Should we expect balanced confessional counts in Survivor?

Confessional counts are highly scrutinised by the Survivor fandom. Fans don’t like seeing their favourites getting “purpled”. My feeling is a perfectly balanced confessional sheet where every player gets the same amount is at the expense of storytelling and some variation should be expected. The story elements of the game, like a tribe losing immunity and going to Tribal Council will be the focus after the immunity challenge as they talk strategy. Ultimately, they will get more confessionals for the episode. Makes sense. In the post-merge part of the game, everyone goes to tribal so there are likely other influencing factors for who gets the confessionals.

I’ll be testing the hypothesis that a castaway gets more confessionals given the following events:

1. The castaway goes to Tribal Council in the pre-merge part of the game. This is where the strategy comes into play. It makes sense that the tribe going to Tribal Council gets the full focus after the immunity challenge
2. The castaway wins the reward challenge. Often when the tribe, or individual wins a reward they celebrate with food and drinks, and they get more confessionals telling you how great it is.
3. The castaway is chosen to participate in the reward. Post-merge they often bring someone along with them and are separated from the others. This is likely similar to them winning the reward.
4. The castaway finds an advantage. If the player finds an advantage there is usually a long scene where they replay the events. Makes sense. It would be strange for them to edit out the effort that went into finding it. It would trivialize the whole process and a moment that could change the game.

All data and code are available on Github.

• Data: survivoR R package
• Code: Confessionals and tribals

TL;DR

Do castaways get more confessionals for the episode when they…

• Visit tribal council? Yes.
• Win reward? Yes, post-merge but not pre-merge
• Chosen to participate in the reward? Yes.
• Find an advantage? Yes.

So, should we expect balanced confessionals in Survivor? No, we shouldn’t expect them to be. A decision has been made to focus on strategy and storytelling with the little time available to cram everything in. You might want them to be perfectly balanced from a philosophical point of view, but shouldn’t expect them to be.

Data setup and considerations

There are a few things to consider when setting up the data and the model.

1. I’m going to test if the castaway gets more confessionals in the pre and post-merge part of the game. Given each player goes to Tribal Council post-merge and the game is quite different I’ll be fitting two separate models.
2. I will be using 44 seasons of the US version of Survivor. It could be done for the other versions as well, however, they come with their own nuances. Incorporating them into one model will increase the variation. It may be interesting but for this analysis, I will focus on the US only.
3. Episodes vary in length so I will standardize the number of confessionals per person to 60 minutes before modeling. They will be converted back for comparison after modeling
4. I’ll use counts rather than time since I only have the timing for a few seasons. (If you’d like to help get the times for past seasons please get in touch!). Worthwhile investigation for a second post using the results from this one as prior information though.

A quick look at the data

I want to quickly examine how confessionals are distributed to inform the model choice and prime my expectations.

The mean number of confessionals for each chart is:

• 2.8 confessionals per person per episode
  • 2.4 pre-merge
  • 3.8 post-merge
• 33 confessionals per episode
• 451 confessionals per season

Confessionals at the episode x person level have a very Gamma-like distribution which should be represented in the model choice.

The tail in the episode chart shows the effect of the longer episodes which is the motivation for standardizing the counts to 60 minutes.

Model

To test the hypothesis I’ll fit a Bayesian regression model with the following specification.

Where = Confessional count/episode length x 60

Gamma distributions don’t like 0’s very much, so I’ll add 1 to the response to fit the model and subtract 1 when making predictions. As long as the model fits the data well you’ll still make the same conclusions.

The priors on the coefficients for tribal council, winning a reward, chosen for reward, and finding an advantage are centered around 0 so if there is a genuine difference we should pick it up.

The number of players left in the game needs to be controlled since the more players there are, the fewer confessionals each individual is likely to receive given the finite time of the episode. This will be one of the predictors.

Analysis

Pre-merge

The model formula is:

y ~ tribal_council + reward + found_adv + n_cast

The model is fit with the {brms} package in R.

prior_b0 <- prior(normal(2.4, 0.75), class = "Intercept")
prior_b1 <- prior(normal(0, 2), class = "b")
priors <- c(prior_b0, prior_b1)

mod <- brm(y ~ tribal_council + reward + found_adv + n_cast, data = df_pre_merge, family = "gamma", prior = priors)

Output

 Family: gamma 
  Links: mu = log; shape = identity 
Formula: y ~ tribal_council + reward + found_adv + n_cast 
   Data: df_pre_merge (Number of observations: 4368) 
  Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
         total post-warmup draws = 4000

Population-Level Effects: 
               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          1.94      0.06     1.82     2.06 1.00     6288     3243
tribal_council     0.33      0.02     0.29     0.37 1.00     5313     2610
reward            -0.05      0.02    -0.09    -0.01 1.00     5586     2729
found_adv          0.58      0.06     0.47     0.70 1.00     6391     2815
n_cast            -0.05      0.00    -0.05    -0.04 1.00     6091     3160

Family Specific Parameters: 
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
shape     2.65      0.05     2.55     2.75 1.00     5692     3074

Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

The posterior predictive check looks very neat confirming the Gamma was a good choice.

