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.
Last updated: August 21, 2018. Now includes a model for supertournaments and also includes Season 34 Teachers Tournament and College Championship data.
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.
Update (August 21, 2018): I have now expanded the model to include supertournaments (of the Million Dollar Masters / Battle of the Decades vein), in a separate model, just in case a future supertournament includes wild cards.
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:
Supertournaments (Battle of the Decades/Million Dollar Masters/etc.)
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