This is just a quick update on my previousposts about the distribution of chocolates in tubs of Celebrations.

I recently purchased two tubs and noticed a change in the distribution, mainly because there is now 12.3% less chocolate (by mass) in a tub than there was in 2008!

This means a typical tub contains around 95 chocolates, down from 107 previously, presumably in reaction to the Current Financial Climate. Two tubs is not enough to make any strong inferences about exactly how the distribution has changed, however, it does seem as if the previously over-represented Mars, Snickers and Bounty account for most of the reduction, with the much-coveted ‘Teasers’ remaining the same at 13 per tub, and the rarest Galaxy chocolates may even have increased from just 22 in a tub to perhaps 25 (adding all three types together).

Personally I still consider Celebrations to offer a superior selection, and there may well have been similar stealthy reductions in other chocolate collections. Perhaps in 2010 we can look forward to a return to 1kg tubs, no doubt accompanied by much fanfare proclaiming “14% more!”.

In the previous post I described my experiment regarding the distribution and popularity of the different chocolates found within a Celebrations tub. After several months of rumination, cogitation, and procrastination, I am ready to publish my findings.

(Incidentally, this is fully the intended publishing style for this blog – posts appearing infrequently, but with a fair amount of thought and effort behind them, which is the style I prefer to find myself when browsing through the RSS feeds I subscribe to).

I should note that I have since discovered some prior work in the field: popular newspaper The Sun reported on the unfair distribution of Celebrations chocolates way back in 2006, although their methods were not so rigorous. In response to claims of ‘scrooge tactics’, Masterfoods responded “The mix is made up of different quantities of various brands. Research shows that’s what people prefer.” We shall see how that statement holds up against a more scientific examination of the facts.

The results of the auctions were, sadly, inconclusive. Only three of the tubs sold (the Mars, Maltesers ‘teasers’, and Galaxy tubs), all for the starting bid. I had thought I could at least use the number of views of each auction as a simple proxy for popularity, but on closer examination this seemed to have been biased by the order in which the listings appeared, with the first and last listed gaining a disproportionate number of views.

(I am currently auctioning off the remaining tubs, still well within their use-by date, in time for Easter and with free postage. The auctions end April 5th 2009 and can be found here.)

Fortunately I discovered an alternative measure of chocolate popularity: The Chocolate Review, where different chocolates are scored out of 10, with most chocolates receiving over 50 votes. With this information in hand, I was able to plot out the relationship between the average number found in a tub and the popularity of a given chocolate.

First conclusion: the more delicious a chocolate is, the rarer it tends to be.

The correlation is clear but not perfect, and it should also be noted that the scores are for the full-size purchase versions of these chocolates, which differ somewhat from the Celebrations size – particularly the Maltesers ‘teasers’. Also note that the Galaxy Truffle is not scored on the Chocolate Review, although I strongly suspect that this would follow the correlation.

One natural explanation for this apparent injustice would be that more delicious chocolates cost more to make per gram, and as such the cost of a Celebrations tub is kept down by skewing the distribution towards cheaper varieties. Checking the details of the chocolates in their standard form on Tesco’s site, I was able to estimate the cost-per-gram of each type, with the following result:

Second conclusion: more delicious chocolates are more expensive, pretty much. Such is life.

This brings us to the final and crucial question: is the distribution of Celebrations chocolates in a tub mercilessly determined by the average cost per gram alone?

The Maltesers ‘teasers’ location is clearly an outlier. This is almost certainly due to the fact that these ‘teasers’ are significantly different to regular Maltesers, so the cost-per-gram used here is incorrect. Checking with two local shops I found the cost-per-gram of Maltesers to be the same, so the Tesco pricing was not an anomaly. Disregarding this datapoint, we can be fairly certain of the final and most damning deduction, which stands in marked contrast to Masterfoods’ disingenuous statement.

Third conclusion: chocolate distribution is determined by price, not deliciousness.

There is one beacon of hope visible from these apparently bleak results. Anecdotally (read: in my opinion), and as suggested by the successful sale of such a tub, Maltesers ‘teasers’ are in fact quite notably delicious, arguably more so than regular Maltesers – yet the results strongly suggest that they are far cheaper to produce. If we examine a cross-section of the two types, the differences become clear:

So we reach our final and most optimistic conclusion:

Fourth conclusion: Maltesers ‘teasers’ may well be more delicious than their cost would suggest, and could potentially be developed into their own independent product line.

