Social Psychology with Jeff

Survivor just finished its 43^rd season. Although the basic premise of Survivor is similar to their early seasons, there have been some meaningful changes in its gameplay and structure. As a refresher: Survivor casts a group of strangers to work together to win challenges and survive for 26 days (it used to be 39 days, but Covid-19 precautions and filming and production scheduling changed it to 26 days). Every few days, someone is voted out of the game until. On the last day, two or three competitors try to convince a jury made up of castmates who they voted out why they should win the game. The jury then questions the finalists publicly before privately voting for who they think should win the season and the prizes associated with winning their season.

One change involves the organization of the penultimate tribal council. Survivor now has three opportunities for contestants to make the final tribal council. A contestant can advance to the final tribal council by winning the last immunity challenge, be selected by the winner of the final immunity challenge to advance, or winning a fire making competition. The game switched from a final elimination vote to a “win and you are in” structure across three opportunities.

During season 43, Noelle (a member of the jury) asked Cassidy (a finalist) why Cassidy did not give up immunity to partake in the fire-making challenge. This led me to wonder whether Survivor was now biased towards winners of the fire making challenge over those who won final immunity or who were selected to advance to the final tribal council by the final immunity winner. This, in turn, led to questions that could be investigated using statistical analyses. My most pressing questions were:

1. What is the relationship between winning or losing the final immunity challenge and winning or losing that season of Survivor?
2. Has the fire making challenge influenced Survivor jurists’ decisions on who should win the season?

How did I compile the data?

I obtained publicly available data through Wikipedia and the Survivor Wiki. I listed every contestant who made the final tribal council from seasons 1 through 43. For all finalists, I classified whether they won or lost the final immunity challenge. For finalists from season 35 and later, I classified their result from the final fire making challenge (e.g., did they win the final immunity challenge, were they saved by the person who won the final immunity, or did they win the fire making challenge). I then classified whether they won or lost their season of survivor.

I also classified how many votes the winner received, how many votes nonwinners received (pooled together), the winner margin (e.g., winner votes minus nonwinner votes), and whether the season occurred before or after season 34. Click here for my data set.

What did I find?

Is there a difference between seasons with and without the fire making challenge?

Out of the 43 contestants who won their season of Survivor (e.g., winners), 26 contestants lost final immunity and 17 contestants won final immunity. Out of the 69 contestants who did not win their season of Survivor (e.g., nonwinners), 43 contestants lost final immunity and 26 contestants won final immunity. Whether a contestant won or lost their season of Survivor was unrelated to whether they won or lost the final immunity challenge, χ²(1) < 0.01, p > .999, Cramer’s V = .02.

Has the fire making challenge influenced jury decision making?

The fire making challenge may influence who juries vote for as the winner of Survivor, but the sample size is still relatively small compared to the observed statistical effect size. Out of the 9 winning contestants on or after season 35: 3 were saved, 5 won the fire-making challenge, and only 1 won final immunity without participating in the fire making challenge. Out of the 18 nonwinning contestants, 7 were saved, 4 won fire, and 7 won final immunity. The chi-square test showed that the role in the fire making challenge (e.g., won final immunity, was saved, or won the fire making challenge) was unrelated to whether they won or lost their season, χ²(2) 3.61, p = .164, Cramer’s V = .36. However, the relatively large effect (as measured by Cramer’s V) suggests a potential effect of the fire making challenge.

This led me to conduct binary logistic regression analyses. Binary logistic regression analyses investigate whether a person’s odds of an event occurring changes based on specific events, categories, or ratings. Overall, the effect size of the fire making challenge is relatively small, McFadden’s R² = .11, AIC = 36.61. The overall odds ratios are relatively large, but there is not enough of a sample size for those odds ratios to be considered reliable. However, they do trend in the direction of showing that contestants who win their way into the final tribal council via the fire making challenge may have a better chance of winning their season than other contestants. Contestants who were saved at the penultimate tribal council had lower odds of winning their season compared to contestants who won the fire making challenge, b = -1.07, SE = 0.93, p = .266, OR = 0.34, 95% CI [0.05, 2.26]. Contestants who won the final immunity challenge were less likely to win their season of survivor compared to the winner of the fire making competition, b = -2.17, SE = 1.26, p = .085, OR = 0.11, 95% CI [0.01, 1.36].

Are final tribal votes more lopsided after the switch to a moderated discussion?

There are no meaningful differences between the margin of victory for winners between seasons 1 and 33 (M = 4.03, Median = 3, SD = 2.77) and for winners of seasons 34 through 43 (M = 4.80, Median = 5.5, SD = 2.09) based on a Welch’s t-test, t(19.47) = 0.93, p = .395, d = 0.31, or a Mann-Whitney U test, U = 126, p = .262. There was also no difference in the ratio of the margin of victory (e.g., votes received by the winner divided by the total number of votes) between seasons with a final 2 (M = 0.43, Median = 0.43, SD = 0.32) and seasons with a final 3 (M = 0.53, Median = 0.50, SD = 0.29) based on a Welch’s t-test, t(30.33) = 1.09, p = .285, d = 0.34, or a Mann-Whitney U test, U = 169, p = .198.

What are the insights from these analyses?

If a friend asked me about how to strategize for the end game of Survivor, I would give them these insights. What is the relationship between winning or losing the final immunity challenge and winning or losing that season of Survivor? Overall, there is not a strong relationship between the two. Across multiple analyses across 43 seasons of Survivor results, there was no positive relationship between whether a person won the final immunity challenge before the final tribal council and whether they would go on to win their season of Survivor.

Has the fire making challenge influenced Survivor jurists’ decisions on who should win the season? Maybe, but more data is needed to make an interpretation either way. Nine events and 27 finalists are not enough data to make an interpretation right now, but the pattern of results offers two possible trends. One possibility is that winning the final immunity challenge has no benefit for the contestant’s chances of winning their season of Survivor. That is, the recent patten of winners (e.g., 5 fire making winners, 3 selected candidates, and only 1 final immunity winner) may represent a world where the final immunity challenge has no relationship with which finalist wins the game. Another potential possibility is that being saved at the penultimate tribal council or winning the fire making challenge may lead to better odds of winning their season of Survivor. Results from the next few seasons may clarify which interpretation is more accurate, or production changes within Survivor may make many of these observations out-of-sample.

Have Survivor winners had more lopsided victories after the switch from individual questioning to a moderated discussion? Not really. There were no differences in the winner’s margin of victory before or after the fire making challenge was introduced nor between seasons with a final 2 or final 3.

Within the world of Survivor, this means that winning the final immunity challenge may be problematic for that contestant’s chances of winning their season. At a minimum, there is no added benefit of winning the final tribal council. The most supported insight from these analyses is that contestants should do what they can to make it to the final tribal council. Once there, they can attempt to justify their decisions and gameplay for why they should win their season.

Outside the world of Survivor, these results and insights also highlight why it is important to collect, analyze, and interpret data. My guesses as to what the research questions would say were opposite of the observed results. Asking meaningful research questions matters when trying to describe events or make inferences about relationships between constructs.