What do Red Deer and Jarno Trulli have in common?

Some of you will know that, in the real world, I’m a student of evolutionary biology. It seems impossible to relate such a subject to F1 – but as I will show in this article, there are a few similarities. In particular, the way teams go about calculating their race strategies is similar to how biologists analyse animal behaviour in the wild.

In F1, the aim of a team is to win the race. One of the key elements for ensuring victory is the strategy – how many times will the driver pit? On what lap? What will the tyre choice be? How a strategy works in race conditions can be the difference between an unexpected victory – such as Jenson Button’s in Bahrain last season, where he overcame the cars ahead of him thanks to a well-timed pit stop – and an embarrassing failure, like Rubens Barrichello‘s at the Nurburgring, where strategic bungling saw him stuck behind Felipe Massa for several laps. The time lost to Massa saw Barrichello drop from an assured podium finish to a dismal sixth place.

In biology, the ultimate “aim” of any organism is to maximise its reproductive success – in other words, to ensure that it produces as many offspring who survive to maturity as possible. This desire is fundamental to evolution: natural selection relies on the most successful organisms passing their characteristics onto their offspring. One of the ways an animal will try to secure mates is through its behaviour – think of red deer stags fighting one another, or the elaborate courtship displays of many common bird species. As in F1, choosing the correct way to behave is an important factor in determining whether or not an individual is successful. Of course, in biology the “choices” are hard-wired into the animal’s brain through its genetic make-up, rather than being active intelligent choices as in F1. But the similarities are there, and I will elaborate on them in this article.

A Brief Introduction to Game Theory

What both F1 and evolutionary biology have in common is a reliance on game theory, a branch of mathematics that examines behavioural relationships in applied situations. Game theory relies on the realisation that a strategy – be it an F1 driver’s pit strategy or an animal’s courtship behaviour – cannot be considered in isolation. Whether your strategy is successful or not depends on the actions of your opponents (that is, individuals competing with you for the same goal).

Let’s go back to the red deer I mentioned, in passing, in the introduction to this article. Male red deer habitually fight one another, using their elaborate antlers, for the right to mate with a particular group of females. We can imagine fighting behaviour as a “game,” where individual deer can choose either to fight, or run away.

We can “score” each particular behaviour; the scores don’t really matter too much in real terms, they are just there for the purpose of comparison. So if our deer chooses to fight, how that affects his chances of mating depends on what his opponent does. If his opponent fights as well, they are likely to tire out, and possibly injure, each other, which carries a negative score. However, if his opponent runs, then he has unhindered access to all the females and scores highly.

On the other hand, what happens if our deer opts to run away? Again, how this pans out will depend on what his opponent does. If his opponent fights, our deer will score nothing as the other deer has “won” the right to all of the females. However, if his opponent runs as well, they will divide the benefit equally.

You will notice that the “best” strategy changes depending on how the opponent behaves. If the opponent fights, it is better to run. If the opponent runs, it is better to fight. This means that there is no perfect strategy – you cannot guarantee the best possible outcome if you do not know how your opponent will behave.

For more information on game theory in evolutionary biology, see the Wikipedia article as a good starting point.

Game theory in F1 strategy

We have seen, then, how game theory can be used to describe the behaviour of animals in the wild. So how does it relate to F1? You will doubtless have noticed some similarities between the problems faced by the red deer and those faced by F1 teams – namely, that no strategy is perfect, and how a strategy works depends on the strategies adopted by other cars.

Game theory is actually used by F1 strategists to calculate the best ways of approaching a race. Of course, the problems faced by F1 strategists are far more complicated than the very simple example of the red deer – for one thing, in 2010 they will have twenty-five opponents rather than just one. Then there are other factors, such as grid position, weather conditions, tyre degradation and so on that must all be taken into account when devising a race strategy (of course, the situation for red deer in real-life situations is equally complicated; the example above is a massive over-simplification). But the basic principles remain the same.

One good example of game theory in action concerns Jarno Trulli, infamous for his “Trulli train,” where his race pace slows from a quick start and holds up many drivers behind him. F1 engineers are known to take the Trulli train into account when thinking up strategies for their drivers. As Barrichello showed at the Nurburgring, failing to account for slower cars on longer strategies can be your undoing.

Race strategy in 2010 and beyond

One of the bigger changes for 2010 is the ban on refuelling, which totally rewrites the book on race strategy. The main change is that strategies will be more flexible, as tyre degradation alone will determine the timing of pit stops – rather than a combination of tyre wear and fuel level. However, the timing of these stops is likely to still be critical in determining the outcome of a race. A change to softer tyres a few laps early could allow a driver to leapfrog someone ahead of him – but then again, too early a change would result in that driver being hopelessly slow as the race came to a close.

Just as it was in the refuelling era, knowing what your opponents are up to is going to be at least as important as knowing your own strategy in 2010. In F1, as in biology, game theory remains the premier tool for evaluating the behaviour of individuals in competition.