Further research is needed in this area, but I think for now I shall move on to other areas of research.

-metatim

Edit (07/04/2009): On the bottom of the tub, the ‘teasers’ have the following description: “Everybody’s favourite, grab ’em before they’re all gone!”. It seems Mars (formerly Masterfoods) have indeed done some research, and it endorses my final conclusion.

Second Edit (14/04/2009): A figure that was conspicuously absent from this analysis: given the standard distributions and cost-per-gram of each chocolate, a natural question to ask is: what is value of the standard tub contents? Assuming truffles cost the same as galaxies and that teasers actually do fit the distribution/cost trend, my estimate is £7.69. Since the standard price of a tub seems to be about £5, this means that these tubs are actually a very efficient way to buy chocolate. This data has been added to the Google Docs spreadsheet.

Third Edit (17/07/2013): Much has changed in the ~4.5 years since this research was originally conducted. For one thing, the amount of chocolate in the tubs was reduced. Mini Twixes have now been added to the mix, (based on a couple of tubs, these appear to have largely substituted Mars/Snickers, so evening the distribution a little). Finally and most importantly, Mars did indeed launch a stand-alone ‘Teasers’ offering. Hooray!

Fourth Edit (11/09/2015): These days there are only 750g of Celebrations in a tub, the truffles are out, Twixes are in. You can find out what the distribution looks like over on Mental Floss.

Around this time of year, everyone’s minds turn to the mathematics of random distribution and Bayesian inference, although these terms are not normally used.

This is all due to those tins or tubs or boxes of assorted chocolates, along with the fact that people have preferences among the chocolates on offer, and the problem that these preferences often overlap.

Two questions inevitably emerge:

1) Why don’t they sell tins of each type of chocolate, and

2) Since they don’t, are the chocolates at least fairly distributed between tins?

In this experiment, I set out to answer these questions. I would simply buy a large number of tins of a particular kind, find the average chocolate distribution, then sort them into tubs of each type and sell these tubs on eBay with all proceeds going to charity in order to establish their value.

Here in the UK there are a handful of big names that sell you a few delicious chocolates among a big tin of much less pleasant ones: Cadbury’s Roses, Cadbury’s Heroes, Nestlé’s Quality Street, and Mars’ Celebrations.

Of these, the Roses seem to cause the fewest arguments. Heroes are a bit boring and odd. Quality Street cause the most trouble with just a few delicious options among a terrible array of toffee-based disappointments.

Unfortunately there are twelve different chocolates in a tin of Quality Street, only two of which seem to be widely appreciated. I would probably have had to buy at least 13 tins, and I would be left with 10 very unpopular sweets to sell on eBay.

Celebrations were the most promising. There are just 8 types, all of which are quite acceptable, but some of which are nonetheless noticeably more delicious.

So over the course of a week I bought 9 tubs of Celebrations from three different supermarkets, the idea being I would have good odds of being able to make up 8 tubs of each type.

I cleaned out three containers, donned a pair of brand new rubber gloves for hygiene (even though the chocolates are individually sealed), and began sorting and counting.

This process took approximately 90 minutes, although would have been a good deal faster if I hadn’t been carefully counting as I went along, and hadn’t been distracted by Robert Llewellyn telling me how buildings are demolished.

It rapidly became apparent that I had made a critical mistake.

It turns out that the distribution of Celebrations is extremely consistent but very far from fair, and I would need an additional tub in order to make up a nice round number of single-type tubs. Over 10 tubs, I obtained the following totals:

213 Mars
202 Snickers
160 Milky Way
140 Bounty
131 Maltesers ‘teasers’
76 Galaxy Caramel
72 Galaxy Truffle
70 Galaxy

Visually, that means a typical tub would look like this:

This presented a problem. In order to run a fair test on eBay, I needed each tub to have an equal number of chocolates, at least the same as the standard amount (which is, on average, 106.3).

The solution I settled on was that since (presumably) the Galaxy chocolates have a similar appeal, and there were so few of each type, I would bundle them together. In this way I was able to make up 9 tubs of 100 of a particular type, with a random additional 10 of the leftovers added so that there were more than the usual amount of chocolates, and also to make the end result look a bit more like some kind of hilariously improbable random sorting.

As I write this, I am about to put said tubs on eBay. These are the tubs I was able to put together, with links to the individual auctions: