Octopi and expectations
Have you heard about Paul the psychic octopus?
Paul has become something of a minor media sensation (at least in Europe) following his correct prediction of the outcome of eight World Cup games in a row – all of Germany’s games (three group games, round of 16, quarters, semis, third-place playoff), and last night the final. He makes his calls by, on being presented with flag-marked boxes, picking a mussel out of one box or the other.
The English media, at least, have seized on the fact that Paul was hatched in Weymouth and milked the story for all its worth in the apparent hope of sustaining waning English interest in yet another World Cup we failed miserably at. Suddenly the psychic octopus is the toast of every newspaper in the country and it is bizarre.
The Guardian alone has run at least ten articles about the psychic octopus, plus an open thread inviting readers to discuss their psychic pets. The BBC have got in on the act; the Daily Mail; the Telegraph; Sky. Twitter is full of octopus-themed tweets even now. Why are people so fascinated?
The obvious answer is that it’s because, duh, psychic octopus. They do not exactly come along every day. However. If we discount the octopus factor for a moment, what do we have? A pundit picks the results of eight games based on no more than a hunch – I think that ‘this mussel smells better’ qualifies as a hunch – and gets all eight right. How likely is that? Not very likely at all, is our gut instinct. Various of the articles, despite a veneer of irony and protective quotemarks around ‘psychic’, still reek of confusion – how unlikely is Paul’s record, exactly?
Of Paul’s eight correct calls, three were group games, and five knockout. Now, there are three possible results in a group game, only two in a knockout; I don’t actually know whether Paul had the option of predicting a draw during the group stages, but let’s assume that he did. So the combined probability of calling all six results correctly, completely by chance, is 1/3 x 1/3 x 1/3 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 1/288 or about 0.3%.*
0.3% is not a very big percent, but think about it. If you took a group of five hundred people calling results entirely at random, it means one or two would get all eight right purely by happenstance. And at any World Cup there are many, many more than five hundred people predicting games, often essentially at random (or certainly with no real basis other than gut feeling). The bookies clean up on the thousands who get it wrong. Given that there are millions of people with opinions on the World Cup, there are bound to be hundreds or thousands who correctly called eight games or even more. The only thing that’s different about Paul is that he’s probably the only octopus, and everything’s more interesting with tentacles.
There’s one more factor, which is the weight of expectations. Being human, and therefore innately inclined to over-value things that seem to come in patterns,** we latch onto things that seem to be accurately predicting the future. People seize onto the ‘hits’ in horoscopes and ignore the misses; people give professional psychics credit for their successes and ignore their failures, and so on. Given the extent to which Paul the octopus and his record were featured in European media, especially in the later stages of the Cup, could he have ended up influencing the games themselves?
I think it’s unlikely that he had any substantial influence. But it is harder for a team to take the field when it’s being confidently announced left and right that they will lose, and it’s harder to ignore pundits who are generally held to have an accurate record on such pronouncements. It depresses confidence, and any player of any sport can tell you how important it is to have your head in the right place going into a match.
You can argue, of course, that professionals should be able to cope with this kind of thing – but at bottom, they’re only people, and people are remarkably quick to take outside signals on board. This is why it’s now accepted that telling children that they’re ugly, or broken, or failures, all their lives will – surprise, surprise – make it a lot harder for them to accept and do well for themselves later on.
Sport punditry is a much weaker version, but it’s on the same spectrum: being relentlessly informed of your impending failure makes it more likely to happen. Not only that, but other parties can be influenced as well: if, say, the referee has also been bombarded with messages that one team is worse, or plays dirtier, or whatever, how will that factor into their decision-making? Well, how does a teacher respond to a pupil with a reputation for troublemaking? Unconscious bias is bias still.
The modern media circus around important sporting events is all part of the fun, and doing away with all pre-game predictions is unthinkable; but I do wonder if, and if so how far, it skews the results.
*This assumes that all results are equally likely, which, given the disparity between teams particularly at the group stages, isn’t always the case. I think it can be safely assumed, however, that Paul the octopus isn’t aware of the current world rankings and picked at random. The Wikipedia article has more in-depth statistical treatment but does not appear to account for the possibility of draws.
**I recommend Ben Goldacre’s Bad Science for some good examples of the human tendency to misjudge the likelihood of things. The classic is thinking that a coin that has fallen heads-up six times in a row is more likely to show heads a seventh time – when in actual fact, if the coin is fair, the probability of heads remains 50%.