Do winners get more confessionals?

Does the person with the most confessionals win the season? That’s a clear no.

A better question is, do winners receive proportionally more confessionals than other players? Yes, they do.

Let’s look at the stats.

Confessionals per hour

There are a lot of differences between seasons such as the number of episodes, the length of episodes, number of players, etc. All of these thing impact how many confessionals a players can receive.

To remove the season effect we can standardise the count to measure the number of confessionals per hour instead of the raw count.

But there’s a bit more to it.

Expected confessionals

The other thing I do is estimate the expected number of confessionals for a player. The reason for this is that there are events in the game where we should expect a player to get more confessionals. For example:

• Losing Tribal Immunity: A tribe that loses the immunity challenge and is going to tribal council should get more confessionals than the others. This is where the strategy comes into play. It would be hard for the producers to craft a narrative for the vote and significant gameplay moments that shape the season if they didn’t.
• Winning the reward challenge: Everyone loves watching the winner of the rewards enjoying their food, comfort, and wine. It’s also where alliances are formed, so it makes sense that those go on reward get a few more confessionals.
• Finding an advantage: Those who find advantages get more confessionals as they replay the events of how they found it. If the producers didn’t show this would be very weird and not convey the effort they put in or the luck they had.

I won’t go into it here, but you can read more about it and the statistical analysis here. In a nutshell, I fit a regression model to estimate the expected number of confessionals using the above as predictors.

The residual value of the confessionals per hour

The rest of this analysis is centred around a key concept – the residual CPH.

The difference between the expected and observed CPH, is the residual CPH. It is a standardised measure we can use for analysis as it removes all the within and between season effects. Mathematically, it is simply…

where is the observed CPH and is the expected CPH.

This is how is distributed for the US and AU versions.

The number itself may be hard to interpret but just remember that the residual value removes all the other stuff from the actual number of confessionals per hour. With this we can see if there is a difference between the groups we care about, like the winners.

Winners vs the rest at the final 6

There are a lot of ways to look at this, but first let’s look at the distribution of the residual CPH, like the above for all those at the final 6 and see if the mean CPH is different for the winners.

I chose to look at the final 6 because this is end game, usually the penultimate episode. The winner isn’t known at this point but we might be able to infer who the favourites are from the CPH. I could have chosen the final 5, final 8, or whatever but I think 6 is a reasonable choice.

Let’s look at the histogram. Do winners have a higher CPH residual on average?

Yes, there’s a difference.

• Winner: 0.6
• Final 6 – runner-up: -0.1

Winners have a higher average residual CPH than the rest in the final 6. But it’s not that much higher, and looking at the distributions, it’s not that convincing, so we need to test if the means are significantly different or not.

The Model

I’m going to fit a regression model where the winner flag is the response and the residual CPH and version are the predictors. I’m including version to see if there is a difference between AU and US.

.place <- 6

df <- survivoR::confessionals |> 
  filter(version %in% c("US", "AU")) |> 
  filter_final_n_episode(.place) |> 
  filter(!is.na(exp_count)) |> 
  summarise_confessionals() |> 
  add_winner() |> 
  add_place() |> 
  mutate(version = str_sub(version_season, 1, 2)) |> 
  filter(place <= .place) |> 
  mutate(
    winner_num = as.numeric(winner),
    winner = ifelse(winner, "Sole Survivor", "6th-Runner up")
  )

mod <- glm(winner_num ~ res_cph + version, data = df, family = binomial())
summary(mod)

Call:
glm(formula = winner_num ~ res_cph + version, family = binomial(), 
    data = df)

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept) -1.61969    0.34899  -4.641 3.47e-06 ***
res_cph      0.27518    0.09317   2.954  0.00314 ** 
versionUS   -0.04547    0.38499  -0.118  0.90599    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 312.49  on 344  degrees of freedom
Residual deviance: 303.87  on 342  degrees of freedom
AIC: 309.87

Number of Fisher Scoring iterations: 4

Yes, the model is showing a fairly strong positive effect. The higher the residual CPH, the higher the chance of winning. And there’s no difference between the AU and US versions.

What about at the end of the game?

Let’s look at the final 3. In the US the final three are the finalists, except for a first seasons. In the seasons with a final 2 the 3rd place finisher gets a lot of screen time in the final episode so I think this is fine.

If I fit the same model but for the final 3 using their confessional counts after the game has finished, I get these results.

Call:
glm(formula = winner_num ~ res_cph + version, family = binomial(), 
    data = df)

Coefficients:
            Estimate Std. Error z value Pr(>|z|)  
(Intercept) -0.70043    0.39237  -1.785   0.0742 .
res_cph      0.25919    0.10585   2.449   0.0143 *
versionUS   -0.09681    0.43363  -0.223   0.8233  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 221.51  on 173  degrees of freedom
Residual deviance: 215.30  on 171  degrees of freedom
AIC: 221.3

Number of Fisher Scoring iterations: 4

The coefficient is about the same size but slightly less significant due to the sample size. It is still a significant difference though.

What does this actually mean?

In simple terms, at the Final 6 a player with a residual CPH of 3 is about twice as likely to win than a player with a residual CPH of 0, or someone who has the same number of confessionals as expected. Or put another way, a player with a CPH of 5 and an expected value of 2 (therefore the residual is 3), they are twice as likely to win than someone with a CPH of 4 and an expected value of 4 (where the residual is 0).

I’ll put it yet another way – at the Final 6, if the residual CPH for player A is +3 higher than player B, Player A is about twice as likely to win than player B, e.g.

I get it, it’s a bit of a mouthful and is not easily understood. How about this – more confessionals means more winning.

The chart shows that as the difference between two players’ residual CPH increases, so do their chances of winning over the other player.

“Your maths is wrong.”

Nah, I just made assumptions to wish away my problems.

The annoying thing about Survivor analysis is that the data within a season is not independent – there is only one winner, which means the others can’t win, and that can blow out your analysis. Read this for why.

I haven’t made any adjustments here. The way to do it is to summarise the data to the season level and model it that way. You also lose a lot of information doing that, so I haven’t.

Modelling it this way is actually more difficult to detect a meaningful difference, so the fact that we have is good evidence that there is something there.

Anyway, I get the point, so I’ll look at it a different way as well.

Comparing against random chance

A relatively simple way of looking at this by the following steps:

• Choose a stage of the game. I’m going to choose the Final 6.
• Choose a cutoff e.g., a residual CPH of 0 and count how many are above and below this threshold. For reference, in S47 there were 3 out of 6 and in S48 there were 5 out of 6.
• Calculate the expected number of winners across all seasons, assuming random chance for this group (those above the threshold)
• Compare this against the observed number of winners in the group. If the observed value is higher it’s evidence that, yes, those with a higher residual CPH are more likely to win the season.
• Calculate the ratio of observed to the expected.
• Repeat for different thresholds.

Here are the results of that analysis.

And a chart of the residual CPH by the ratio

The ratio has an increasing trend, which suggests there’s a relationship here. If it were flat around 1, there wouldn’t be.

In conclusion…

Yeah, winners tend to have proportionally more confessionals than the players who don’t win. It’s still useful to pay attention to confessionals (at least the confessionals per hour numbers I put out, the raw counts not so much).

It makes sense for this to be the case. Each season, the producers need to tell a story. Each person who is voted out is part of the story, not as much as who is voted out but rather who orchestrated it. They need to edit it in such a way that by the end of the final episode when the winner is crowned, it makes sense why the jury voted for them. Therefore, it makes sense for the winner to get more confessionals – they need to tell that story.

They also need to be careful not to telegraph the winner of the season too easily so it remains exciting to the viewers. They’ll balance it out with the next strongest contender. There are always those that are very unlikely to win, and typically, they’ll receive proportionally fewer confessionals because their story isn’t as important to the narrative of the season.

In Season 48, Kyle ended the game with the highest difference of 0.7 out of the final 6 and won the season. I’ll take the anecdotal evidence when it supports my claim.

As an aside, this may seem obvious that higher confessionals means higher chance of winning. But I’d wager that this is potentially one of the only analyses that supports the claim of a “winners edit” – a phrase I tend to avoid.