Analyzing the Great British Bake Off
By: Nick Ahamed
Tags: Gbbo, Machine Learning, Data Science, Great British Bake Off, TV Series

Analyzing the Great British Bake Off

Part 1: Initial analysis and some basic predictions

Photo by Brooke Lark on Unsplash

Episode 7 (Festivals) of Series 10 of the Great British Bake Off (Show, for us American viewers) premieres tonight in the UK. The six remaining bakers will compete for Star Baker, and to continue on to the quarter finals. What can the nine preceding Series tell us about who is likely to win Star Baker, continue on, or be awarded the cake stand in the finale?

Since premiering in 2010 and over the last 90 episodes, nine winners have been chosen from 120 contestants. That yields a data set of 1,084 distinct baker-weeks, which I have assembled here. Bakers have only been eligible to compete in 685 of those (i.e. have not been eliminated). Star Baker ⭐ has been awarded 84 times, from 176 baker-weeks mentioned as favorites. In contrast, 185 baker-weeks have been mentioned as least favorites. Paul has given out 30 handshakes 🤝 following stellar bakes in the Signature challenge, but only 2 for the Showstopper. But do these numbers actually mean anything?

Below, I analyze which of these statistics matter to winning Star Baker and which matter to getting eliminated using common machine learning techniques. Next week, in Part 2, I will attempt to predict who will win the show.

How do you win Star Baker?

To identify the factors that predict winning Star Baker, I collected features about the bakers (age and gender), their performance in each episode, and their performance in the previous episode. Performance in an episode is characterized by getting a handshake following the Signature and/or Showstopper challenges, being named a favorite or least favorite, and the bakers’ rank in the Technical¹. Additionally, I included whether or not the baker won Star Baker the previous week.

Since I was using a relatively large number of features given the number of rows, I started with LASSO regression to identify which of these was actually predictive of the desired outcome. I then fit only those features in a logistic regression.

Only two features were selected in the LASSO model. All else being equal, being named a favorite heading into the Showstopper increases a baker’s odds of winning Star Baker by 25 percentage points (pp). Additionally, ranking first in Technical increases a baker’s odds of winning Star Baker by 6pp relative to performing in the middle of the pack.

Of course, this assumes Technical performance is related linearly with winning Star Baker. To investigate that, I fit a GAM (generalized additive model) of a spline of Technical rank, and Favorite status. Below, I’ve plotted the spline. While there is some non-linearity in the relationship, Technical performance really becomes salient once the baker is in the top quartile.

Lastly, I wanted to investigate the relative importance of the different challenges. I fit a logistic regression using only handshakes and Technical performance. Both the Signature handshake and Technical rank have statistically significant positive relationships with winning Star Baker. So does, a Showstopper handshake, but with only two on record, significance was not achieved.

However, conditional on getting last in the Technical and not getting a Showstopper handshake, getting a handshake following the Signature increases a baker’s odds of getting Star Baker by 7pp. On the other hand, conditional on not getting any handshake, getting first in the Technical instead of last increases a baker’s odds of winning Star Baker by 30pp. And, getting a Showstopper handshake, conditional on getting last in the Technical and no Signature handshake, increases a baker’s odds of by a massive 48pp. But, only two bakers² have ever gotten a Showstopper handshake!

What gets a baker sent home?

Unsurprisingly, the two things that predict winning Star Baker also predict who gets sent home. Following a similar methodology, I used LASSO regression to identify which features were predictive of being sent home, and then fit logistic regression on those selected features.

Both being named a least favorite and a baker’s technical rank are related to elimination at a statistically significant level. Controlling for a baker’s Technical performance (at the median), being named a least favorite increases a baker’s odds of going home by 19pp. Similarly, controlling for least favorite status (not named), bakers who rank last in Technical are 13pp more likely to be sent home than bakers who perform at the median. Looking at only performance across all the bakes, handshakes have negative relationships with being sent home, but not significant ones.

Again, there is a somewhat non-linear relationship between Technical rank and elimination. Rank is roughly linearly associated with an increased probability of going home in the bottom half. But among the top half, getting first is not associated with a decreased probability of going home.

Curse of the Star Baker

If Technical performance and being a least favorite are the only two features predictive of elimination, then doing well in the previous episode has no bearing on going home in the current episode. That appears to dispel the Curse of the Star Baker³.

In fact, winning Star Baker last episode is not predictive of losing Star Baker this episode, of doing poorly in the current Technical or not getting a Showstopper handshake.

However, winning Star Baker in the preceding episode is predictive of not getting a handshake for the Signature challenge in the current episode. The incoming Star Baker only has a 1% chance of a Signature handshake. In contrast, the other bakers have a 6% chance. If there is a Curse of the Star Baker it is most relevant in the first challenge of the new episode.