The Jeopardy Lectern Effect: Does Order Matter?


[Side note: this is probably something that’s been done many, many times, but I’mma do it anyway ‘cause I’m bored and I have J! Archive.]

We all know Jeopardy!, right? And we all know how it’s played. Three people stand at three lecterns and give the correct questions to answers coming from a few topics of interest.

If you buzz in to give a question and you give the correct question, it’s your turn to select the next answer. That’s how the game progresses through the answers. But at the start of the game, it’s the person in the left-most lectern who gets to choose the first answer.

Here is my question: does this “first to pick an answer” give an advantage to the player in the left-most lectern? More specifically, does the person in the left-most lectern win significantly more games compared to the other players?

We can actually look at this from two different standpoints. Before we do that, let’s just make this a bit easier by calling the left-most lectern (from the viewer’s standpoint) Lectern 1, the middle lectern Lectern 2, and the right-most lectern Lectern 3.

  1. Games where the player in Lectern 1 is a returning champion. If you win a game of Jeopardy!, you get to come back for the next game and you stand at Lectern 1. An argument might be made that returning champions are “stronger players” than the other two people at the other two lecterns, which would thus lead to those in Lectern 1 winning more often than the others. That might be the case, but we also have…
  2. Games where the player in Lectern 1 is not a returning champion. This is not too common anymore due to the unrestricted number of games a person can win, but in older seasons, a person was limited to a maximum of five consecutive winning days. Thus, there were more cases where all three players were “new” to the Jeopardy! Scene. In such cases, an argument could be made that the person at Lectern 1 would have no consistent advantage over the other players apart from the fact that they get to pick the first answer (and from what teh interwebs tell me, the players are seated randomly if there is no returning champion).

So let’s analyze!


Hypotheses

  1. If Lectern 1 is occupied by a returning champion, then a significantly larger proportion of Lectern 1 individuals will win (be in first place at the end of a Jeopardy! game) compared to the other two lecterns.
  2. If Lectern 1 is not occupied by a returning champion, then there will not be a significant difference in the proportion of Lectern 1 individuals who will win (be in first place at the end of a Jeopardy! game) compared to the other two lecterns.
  3. If Lectern 1 is occupied by a returning champion, then they will not earn a significantly larger amount of money compared to the other two lecterns (I think there’s way too much variability with the end monetary result to suspect that Lectern 1’s returning champion will have a significantly larger winning sum than the others).
  4. If Lectern 1 is not occupied by a returning champion, they will not earn a significantly larger amount of money compared to the other two lecterns.

Data Collection and Analyses
I used the massive database that is J! Archive for my data collection. I randomly selected 25 games that had a returning champion at Lectern 1 and another 25 games that did not have a returning champion at Lectern 1. For each game, I recorded the rank of the players for each lectern (who finished first, second, and third) as well as the monetary earnings for each lectern.

For testing hypotheses 1 and 2, I chose to use a two-sample z-test for a difference of proportions. I used my Lectern 1 sample as my “sample 1” and then grouped the Lectern 2 and Lectern 3 samples to treat as my “sample 2.”

For testing hypotheses 3 and 4, I chose to use a two-sample t-test for a difference of means. Again, I used my Lectern 1 sample as my “sample 1” and then grouped the Lectern 2 and Lectern 3 samples to treat as my “sample 2.”

I decided to group Lecterns 2 and 3 together just because I don’t really care about any differences between Lecterns 2 and 3—just the difference between Lectern 1 and the other two lecterns.


Results
Testing hypothesis 1:

08-27-2019-a

Testing hypothesis 2:

08-27-2019-b

Testing hypothesis 3:

08-27-2019-c

Testing hypothesis 4:

08-27-2019-d


Conclusions (using α = 0.05)
Hypothesis 1: Based on the data, we can conclude that the proportion of winners at Lectern 1 is significantly higher than the proportion of winners at the other two lecterns if Lectern 1 is occupied by returning champion.

Hypothesis 2: Based on the data, we can conclude that the proportion of winners at Lectern 1 is not significantly different from the proportion of winners at the other two lecterns if Lectern 1 is occupied by returning champion (more specifically, also, the proportion of winners at Lectern 1 is not significantly higher than the proportion of winners at the other two lecterns.

Hypothesis 3: Based on the data, we can conclude that the average amount of winnings at Lectern 1 is significantly higher than the average amount of winnings at the other two lecterns if Lectern 1 is occupied by a returning champion (this is not what I thought would happen!).

Hypothesis 4: Based on the data, we can conclude that the average amount of winnings at Lectern 1 is not significantly different (more specifically, higher) than the average amount of winnings at the other two lecterns if Lectern 1 is not occupied by a returning champion.


Comments
So this is a relatively small sample, yes, but it supports the idea that the “advantage” of being in Lectern 1 to choose the first answer is not really a thing. Really, the advantage is whether or not you’re a returning champion. If you’re a returning champion, you are probably a pretty strong Jeopardy! player (and maybe good at wagering, too), so you’re probably going to do better than your competitors a decent amount of the time.

Anyway. A larger sample size for this analysis would be an interesting thing to do.

 

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