I often wondered how racing teams decide whether their drivers should use faster but less durable tires that require more pit stops to change tires during the race or slower but more durable tires that require fewer pit stops. I made an Excel model to analyze this strategic decision.
The answer hinges on parameters relating to the interplay between the tires and the racetrack:
- Pace on prime/option tire: The more durable prime tire will have a specific predicted average lap time as will the faster option tire.
- Pit stop delta: Changing tires takes time, both because the mechanics have to work on the car and because the car must go more slowly as it drives down pit lane.
- Number of laps possible on prime/option tire: Each type of tire will have a notional maximum number of laps at that track, after which its performance falls off rapidly.
- Number of laps in the race: Each race will have a different number of laps.
To use the model, input the race parameters in the upper right. Then, decide on the two strategies you want to compare. For each strategy, input the tire choice and number of laps for each interval between pit stops, also known as a stint.
The model will automatically check for errors, such as whether you’ve pushed a tire past its notional maximum number of laps. It will also summarize the results of each strategy, including the number of stops, tire choice, and total race time.
I’ve made an important simplifying assumption that the tires deliver their average lap time up to a set maximum number of laps after which the tire is no longer used.
In reality, the lap time will vary with the number of laps according to a U pattern. The first few laps will be slower than average as the tires warm up, then the tires will be faster than average as they hit their sweet spot, then they’ll be a little slower than average as they start to slowly degrade, and finally they’ll rapidly become much slower as they hit and exceede their notional maximum.
This simplifying assumption is normally reasonable. A racing team would typically use a tire for as many laps as possible and then discard it after its performance began to rapidly degrade. This would yield a set number of laps at the average lap time as the model predicts.
But it is not absolutely accurate. It is physically possible to use a set of tires long after its performance has begun to rapidly degrade and it is possible to change tires before they reach their notional maximum number of laps.
This simplifying assumption becomes relevant in two cases. First, a team might find itself at its tires’ notional maximum number of laps with just one or two laps to go before the end of the race. In this case, the team would probably stay on those tires rather than suffer the time cost of the pit stop delta.
This is not a critical issue with the model because it would not cause the team to make a bad decision. The team would get the right advice for all of its pit stops until the end of the race. At that point, the model would say to make an additional pit stop; but this would obviously be a flaw in the model and the team would continue racing.
Second, a team might need guidance regarding a strategy that involves using a set of tires for fewer than the notional maximum number of laps. For example, some short races require that the teams make a pit stop and use both types of tires even though it would be mechanically possible to complete the race on just one set of tires. In this case, the team would need to know, for instance, whether to change its option tires at 40% of their notional maximum or at 70% of their notional maximum.
This is an important limitation of the model because it means that the model provides no guidance on pit stop strategy under these circumstances. Fixing this limitation would require creating a function to predict the lap time on each specific lap.
Sadly, Excel does not have a macro for engine noise. If anyone has ideas for that, let me know!
