114,000third4cut-off wild card bubble7,800RFJR14,000
S32Vaughn Winchell1QF116,599second217,200WFJW16,599
S32Catherine Hardee1QF117,600firstwinner17,800WFJW17,600
S32Greg Seroka2QF211,500third6eliminated13,000WFJW11,500
S32Brennan Bushee2QF218,000firstwinner12,000RFJR18,000
S32Kristin Sausville2QF212,800second5alternate eliminated bubble12,800WFJW12,800
S32Matt Jackson3QF324,898firstwinner24,900WFJW24,898
S32John Schultz3QF315,000second317,800WFJW15,000
S32Jennifer Giles3QF33,800third9eliminated10,400WFJW3,800
S32Kerry Greene4QF422,000firstwinner18,000RFJR22,000
S32Andrew Haringer4QF419,400second117,200RFJR19,400
S32Elliot Yates4QF47,200third7eliminated3,600RFJR7,200
S32Alex Jacob5QF526,657firstwinner26,800WFJW26,657
S32Scott Lord5QF56,200second8eliminated10,200WFJW6,200
S32Michael Bilow5QF50third10eliminated8,400WFJW0

Here are search terms you can use to filter:

  • By season: “S#” (e.g., “S32” for the most-recent ToC), “MDM”, “BOTD”
  • All in a particular QF: “QF#” (e.g., “QF3”)
    • You can combine these: “S32 QF3” will give you a single game
  • All QF winners: “winner”
  • All wild-card qualifiers: “wild card”
  • All #4 wild cards (last in): “cut-off”
  • All #5 wild cards (first out): “alternate”
  • All #4 and #5 wild cards: “bubble”
  • All eliminated players: “eliminated”
#1 spot
vaughn
16,599 (95%)
#2 spot
dan
14,000 (82%)
#3 spot
kristin
12,800 (78%)
#4 spot
greg
11,500 (71%)
Non-winners yet to play:
johnjenniferandrewelliotscottmichael
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