Ferrari's Melbourne strategy goof-up

Possibly Sebastian Vettel's tire blow-up was just bad luck, but in Austria Ferrari again failed to translate the potential of the car into good results. Again they were beaten by a Red Bull and, of course, a Mercedes. Canada and Spain were also missed opportunities. Ferrari could have won those races, but their strategy failed to deliver the desired result, which has been all too ofthen the case this year.

It all started in Australia, which was possibly the most obvious strategy goof-up. Ferrari were leading the race after the start and therefore they were in good shape to win the race. Rosberg managed to undercut Räikkönen to claim second place, but soon afterwards the race was stopped to clear the debris of the Alonso-Gutiérrez accident. This presented the teams with the opportunity to make a free tire change. Mercedes decided to put Rosberg on the medium-compound tire, while Ferrari left Vettel on supersofts. After the restart Vettel was able to pull away slightly, but he soon started to lose time and his inevitable pitstop eventually dropped him behind even Hamilton's Mercedes.

In order to understand why Ferrari could make such a horrible error of judgement, it may be helpful to use some game theory. I assume that both teams have the same information about the tires, that is:
1) the medium-compound tire is slow, but will last the remainder of the race

2) the soft and supersoft tires are faster, but less durable, so they have to be replaced at some point

Ferrari had track position, Mercedes likely had speed. The ideal scenario for Ferrari would be to simply copy Mercedes' strategy. However, both teams had to choose their tires simultaneously, so Ferrari had to guess Mercedes' tire choice in order to make their choice. There were four different scenarios: both teams choosing mediums, both choosing the softs or supersofts (which are treated the same in this analysis) or both would choose a different compound (medium or non-medium). How would these choices work out?

If both were to choose the medium-compound tire, then Vettel would be reasonably safe. Overtaking a car on the same tires would be incredibly difficult and there were no more scheduled pitstops to spoil the party. If both drivers were to choose the softer tires, then there would be a possibility for Rosberg to undercut Vettel. The other possibility was for Rosberg to stay out longer so his fresher tires could help him to overtake. Still the chances of Ferrari to win the race would be very real, but it wouldn't be as easy as in the first case. Then the deviation strategies. If Rosberg were to pick the softer tires, he might have the possibility to overtake Vettel, build a lead and chase him again after the pitstop. It was a bit of a risk, but it might work. If Vettel were to pick the softer tires, he would certainly lose the lead due to the pitstop, but later he would possibly be able to regain the lost place on better tires.

Now the ideal strategies depend on the expected pay-off matrix below. The probability that Vettel wins in a particular scenario (left number) is always 1 minus the probability that Rosberg wins (right number), under the assumption that no strange things will happen.

Pay-off matrix.

In this case we assume that probability a is fairly high (for example: 90%). So if both drivers choose the medium-compound tire, then Vettel's chances to win the race are high (and Rosberg's are low). In case they both choose supersofts, then Vettel's chance c is still high, but not as high as in case they both choose mediums (c < a and c > 1-c). In case both drivers choose a different strategy the probability of the driver on the harder tire compound to win the race is higher (1-b > b).

If c > 1-b, there is no Nash equilibrium, as both teams have different interests (Ferrari wants both drivers to be on the same strategy, Mercedes wants to deviate). However, if 1-b > c, then there is a Nash equilibrium at (M,S), so Vettel would choose mediums and Rosberg would choose the softs or supersofts.

This is, however, completely the opposite of what really happened. The actual tire choice was very likely not a Nash equilibrium (if it was the probabilities would make no sense), which is puzzling. Ferrari's strategy wasn't "optimal", nor was Mercedes' response. If both teams had done the "right" thing, Vettel would have been on mediums and Rosberg would have been on softs or supersofts.

Possibly Mercedes played some good poker game and decided to do something unexpected in an attempt to outwit Ferrari, but it might also be that Ferrari out-thought themselves. Their line of reasoning might have been like this: "If Mercedes chooses the medium-compound tires, we will do likewise and we will win the race. So Mercedes will not choose the medium tires. In that case, it's safer to fit the softer tires as well."

This indicates that according to Ferrari c > 1-b (so if Mercedes were to choose the softer tires Ferrari's best response was to fit the softer tires as well) and therefore there was no Nash equilibrium. Ferrari then made the logical assumption that Mercedes wouldn't risk being on a dead strategy (both drivers on mediums) and go for a riskier strategy, which Ferrari then copied. They were wrong, because Mercedes went for the possible easy position gain in case Ferrari would have to stop again. They were proven right, but probably it was more luck than good judgement.