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Octopi and expectations

July 12, 2010

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.

From the Guardian. (c) Getty Images.

A large orange-brown octopus sits in a plastic box with a Spanish flag on it. Adjacent is another, lidded, box bearing a Netherlands flag.

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%.

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5 Comments leave one →
  1. Paul Skinner permalink
    July 12, 2010 12:34 pm

    Just to throw in some more, I believe I overheard that Palpo Paul hasn’t got a game wrong since 2002’s World Cup (he does European Championships and World Cups only, I think).
    But I may have misheard.

    “when in actual fact, if the coin is fair, the probability of heads remains 50%.”

    Probably not. If it’s landed on heads proportionally more it’s more than likely because that side of the coin is weighted differently. Fair coins don’t exist. It’s unlikely to be more than a single percentage point though.

    I understand the point you were making though. 1 in 128 (if my maths hasn’t failed me) is reasonable odds of getting 7 heads in a row.

  2. July 12, 2010 1:02 pm

    Well yeah, hence the ‘if the coin is fair’ caveat. Real-world coins, same as real-world dice, tend not to be perfectly fair because of the way we make them, but the point stands.

    Apparently Paul got a couple of calls wrong at the last European championship, so he doesn’t have a 100% record.

  3. July 14, 2010 12:29 am

    If you actually look at his results, Paul almost always picks Germany, with 11 bets for, 2 against (and like Wikipedia says, the only times he doesn’t pick Germany, he picks a country with a very similar flag). In fact, for every single game of Euro 2008 he chose the German box.

    Germany are one of the best teams in the world and, if you were to simply bet on them winning every match, you’d do pretty well. Presumably, at some point early in his career as a “pundit”, he was conditioned to choose food from the box marked Germany. Perhaps he was trained to by aquarium, perhaps they accidentally conditioned him without being aware of it (like “psychic” dogs and horses who in fact just read their owners’ body language), or perhaps it’s down to recognition (every match he predicted except the World Cup Final involved Germany, so every time, a German flag was presented to him with his food; presumably the flag is associated with food to him now).

    Whichever way, I’m almost sure there’s bias there. I’d like to what predictions he’d make in matches where Germany weren’t playing – that would be interesting.

    (Cynically, I think that’s also why he’s been retired. If asked to prognosticate on anything other than German international football, he’d probably score little better than 50:50. The aquarium staff know his lucky streak will end sooner or later.)

  4. July 14, 2010 2:13 pm

    I suspect you’re right on the question of Paul’s retirement.

    And you also have a very good point with regard to the possibilities of some form of practical bias.

    My main point was meant to be the one about how people forget that there are thousands if not millions of people predicting World Cup games, and so it’s not surprising that somebody got a string of them right for whatever reason. And then I got sidetracked with maths, which I should really leave to people who know how to do these things.

    I’d be interested to see whether the flags had something to do with it – the Wikipedia page mentions that cephalopods are attracted to bright horizontal stripes, which would explain his affinity for both the Spanish and German flags. I wonder what would happen if, say, the boxes were marked in writing?

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