Lap-time based stint analysis
A look at performance evolution though a F1 race (influences not limited to but also inclusive of tire degradation) for the Portuguese GP podium finishers. The effect due to possible tire wear and driving/car capability has been attempted to be isolated by using a correction factor for the true lap speed. Since each lap the fuel/weight is decreased (burned), an increase in car/lap speed is often seen towards the end of the race (also with other contributions from weather, temperature, track surface, etc.). Assuming a race runs from full fuel tank to empty, this analysis uses a linear correction factor of 0.056s time degradation per lap and a 2nd degree polynomial as seen in Figure 1. With the set correction factor (time penalty) acquired for the appropriate lap, it is then added on to each raw lap time. By doing so the final lap time presented within this work is rated for a car assumed to be with full fuel throughout the race until the finish line.
The correction factor was was estimated through a previous personal analysis based on stint averaging for a soft tire during different race stages in the 2020 Eifel GP. An outlier elimination procedure was conducted to negate lap times with pit stops, safety car, etc. accounting for data within an upper limit of 85% of the mean fuel corrected lap time for each driver. Note the performance trends for the SOFT, MEDIUM and HARD tire compound in the plots below.
Linearly fuel-corrected performance overview
Linearly Fuel-Corrected Performance - 3rd degree polynomial data fitting
Linearly Fuel-Corrected Performance - 3rd degree polynomial data fitting
The warming up of tires, slow degradation of hard tires, and the effective starts from the medium tires can all be seen in the comparisons. Bottas was saying during the post race interview, he didn't know how Hamilton got his hard tires to work towards the end... yeah, that looks quite contrasting to what the other two had in comparison for that 2nd stint. Really puts the difference in tire/driver performance between Hamilton and Bottas into perspective. Seems like Bottas couldn't make them work at all, he didn't get anything close to what Hamilton got but compares closely to his completion in Verstappen. Both 2nd and 3rd degree fitting curves for regression was used on the analysis data. Based on observation, while faster, more aggressive efforts where put in during the last few laps of stints, a 3rd degree polynomial skews the trendline due to this data. However a 2nd degree polynomial is seen to fit better and displays the general trend in race time degradation (possibly due to tire degradation) with amounting laps in specific stints.
2nd degree polynomial fuel-corrected performance overview
Polynomial Fuel-Corrected Performance - 3rd degree polynomial data fitting
Polynomial Fuel-Corrected Performance - 2nd degree polynomial data fitting
In addition to the linear approximation, a 2nd order polynomial correction was also tried based on previous data from the Eifel GP. As noted above the first stints for all drivers remain fairly similar to that of the linear condition due it being less impacted by fuel weights early on. However a change in the second stint is seen in all data presented in the plots above (steeper degradation aligned with the correction factor curve). While the publicly available data is very limited, I would guess data such as what we're after would be exclusively in the teams. Since the teams would strategize and have prior knowledge of information regarding which laps drivers where saving tires, charging systems and pushing etc they would be privy to a much better understanding of the performance comparisons especially between teammates. Regardless, we still are able to represent through available data the consistency Hamilton is able to achieve in comparison to his opponents.
This analysis is more a comparison between the drivers where a certain strategy and implementation can be quantified in terms of relative efficiency. Both Bottas and to a lesser degree Lewis, have pace fluctuates much more than Max's stints. While the start (stint 1) seems a bit more obvious for fluctuation, Max really had a nice consistent string of laps on his second stint on those medium tires.
Race pace distribution
This work displays a representative race lap-time distribution comparison for the top 5 finishes in the 2020 Portuguese GP. In having to present this data some “outliers” have to be taken off from the raw lap times that are recorded. A data treatment process was first used and then the filtered data is plotted as shown in the ridgeline plots below.
Raw-data based lap time distribution plots
Fuel-corrected data based lap time distribution plots
Race pace distributions were also plotted as boxplots to identify the mean raw lap speeds as well as their associated variance in times.
Raw race pace distribution as box plots
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