Though it’s had a couple of lapses and the format has evolved, ‘Smartodds loves Statistics’ is 5 years old now. In that time there have been 210 posts covering many topics, all having at least some slight – and sometimes very slight – connection with Statistics. Though the primary aim of the blog is to share ideas about Statistics that are relevant to individuals working in the context of sports modelling, the posts themselves haven’t always been directly related to sport. In fact, the majority haven’t. During the Covid lockdown period, for example, the blog was dedicated explicitly to statistical issues connected to epidemiology in general, or the specifics of the Covid pandemic. It’s been fun to write, and I hope it’s been interesting and informative to read.
But… it’s a lonely process. You get an idea, research it, try to turn it into something that will be readable and interesting to people who either do or don’t know anything about statistics, send it out to the universe via the internet, and then, mostly, get nothing back. There are some exceptions. Some posts generate quite a bit of feedback. And some individuals within Smartodds have provided quite regular feedback over the years (thank you especially: Richard G, Peter L, Paul B, Fab T and Nity). Puzzles and activities also generate quite a lot of interest. But generally, posts get sent out and I don’t really know whether anyone found them interesting or not.
So… I was delighted – well, let’s say thrilled – recently to get a mail from Anders. Anders, it turns out, is a researcher at a government institute in Denmark and had developed a passing interest in the use of Statistics for helping to price football matches. Because of this, he had stumbled across the blog and found it interesting enough to read back through all the old posts. He subsequently wrote to me about this statistical issue he’d been thinking about.
Like many countries, Denmark has its own version of the TV quiz show ‘Who Wants to be a Millionaire?‘. The format and rules are identical to the UK version, but the prize money is in Danish Kroner. Anyway, a while back on the 22 February, 2022, one contestant, Balder Kringelbach, got to the final question, which was as follows:
Which of these Danish comedy movies premiered first?
A) Sover Dolly på Ryggen
B) Klassefesten
C) Blå Mænd
D) Superclasico
Balder had already used the three ‘lifelines’ that the game offers contestants – ‘phone-a-friend’ etc. – so his choice was either to gamble in a ‘double-or-nothing’ bet on this final question, or to quit without answering and leave with the half-a-million kroner already won. Balder was certain that Blå Mænd was older than each of Sover Dolly på Ryggen and Klassefesten, but had no idea which of Blå Mænd and Superclasico was the older. He reasoned that the choice between answers C and D was therefore 50-50 and decided the risk was too great and stopped, keeping the half-a-million Kroner, but not giving himself the chance to become a millionaire.
However, Anders argued that from a statistical point of view Balder should have answered the final question.
To simplify discussion, denote the movies by the quiz answers. So, ‘Sover Dolly på Ryggen’ is film A, and so on. Then, assume that the ordering of the letters A, B, C, D corresponds to chronological order. So, for example, the ordering A, B C, D would correspond to Sover Dolly på Ryggen being the most recent release, followed by Klassefesten, and so on. There are 24 different arrangements of the letters A, B, C, D and therefore 24 possible chronological orderings for the films. Without any additional information, each of these arrangements is equally likely and therefore has probability 1/24. But Balder Kringelbach believed (correctly, as it turned out) movie C to be older than each of movies A and B. We can therefore rule out all combinations in which A or B come after C, leaving only the following 8 possible combinations:
A B D C
A D B C
B A D C
B D A C
D A B C
D B A C
B A C D
A B C D
Of these 8 remaining possibilities, each of which is equally likely, 6 have C after D. So, in actual fact, given the knowledge that Blå Mænd is older than two of the other movies, the probability that it is also older than Superclasico is 6/8 or 3/4. These are much better odds than the 50-50 win probability assumed by Balder Kringelbach, and it would have been in his best interests to take the question on, winning an extra half a million Kroner with probability 3/4 while losing the same amount of money with a probability of just 1/4.
But is Anders right? Please feel free to mail me your thoughts and I’ll give my own take on the issue in the next post.
Postscript: I did once receive several messages in response to my post about a book that comprised solely of numbers generated by a roulette wheel. The aim of the book was to help potential gamblers spot patterns in sequences of roulette numbers that might be useful when playing roulette. And the point of my post was to explain why this is completely futile.
In summary, casino roulette wheels are precisely engineered instruments. The dynamics and physics involved make number prediction virtually impossible, even if a sequence of previous results is available. So, there can be no benefit at all in using generated numbers obtained from anywhere to assist with prediction. In a very small number of published cases, slight defects in individual roulette wheels have been detected, leading to slight biases in the numbers generated. But you would have to have sequences from that same machine for them to have any utility in predicting future outcomes.
Anyway, my post was intended to be tongue-in-cheek, while also emphasising the points I’ve just made here. The author of these books stands to make money from people who don’t really understand the statistics enough to see the futility in using them as a gambling strategy, and that just didn’t seem fair to me. I also included this single page from the book in the post just to give an idea of its contents.
To my surprise, I got a reply from the author himself, which led to a sequence of exchanges with me trying to explain the same points I’ve made above, and the author making an alternative case – which I still don’t accept – for the value of his book.
I also got the following message from another reader who had stumbled across the blog somehow:
Thanks for that picture of 1,000 random numbers. Really appreciate the work. I can see a lot of probabilities now in it. If you circle in red the Nrs. like (35 and 2) and blue (1-19) or green (0 and 4) you will get a picture out of it.
While I am sincerely grateful to receive any responses to my posts, this one does confirm that the blog still has some way to go to achieve its aims of developing a wide understanding of the statistical issues that are important in a gambling context.
