Is Star the most popular, under-edited player in Survivor?

Kosta, the Survivor Fact Checker, was kind enough to share some data with me to test two hypotheses:

1. A player’s popularity is associated with confessionals and
2. Star is the most popular player of all time, accounting for confessionals.

The reason why I wanted to look into this was that some players get more confessionals than others and it makes sense that the more we see someone on the screen, the more we learn more about them and relate to them. I also expect that there could be some divergence as confessionals increase – there may be players we love and love to hate (although there aren’t really any villains anymore).

Throughout S48, Star only received 2.3 confessionals per hour (the average is 3.5), but was very popular in the fandom. I wanted to see if there was data that supported my hypothesis and show that there’s more to Survivor than just confessionals

The poll data

The key data here is the popularity poll Kosta runs on Instagram. People can leave a rating for each player – Love, Like, Neutral, or Not a Fan, which is then converted to a percentage. The data covers seasons 43-48.

If a player has a Love percentage of 56% that means 56% of responders ‘love’ that player. Pretty straightforward interpretation. There may be some nuance between the Love and Like categories, so I’ll mostly be looking at the Love rating.

The key thing is that this data is a poll. Polls are interesting because they are very dependent on who responds and what motivates them to spend a few minutes of their time to cast their votes.

In a world where we are constantly walking around with a device in our pocket trying to get our attention with a seemingly endless battering of notifications and psychological hooks, it’s important to ask the question who feels strongly enough to have their say, and who doesn’t. The resulting data is then only reflective of those responders and not all viewers as a whole.

Polls are still very useful, we just need to be careful in the interpretation of the data. As a survey statistician, I can’t emphasise enough how important this point is. Poll data is more of a reflection of the responders than it is the subject of the poll.

Let that point marinate on your mind as you read this post.

Are confessionals correlated with the poll ratings?

Let’s look at a few charts. For this analysis I’m going to use the total confessional time rather than the confessional count. It will capture the nuance a little better, and I have the data for all seasons.

A few call-outs:

• There looks to be a clear positive relationship between confessionals and the Love percentage. As the player gets more confessionals, they strike a chord with the fandom
• The Like percentage is very flat, showing no relationship.
• The Neutral category decreases as the player’s confessional time increases. This makes sense since as you get to see more of someone, the more likely you are to have an opinion about them so the responders’ vote will be, probably, in either Love or Not a Fan.
• The Not a Fan category is pretty flat as well, which is actually kind of surprising to me. I thought this would be a positive relationship as well, as you see more of someone, you are either going to grow towards them or begin to not be able to stand them.

I have to quickly call out the 4 outliers in the Not a Fan cat – Hannah, Sean, Rome, and Bhanu! This should make sense to people – two quitters and two very full-on people! More on Bhanu later.

Let’s talk about Love 💖

Let’s have a closer look at the Love cat. The thing that stands out to me is the relationship as the confessional time increases, so does the Love percentage and the variation of the Love percentage. There is clearly a heteroskedastic variance structure here.

To factor this into the analysis, I’ll just use a weighted regression with the weight being .

glm(formula = p ~ time, data = filter(df, score == "Love"), weights = 1/sqrt(time))

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 0.095773   0.018320   5.228 8.67e-07 ***
time        0.017138   0.001964   8.726 4.10e-14 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 0.0079743)

    Null deviance: 1.45241  on 107  degrees of freedom
Residual deviance: 0.84528  on 106  degrees of freedom
AIC: -105.55

As expected, there is a pretty strong relationship here. First hypothesis confirmed.

Star is a star, but someone else gets the popular vote

Now to test my theory that Star is the most popular player with the fewest confessionals. By just looking at the scatter chart, you may wonder why it’s not Carolyn who’s right at the top, but we need to factor in the linear trend and the expanding variance.

A player way out on the right can vary a lot more than those closer to the left. This needs to be accounted for so we don’t make incorrect conclusions.

To measure this, I’m going to use the fitted model above and look at the residuals.

Star comes in at 9th place so I was wrong about that one. Kaleb takes out top stop! I wonder what would have happened if his Shot in the Dark hadn’t landed.

A big caveat is that this is all based on my assumptions and choice of weighting to control the heteroskedasticity. I think they’re reasonable, though.

More?

I found a few more interesting things in the poll data.

Continue reading…