Archive: game-theory

Shortly after the Canadian Grand Prix finished, Bill asked me in the comments what I thought about the latest tangle that Lewis Hamiton has found himself in.

It was another bad race for Hamilton. Two more clumsy clashes were added on top of the controversial incidents in Monaco that are still fresh in the memory.

It is starting to look like a bad habit.

Montreal incidents weren’t so bad

But the thing is, I don’t think either of the incidents in Montreal were nearly as bad as what he got up to in Monaco.

Yes, the move up the inside of Mark Webber at the start was too optimistic. But in the dry it probably would have worked. If you look at Hamilton’s onboard camera shot, Hamilton looks like he is going to make it, but then understeers through a puddle.

It would be right to argue that Hamilton should have taken the conditions into account. So in that respect, it was a dodgy move on Hamilton’s part. But at least he didn’t just steam straight into Webber in stable conditions, as he did to Felipe Massa and Pastor Maldonado in Monaco.

As for the crash with Jenson Button, I think this was an unfortunate racing incident. Hamilton got such better drive than Button, that it is perfectly understandable that he had a go. Plus, the racing line along the pit straight at Montreal effectively goes from the extreme right to the extreme left, back to the right again.

No matter which way Hamilton went, he would have found himself getting squeezed eventually. It was just a bad deal that Button couldn’t see him in his mirrors due to a mixture of bad conditions and confusion. Again, Hamilton should have taken the conditions into account. But, again, at least it wasn’t as malicious as what went on in Monaco.

Why does Hamilton get himself in so much trouble?

It does strike me, though, that Hamilton is taking on far too many of these marginal overtaking attempts. Hamilton has always been a little bit like this, though he had seemed to calm down a bit. His excitable inexperience is no longer an excuse — this is his fifth F1 season. He has more than enough grands prix under his belt to know what’s what.

But what is making him go for all these half gaps? One theory is that he just has to push harder this year to beat Red Bull, and is becoming desperate as a result. Undoubtedly that is part of the problem. But Hamilton had a much worse start to the season in 2009 and he wasn’t quite as clumsy as this then.

Senna’s influence

All the hype surrounding Ayrton Senna, following the release of the successful eponymous film, has brought one Senna quote to the fore:

If you no longer go for a gap that exists, you are no longer a racing driver.

Senna was known for his high-risk, sometimes dangerous moves. The key to Senna, though, was that he was often able to intimidate drivers into moving out of his way. Michael Schumacher also had this trait.

It is well known that Hamilton idolises Senna. When Hamilton goes for a half opportunity, you can imagine him repeating the Senna quote to himself in his head.

It’s more than just “going for a gap”

But overtaking is about so much more than simply driving round another car by going faster. You need to assess the situation; analyse what the opposing driver has at stake, work out what he is thinking and how much he will yield. It is effectively a 200mph game of chicken.

Senna and Schumacher managed to balance the scales of this game of chicken massively in their favour by building up a fearsome reputation. They were the hard-chargers who would impose themselves on their opponents through a mixture of speed and aggression. Perversely, this possibly made it easier for them to overtake.

Hamilton, on the other hand, is very quickly building himself the opposite reputation. He is becoming clumsy Lewis — probably about to cause another crash that will be all his fault.

Even in a situation where Hamilton may have the upper hand on track, he may begin to find overtaking more difficult. Hamilton’s reputation is such that even in a racing incident, he could well find himself being blamed for every clash he is involved in. This, in turn, could make his opponents more open to defending more aggressively.

Could it be that in his attempts to become this generation’s Senna, Lewis Hamilton has actually achieved the reverse?

I was browsing Wikipedia articles about game theory. I learned on the Rock, Paper, Scissors article that there is a Rock, Paper, Scissors world championship — and the world champion is Scottish. How could you possibly not be proud to be Scottish now?!

