Cake Club – statistical analysis

Cake Club was a roller coaster ride of unexpected triumphs, unforeseen trouncings and – let’s be honest – a winner that nobody could have predicted.  If Nick’s win – after having to be persuaded to take part at all – taught us anything it is that in the topsy-turvy world of Cake Club, appearances and prejudice count for very little in the face of the wild whimsy of fate.  Or does it? Maybe Cake Club is a numbers game; maybe the results are predetermined by the influence of factors which are quite readily observed and quantified.  Only one type of person can help unravel such mysterious conundra – a statistician!

Sadly, we don’t have one of those on the staff so you’ll have to make do with me.  And I haven’t been in a statistics lecture for the fat end of a decade.

The first thing to do was obtain the data.  Obviously my memory is perfect in every way but, as it happens, I wasn’t present for every round so I just needed to double-check.  I had a look on this blog but sadly certain people have been less than rigorous about publishing up-to-the-minute status updates with regard to cake club concoctions and results so there were still some gaps, hem hem.  I did what I usually do in such situations and whinged at some volume to nobody in particular until I got some attention.  Luckily for all within earshot, Louise told me she had all the Cake Club emails saved in her outbox and promised to email them over once she had done some actual work, thanks Carl; shut up now.

The emails were a massive boon and I quickly decided on a strategy for recording the data, keying in names and departments into a big spreadsheet.  Here are the distributions by department:

Interesting what a disproportionate slice is given over to Marketing, given that only one of them actually got to the final.  This is, as any Liberal Democrat will tell you, a failing of the tournament system.

However, backslapping was not on my agenda.  I was interested in something far more interesting: the perfect Cake Club recipe!  I went back to the spreadsheet and created eight columns which contained 1 and 0 for ‘yes’ and ‘no’.  The first column recorded whether that cake won or not and the remaining seven recorded attributes of the cake.  The attributes ranged from ingredients (chocolate, fruit) through style (sponge, pie) to presentation (individual servings, sandwich).  I felt fully confident that I could seive out the statistically most successful cake and, with this information, travel back in time a fortnight and make sure that I won the final!

Here are the distributions of the various attributes.  Remember, there were 30 cakes in the tournament total:

Two thirds were sponge!  And over half had chocolate in!  But did popularity among bakers curry favour with the voters, or was it a recipe for disaster?  The proof is in the pudding.  I set up a more complex calculation, looking at the percentage of times a particular attribute won on occasions where it was used.  With such a small sample size (only three cakes in some cases) the results weren’t ever going to be accurate but I reckoned I could make some sort of rough comparison.

If an attribute had no effect we could assume it would win  exactly 50% of the time (as you can only either win or lose you have a 50% chance of either, assuming it’s random) so I subtracted 50% from each result to see which ones affected the score negatively (winning less often than 50% of the time) and which affected the score positively (winning more than 50% of the time).  The results are intriguing:

Notice that the best-performing ingredient, nuts, is one of the least common and chocolate, by far the favoured flavour, makes a rather poor showing, doing worse than random.  People are indifferent about pies but sponge sandwiches are the way forward and despite the time and effort it takes a pretty special person to make a success out of cupcakes, almond mice etc.

It seems that the best possible cake is one in a sandwich format, with sponge and nuts – weirdly, this describes precisely the cake I made in the semi final!  If someone in Marketing had made it, that would have made it a statistical dead cert to win any heat.  However, individual serving cakes made by a salesperson with fresh fruit and chocolate .. well .. sorry, Stew; I guess the numbers were against you!

The eagle eyed among you will notice that in the departmental section of the graph I’ve sneaked in a line for baker gender.  Very, very interesting to see that not only did no girls make the final, being female actually counts against you generally; nearly a 10% skew towards miserable failure for anyone who actually follows a recipe and cleans up after baking – let that be a lesson to you, girls!

There’s been a lot of smack talk and scandal in Cake Club this inaugural year and it was good to get some real numbers down.  Finding out that blokes really are 8.33% better at baking was just the icing on the cake! Hope you enjoyed seeing some hard facts.  All I can say is, next year you’d better watch out for nut sponges made by men from Marketing.

Oh, and if you can spot all the cake-related puns in this post… you need a hobby.  Baking, perhaps.