Formula One Motor Racing is one of the most fiercely contested sports in the world. Racing teams pour millions of pounds a year into making their car the fastest, and the very best, with the rewards even greater skill. Drivers put their lives on the line, pushing to the very extreme of human capacity in that search for glory, and the right to be called a World Champion. In such high-stakes situations, it is crucial that each team get their optimal strategy during a race, so that they can achieve the best result possible. This comes to a crux at the Monaco Grand Prix, often seen as the highlight of the season with special prestige reserved for the winner of this race.
- Soft tyres, faster but also much less durable
- Hard tyres, slower but able to last much greater distances
The optimal race time would be running all 78 laps on new soft tyres. This is not possible however, as tyres wear down after periods of use. Once they are in this worn state they will lose approximately 1 second a lap[1]. Consequently both tyres and their states, as well as pit stops can be compared with the optimal race time as such:
In this model I will use two drivers, Lewis Hamilton and Fernando Alonso, and compare their contrasting fortunes with two different strategies. Alonso will use a two stop strategy. Lewis Hamilton however is known to be a very aggressive driver, and in Monaco he can only make tyres last around 25 laps[1] before they become so worn and used that they would explode and force him to retire from the race. He must therefore us a 3 stop strategy, since there are 26 laps between pit stops in a two stop strategy. I have picked these two drivers as the cars they were racing in, McLaren and Ferrari respectively were of a broadly similar speed, and any minor speed difference is negated by the tight twisting nature of the Monaco GP. We are also making the assumption that they start together i.e. There is a negligible distance between the two as of Corner one of Lap 1 of the Grand Prix. This is slightly unrealistic, as different qualifying positions could increase or decrease the initial gap between the two drivers, and the gap can fluctuate depending on position, but this point will be revisited later.
The ‘optimal time’ to cover the 78-lap Monaco Grand Prix would be all 78 laps on new soft tyres. But since soft tyres are not very durable, due to new tyres brought in by Pirelli at the start of the 2011 season, they would only last 10 laps[2] before becoming worn in this example. The hard tyres however are much more durable, able to last 20 laps[2] before becoming worn down.
Therefore, Alonso’s and Hamilton’s total time lost from the optimal time would look like this:
This would mean Hamilton over the full race distance is 5.8s slower around Monaco than Alonso. And on Monaco, known for being very difficult to over-take when on the same tyre, this means Alonso would most likely finish ahead of Hamilton.
Branching out and assuming that the drivers could pick their strategy, the Two Person Zero Sum game for Lewis Hamilton’s race strategies would look like this:
The Monaco GP and its tight twisty circuit is notorious for accidents and collisions. Such incidents often bring out the safety car, which is designed to slow down the cars racing while debris from accident is cleared away. No racing is allowed during this time, and this drastically changes the time lost by each strategy. Since a safety car effectively pauses the race, anyone taking a pitstop at this moment would not lose any time from that pitstop, as while the cars will all slow down to around 2 minutes a lap[4]. With those extra 42s per lap it would be easy to take a pitstop, and the 25s penalty that it incurs in that time. After that moment of pitstop, all the cars bunch up together so any gap between two cars is nullified as well.
The safety car has a 70% chance of appearing during the Monaco GP, so assuming a uniform distribution of safety cars the chances of it appearing in the second half of the race (after lap 40) is 35%. Were the safety car to come out in the first half of the race, it would be very unlikely to have any dramatic effect on the overall strategy, or the team would most likely change the strategy altogether, which I am not looking at in this model.
If the safety car comes out, then the gap between the two cars get nullified, and in essence a new race will begin. If this happens between laps 40-52 (before Alonso’s second stop) they will both pit, and Hamilton will have to make an extra third stop as well during the race. However Hamilton has the advantage of soft tyres and new hard’s when Alonso’s are worn, meaning he will have much faster tyres, be able to overtake him at a later point and beat him in the race. If this happens after lap 52 (after Alonso’s stop), Hamilton gains a free pitstop and will have considerably less worn tyres than Alonso, resulting in him being faster and again far more capable of over-taking. We shall assume that he indeed does so. Thus in all scenarios a safety car allows Hamilton to beat Alonso in the second half of the race.
This model makes the assumption that the cars start and race with no distance apart before the first sequence of stops. In reality there would be a distance between the two, with one being ahead of the other due to factors like grid starting positions and on-track battles with other cars. This model would have to be improved to be flexible for different distances between two drivers
A safety car appearing in the first half of the race is not taken into account. This is because of the variability of strategies at this phase. For example in the 2011 Monaco GP the top 3 were as follows:
- Vettel: 1 stop
- Alonso: 2 stops
- Button: 3 stops
While this model only looked at the Monaco Grand Prix, there are 19 other races in the season to take account of, each race unique in its required strategy and indeed the likelihood of a safety car appearance, which is the core variable of this model. This percentage would therefore change respective to which track was being raced on.
[2] The tyres will not always last the exact predicted time periods. Other aspects such as the aerodynamics of the different cars, the driver characteristics and the state of the racetrack itself can fluctuate these numbers. Thus, much like point 1, I have picked two easy to work with, straightforward numbers, but the results of this model can easily be re-worked with more precise data, to incorporate the gradual decrease of tyre quality .
[3] During the third stint for the last 8 laps (Laps 52-60) Hamilton would only lose 2.4s in total, as he will be on used softs while Alonso is on new hards (giving the hards an advantages of 0.3 seconds). These changes mean the total time lost now becomes 24.4s instead of 30s.
[4] Depending on the nature of the incident, the safety car may last a variable number of minutes per lap. Two minutes is a fairly accurate representation, but the model can be adjusted for this.
[1] This data is very difficult to come by without hindsight, as F1 teams are very secretive about their information lest they should give away some advantage to the opposition on the day of the race. At best the media can only guesstimate the durability. Thus I have picked uncomplicated, easy to work with numbers, but the results of this model can easily be re-worked with accurate tyre and car data.