I remember hearing years and years ago about a study that suggested that talented footballers were likely to come from a background of poverty. It seems to make sense. I have a romantic picture in my head: a group of kids, at the end of a hard day’s slog pushing bikes up hills and climbing up chimneys, kicking a ball around in a street of tightly packed terraced houses; jumpers for goalposts, driver angrily beeping his horn, and so on.

Of course, such things are not allowed these days. The complex of council flats at the bottom of the street contains a huge space in the middle, with nothing filling it but lots of pavement. It is surely the ideal place for youths to kick a ball about, socialise and get fit. There is one stumbling block though: “NO BALL GAMES” pinned to the wall. Some old curmudgeonly busybody comes out of his flat, acts all frail and vulnerable, and threatens to (and sometimes actually does) call the police, acting as though a little kickabout is the beginning of the end of civilisation. So instead, youths these days spend their time standing on corners and knifing people.

Anyway, I can’t find any reference to any hint of a suggestion that being in poverty makes you more likely to grow up to be a footballing genius, so maybe I just dreamt it, or it was a narrow-minded and prejudicial assumption of mine. Greg Mankiw asked on his blog why per capita (rather than total) GDP is highly correlated with success in the World Cup, unlike in the Olympics where total GDP counts for a lot.

This week’s Economist has a little editorial about the World Cup, and notes that the footballing hierarchy is delightfully out of step with political hierarchy. This makes the World Cup refreshingly free of the political issues that sometimes mar the Olympics.

Think of all those robotic East German sprinters, Romanian gymnasts and Chinese swimmers churned out by state-backed programmes. By contrast, a winning football team needs not just athleticism but also a spark of creativity and style that cannot be manufactured by sport’s central planners.

If GDP and success in football are linked, how do you explain poor Brazil’s world dominance and rich USA’s relative mediocrity in football? A comment by Colin on Mankiw’s blog had me convinced for a second:

I believe every one of Brazil’s players competes for a European club. So a big reason Brazil is so successful is that wealthy Europeans are helping to develop their players.

You’ll find that a heavy presence of players in Europe is also found among the more successful African teams.

So really your own GDP can be somewhat irrelevant if other countries are paying to develop your players.

So this kind of turns Brazil’s success on its head a bit. Brazil’s GDP doesn’t matter because talented players will be picked up and developed by European clubs. Maybe the link between GDP and a strong domestic league (rather than a strong international team) is stronger. But while South America has weak domestic leagues, GDP still wouldn’t explain why the MLS in the USA is a load of old pants. Surely, no level of GDP can bridge cultural differences.

I also found this paper on game theory and penalty kicks (via the comments in Mankiw’s post to here to here). At university, the penalty kick was the scenario used to introduce us to the concept of mixed strategies, so I was interested in reading this. I didn’t actually read it all, because I am a lazy bastard. But I want to comment on this quote:

Probably only a trio of economists would have watched videos of 459 penalties taken in the French and Italian football leagues. The authors were testing a complex point of game theory. What they found was that the best place to put a penalty was the middle of the goal, largely because goalkeepers always dive. Yet few penalty-takers actually choose the middle. “I think one reason people don’t is that it’s just incredibly humiliating to a kicker if he kicks in the middle and doesn’t score,” guesses Levitt.

I’m not so sure about this. The paper seems to assume that penalty takers and goalkeepers have only three choices during a penalty kick: left, right, middle. That is far too simplistic in my view. I asked my dad what he thought about penalty takers not aiming for the middle of the goal. We came to the conclusion that, even though the goalkeeper almost always dives, a quick-witted goalkeeper can always use his feet to save a ball heading for the centre of the goal.

So I guess it is actually wise for a penalty taker to avoid aiming for the middle of the goal. Say the goalkeeper is 50% likely to dive left and 50% likely to dive right, and in both instances has a chance to save a ball heading for the middle. If the keeper dives left, he won’t be able to save a ball heading for the right, but he could be able to save a ball heading towards the middle. So surely a striker will always have a better chance of scoring a penalty by striking away from the middle.