The Power of Jeopardy’s Daily Double

(While contestants who answer correctly have the best odds, even a wrong answer to a Daily Double appears better than no Daily Double.)In order to adequately measure the impact of the Daily Double, we need to account for player quality.The data so far seem to confirm my initial hypothesis that landing on the Daily Double greatly increases a contestant’s chance of winning the game. Contestants who answer one Daily Double correctly are nearly twice as likely to win the game as those who don’t land on the Daily Double. However, there is a lurking variable we are overlooking: player quality.The better a player is, the more clues they get to pick off the board, since whoever answers the current clue correctly gets to pick the next clue. The more clues they pick, the higher their chances of running into the Daily Double. This means that we’d expect contestants who are better to naturally run into more Daily Doubles. The following plot confirms this; note that the more questions a contestant gets right, the more likely they are to be in the one, two, or three “Daily Doubles Found” categories.To adequately measure the impact of the Daily Double, we need to account for player quality. I broke up the population of contestants into three groups: 1) those who didn’t land on a Daily Double, 2) those who landed on a Daily Double and got it wrong, and 3) those who answered a Daily Double correctly..For each group, I measured how a contestant’s probability of winning changes as their number of correct answers changes.I decided to focus only on those who either had one or zero Daily Doubles..I felt there wasn’t sufficient overlap in the distribution of correct answers between the no Daily Doubles group and the two or three Daily Doubles groups to make a sound comparison.The following plot shows how the probability of winning changes as a function of correct answers given..The average Jeopardy!.contestant answers about 13 to 18 clues correctly..When a contestant from this average range gets the Daily Double correct, they get a 2-3 percent bump in their chance of winning, compared to if they hadn’t gotten a shot at the Daily Double.This bump increases as a contestant answers more questions correctly—in other words, an above-average contestant who correctly answers a Daily Double will get a bigger boost in their chances of winning..Now that we’ve accounted for player quality, we also see that getting the Daily Double wrong leaves a player worse off than if they hadn’t landed on it at all, which makes sense.ConclusionThe data show that after taking into account player quality, correctly answering a Daily Double increases a contestant’s chance of winning, with this increase being bigger for players who are better..However, this doesn’t mean the Daily Double determines the winner of the game..Most players answer between 15 and 20 questions correctly, and in this range, the bump from answering the Daily Double correctly is only 2-3 percent..I guess this means I should stop hiding behind the Daily Double as an excuse to not take my Jeopardy!.dream seriously.. More details

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