Last updated: November 25, 2017. Now currently includes all College Championship scores in the show’s history and all Tournament of Champions scores in the show’s history. Updates to come: Re-compiling Teachers Tournament and Teen Tournament data to fit the new model.
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). Once the update is fully complete, I will include all tournament quarterfinal scores that I can find; I recently analyzed the difference in Daily Double bets pre- and post-doubling to find that there was not enough of a significant difference to justify not including pre-2001 scores in my model. 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.
Because my update now includes all possible data, I have returned to using a Z-score instead of the Student’s t-score for the College Tournament and the Tournament of Champions. The Teachers Tournament will still use the Student’s t-score in its model for the foreseeable future, due to there having been significantly fewer Teachers Tournaments.
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.)
These graphics show the percent chances of qualifying from each position (known and unknown) for each $1,000 score between $0 and $20,000, as well as other pertinent data.
Tournament of Champions:
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