The model the coefficients can’t be directly interpreted but it does show a strong difference between those who go to tribal council and those who don’t, and those who find an advantage. Those who won the reward challenge were not different from those who lost. The number of castaways left in the game was significant, meaning for each additional castaway they would receive proportionally fewer confessionals.

Note that the difference in confessionals per person gets larger when there are fewer players in the game.

Post-merge

Post-merge everyone goes to Tribal Council and the nature of the game changes. The model I’ll be fitting here is as follows:

y ~ reward + chosen_for_reward + found_adv + n_cast

prior_b0 <- prior(normal(3.8, 1), class = "Intercept")
prior_b1 <- prior(normal(0, 2), class = "b")
priors <- c(prior_b0, prior_b1)

mod <- brm(y ~ reward + chosen_for_reward + found_adv + n_cast, data = df_pre_merge, family = "gamma", prior = priors)

Note the prior for the intercept has been updated to something more relevant for the post-merge stage of the game.

Output:

 Family: gamma 
  Links: mu = log; shape = identity 
Formula: y ~ reward + chosen_for_reward + found_adv + n_cast 
   Data: df_post_merge (Number of observations: 2362) 
  Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
         total post-warmup draws = 4000

Population-Level Effects: 
                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept             2.08      0.04     2.01     2.17 1.00     5781     3067
reward                0.12      0.03     0.06     0.19 1.00     4980     3041
chosen_for_reward     0.11      0.05     0.01     0.21 1.00     5469     3136
found_adv             0.56      0.07     0.42     0.71 1.00     4403     2652
n_cast               -0.04      0.00    -0.05    -0.04 1.00     5700     3306

Family Specific Parameters: 
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
shape     2.53      0.07     2.39     2.66 1.00     5338     2707

Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Again, the posterior predictive check looks great confirming a good fit.

All of the coefficients show a clear difference in the means in the post-merge stage. Unlike the pre-merge stage, winning the reward challenge is attributed to increased confessionals, which makes sense. Similarly, being chosen for the reward yields a similar bump in confessionals. However, it is dominated by finding an advantage that attributes 3-6 more confessionals on average. My theory is, in the later stage of the game advantages become more important and a well-played advantage can turn the game on its head, so there is a lot of focus on the advantages.

Adjusting confessionals

With these models, we can adjust the confessional count for a season, and see who truly received more confessionals than other players when the story effects of the game are removed.

I’ll test this on Season 44. The methodology is:

1. Estimate the expected number of confessionals per 60mins with the above models for the pre and post-merge stages of the game, by episode and castaway.
2. Scale the number of confessionals to the length of the episode .
3. Aggregate to find the total expected , and observed confessionals per castaway for the season.
4. Calculate the index relative to the expected: .

Yam Yam received 35 more confessionals than expected and Lauren received 21 fewer than expected on the extremes. Overall most castaways received more confessionals than expected with respect to other seasons. It’s really just Heidi and Lauren who didn’t receive the confessionals expected given their time in the game.

The table below compares the calculations assuming equal distribution and the model-based adjustment. In some ways, the model adjusted index looks more extreme since under the assumption of equal distribution Yam Yam’s index is +56% but the adjusted is +72%. Tika got slammed in the pre-merge and Yam Yam didn’t find any advantages. With those things factored in he received 72% more. Conclusion – the camera loved him. But overall it’s a better representation.

There are some big differences between the indexes, Matt for example. They really doubled down on the showmance which would explain it.

The model based adjustment is better for seeing which castaways are getting more confessionals than others by factoring in the story and game elements. It is also useful for comparing the trends across seasons. For example, it’s possible castaways for a season could have had more confessionals compared with similar castaways from other seasons. In which case, all castaways for a given season could have received proportionally more. In season 44, only 5 players received less than expected showing that overall it was a good season from a confessionals per person point of view.

Final thoughts

Should we expect balanced confessionals in Survivor? Nah. There’s a clear difference between those that go to tribal, find an advantage, and win reward challenges or participate in them. The editors have chosen to focus on strategy and storytelling, over faffing around on the beach with the little time they have to cram everything in (not to say that faffing around on the beach isn’t fun or needed to understand their personalities and tribe connections).

If everyone went to tribal the same amount of times and found the same amount of advantages and won/went on the same number of rewards, the expectation would be the same for everyone. But would we actually expect to see the confessional counts, as arbitrary as they are, equal for everyone? I don’t think so. There’s still an underlying narrative for the episode and the season which would be diluted if they were.

This is my opinion more than evidence backed by data, but I think we can infer that if the “purpled” players were pivotal to the story beats of the season they wouldn’t be “purpled”. We should be reassured they’re telling the best story they can.

Finally, the differences in the counts associated with tribals and so on are estimated from the observed counts across the 44 seasons. They measure the editing decisions made by production. If for philosophical reasons you don’t agree those going to tribal pre-merge or those who find advantages should receive more confessionals, then, oh well. Since those differences exist I don’t think we should expect perfect balance.

Code bits

There is a lot of code for this analysis and is available in full on Github.

Extra charts

I’ve visualised season 44 in a slightly different way which shows how many confessionals they received and their expected values. With all castaways being on the same scale it pulls it into perspective. Important to keep in mind how long each castaway was in the game. Not shown here though.