Prior to the College Tournament, I introduced a model for predicting a player’s chances of qualifying as a wild card for the semifinals if they did not win a game. This model took the combinatorics from Keith Williams at The Final Wager back in 2015 but used slightly different percentages.
I have now analyzed all four of Jeopardy!’s regular tournaments (Teen, College, Teachers, and the Tournament of Champions). For each of these tournaments, I have included every tournament since the dollar values were doubled (November 26, 2001), as I feel that the doubling of the dollar values changed the Daily Double bets just enough that doubling the pre-2002 scores doesn’t quite work out, in my eyes. I also have not included the Battle of the Decades and Million Dollar Masters in with the Tournament of Champions data, because I feel that the field quality in the super-tournaments are different enough that I think it would skew the data.
One change I have made to my prediction model from the College tournament is that instead of taking a Z-score, I am taking a Student’s T-score (using the number of tournaments in the dataset as my degrees of freedom). This has about a 0.5 to 1% effect on the percentages of advancing, but it makes me feel more comfortable in dealing with the possibility of an outlier result (especially in the case of the Teacher’s Tournament, for which there have only been six).
The combinatorics calculations are similar to that mentioned in my College Wild Card post. However, in these charts:
- For the QF Finishing Position: Unknown column, 9 non-winning scores to come are assumed (with a maximum of three scores beating the player’s score.)
- For the QF Finishing Position: 3rd column, 8 non-winning scores to come are assumed (with a maximum of two scores beating the player’s score.)
- For the QF Finishing Position: 2nd column, 8 non-winning scores to come are assumed (with a maximum of three scores beating the player’s score.)
The following table shows the 50% threshold, per the model, of each tournament, in each finishing position (known or unknown):
|QF Finishing Position|
|Tournament of Champions||$7,601||$8,907||$6,798|
And these graphics show the percent chances of qualifying from each position (known and unknown) for each $1,000 score between $0 and $20,000.
Tournament of Champions:
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