Bake Off, By the Numbers

I enjoy watching the Great British Bake Off¹Called the Great British Baking Show in the US because of trademarks. There’s got to way to take something as kind and enjoyable as that show, and crunch it down to numbers, right? Let’s try.

For those unfamiliar, the show is a baking competition. Each week, a tentful of bakers make three different creations under time constraints. At the end of each show, the best baker of that week is pronounced Star Baker, and one unfortunate soul is sent home. Then it starts again the next week, with one less baker.

There’s a little more information. Each week, before announcing the results, the hosts and judges discuss who has done well that week and thus may be in line for Star Baker, and who is at risk for being eliminated. So we sort of have a way to grade the contestants each week. I’ve assigned some totally arbitrary point values:

Performance	Points
Star Baker	6
Had a good week, but not Star Baker	3
Everyone else	0
Had a poor week, but not eliminated	-3
Eliminated	-6

As the weeks progress, we can keep a score for each baker, based on these values. The following table shows the average score for the bakers, going into the week in question. Week 1 isn’t included, of course, because no one has a score yet.

Week	Average score of all remaining bakers	Average score of eliminated baker
2	0.5	-0.3
3	1.1	-1.5
4	2.1	0.9
5	2.7	-2.5
6	4.3	1.7
7	5.7	2.4
8	7.7	3.6
Semifinal	9.8	1.8
Final	14.4	14.7

In all cases (except the final week), the baker that ends up getting eliminated has previously been doing worse than average. There is some variation; the bakers eliminated in week 4 had actually done pretty well up until then, whereas week five seems to be the time to clear out those who had been barely hanging on. But those variations are likely just random. The key point is that at each step of the way, the bakers who haven’t been as strong are the most likely to get bounced. And this makes perfect sense; watching the show, you get the feeling that some contestants just hanging on by a thread.

But when it comes down to the final three, past performance is no indicator of future results. At this point, we’re dealing with three skilled bakers, and there’s probably not a lot of difference between them.

What about Star Baker? Here’s the same table, except we show the average score of the Star Baker (going into the week in question).

Week	Average score of all remaining bakers	Average score of Star Baker
2	0.5	0.3
3	1.1	2.0
4	2.1	3.9
5	2.7	4.1
6	4.3	1.5
7	5.7	5.7
8	7.7	7.5
Semifinal	9.8	11.3
Final	14.4	13.8

The first few weeks look reasonable; through week 5, the better you’ve done previously, the better your chance at Star Baker. But then, week 6 throws a monkey wrench into the mess; typically the Star Baker is well below average! And in all the weeks after that, there is basically no correlation between a baker’s past performance and their ability to get Star Baker (or win the competition).

Bottom line, if someone looks shaky on the show, they are probably going to get eliminated pretty soon. If you’re below average, you’ll get bounced. The cream rises to the top, but how that cream is eventually ranked is anyone’s guess.