It’s time for a change.
However, the play styles of Austin Rogers and James Holzhauer have caused me to update and revisit the model. For one, Austin had a slightly-above-average Coryat, but he was able to harness Daily Doubles to larger scores going into Final Jeopardy! than would otherwise be predicted by the model. Thus, I have created Version 2, which takes into account score going into Final Jeopardy as opposed to Coryat score:
As with Version 1, the trend line (now a logistic sigmoid curve) corresponds to a percentage chance of winning the game.
As with Version 1, to run my simulations, I will still use a Python script to generate 1,000,000 normally distributed scores (given the mean and standard deviation of the player’s scores going into Final Jeopardy thus far) and from there, generate the mean winning percentage to determine both the player’s chances of winning their next game as well as a predicted length of their streak (in this case, r / (1 – r), where r is a player’s chances of winning one game).
For runs that have yet to reach 11 games, the model will adjust the standard deviation when generating scores. A 1-game champion will use the standard deviation of a player score ($6,509); A 2-game champion will use a weighted average of 10% their standard deviation and 90% the population standard deviation (the $6,509), and so on through to the 11th game.
Hopefully this update to the model will allow for even better accuracy going forward, especially when it comes to outlying data. The new model will be used starting with the April 22, 2019 game.
Since Alex Trebek’s diagnosis of stage 4 pancreatic cancer, many community members have been raising money. The Jeopardy! Fan Online Store is as well! All proceeds from any “Keep The Faith And We’ll Win” shirt sold will be donated to Alex Trebek’s preferred charity. (The de facto alumni association is currently inquiring with the show in order to determine Alex Trebek’s preferred charity; this will be updated when that has been determined. To date, over $250 has been raised.)