Bill Edgar in the paywalled Times draws our attention to a nice contrast - that the chances of New Zealand getting a draw against Italy were in fact higher than the chances, before the tournament began, of Brazil winning the Cup: 5-1 against 11-2.
However, the Kiwis’ result is being described as a “shock” and “surprise” in a way that Brazil winning the Cup wouldn’t be. How can this be?
The answer, I think, lies in two cognitive biases.
One is the availability heuristic. When we’re challenged to think of the chance of something happening, we often respond by trying to imagine the event. And it’s easy to imagine Brazil winning the World Cup because they’ve done so five times, whereas New Zealand have never got a result against Italy (though they did run them close last year in their only previous meeting).
The other bias is a version of the conjunction fallacy - the failure to see that the combination of even quite likely events is in itself an unlikely out-turn.
For Brazil to win the World Cup, they must succeed in their group and then win four games. This is five events. Even if success in each is a high chance, success in all is improbable. For example, a 70% chance in each amounts to a less than 17% chance overall.
What we have here, then, is an example of how markets can be wiser than individual intuition. Our intuition is that New Zealand’s result was a shock whereas Brazil winning the Cup would not be. But the market, which set the odds, was not so easily fooled.
Sometimes, then, it’s wiser to trust the market than our intuition.
You might object here, reasonably, that markets often go horribly awry. Which brings me to this paper (pdf) by Brock Mendel and Andrei Shleifer. Markets go wrong, they say, because sometimes rational but uninformed traders mistakenly believe that a price rise is driven by informed traders and not by noise traders. However, this mistake is only possible because very often - as in our example - prices really are right and do embody genuine information.
In this sense, markets are occasionally inefficient precisely because they are so often efficient.
However, the Kiwis’ result is being described as a “shock” and “surprise” in a way that Brazil winning the Cup wouldn’t be. How can this be?
The answer, I think, lies in two cognitive biases.
One is the availability heuristic. When we’re challenged to think of the chance of something happening, we often respond by trying to imagine the event. And it’s easy to imagine Brazil winning the World Cup because they’ve done so five times, whereas New Zealand have never got a result against Italy (though they did run them close last year in their only previous meeting).
The other bias is a version of the conjunction fallacy - the failure to see that the combination of even quite likely events is in itself an unlikely out-turn.
For Brazil to win the World Cup, they must succeed in their group and then win four games. This is five events. Even if success in each is a high chance, success in all is improbable. For example, a 70% chance in each amounts to a less than 17% chance overall.
What we have here, then, is an example of how markets can be wiser than individual intuition. Our intuition is that New Zealand’s result was a shock whereas Brazil winning the Cup would not be. But the market, which set the odds, was not so easily fooled.
Sometimes, then, it’s wiser to trust the market than our intuition.
You might object here, reasonably, that markets often go horribly awry. Which brings me to this paper (pdf) by Brock Mendel and Andrei Shleifer. Markets go wrong, they say, because sometimes rational but uninformed traders mistakenly believe that a price rise is driven by informed traders and not by noise traders. However, this mistake is only possible because very often - as in our example - prices really are right and do embody genuine information.
In this sense, markets are occasionally inefficient precisely because they are so often efficient.
Surely also it's to do with the alternatives? The chance of any team winning is small, but (if they were favourites, not sure) Brazil is higher than any other. Therefore if Brazil win, it was the least unlikely victory, and hence not a surprise.
But in Italy/NZ there are only three options, and two (NZ win and draw) are (say) only 1/4 as likely as the other (italy win).
Posted by: Matthew | June 21, 2010 at 05:05 PM
It's more to do with the fact that the odds you quote are bunk. If NZ has only once done well against Italy in the past, what idiot would say their chances of drawing was 5-1?
Further, given that there have been 16 world cups since WW2, and Brazil have won 5 times, shouldn't their odds be more like 11-5, rather than 11-2?
Posted by: william | June 21, 2010 at 06:14 PM
I agree with Matthew on this. It's like the old Feynman thing: if you see a car at random, then the chances of it having the licence plate ARW 357 are very low - but so are the chances of it having any other specific licence plate. You don't treat that multi-million-to-one-shot as a shock. On the other hand, it's much, much more likely that you'll see a Rolls-Royce, but that will seem more unusual and surprising if it happens.
Posted by: Tom | June 21, 2010 at 07:54 PM
Another issue - a priori, football matches are very often draws. World Cups, however, always have a winner but it's highly uncertain who it will be. Winning the World Cup is unlikely for all teams, even Brazil, but the draw is on the cards in all football.
Posted by: Alex | June 22, 2010 at 12:49 PM
I think the psycholgical effect going on could be described slightly differently.
what is the alternative to Brazil winning? Mathematically is is Brazil NOT wining, but psychologically the alternatives to Brazil winning are are Germany winning, England winning, France winning etc.
So Brazil winning might me the *most likely* of the range of alternatives. Which might give it a halo effect - Brazil winning is the 'most likely' outcome.
Posted by: botogol | June 22, 2010 at 04:13 PM
The odds against France winning are likely to be bountiful at the moment. Betting against England is also a nice proposition but the two bets are not comparable for obvious reasons though a mishap (for England) this coming afternoon could make them so. So what are the odds of the two likelihoods gaining similarity?
Posted by: Cliff Tolputt | June 23, 2010 at 01:03 PM