OneFormula
calculations

The fastest F1 driver of all time does not exist. Pure speed in Formula 1 is almost entirely decided by the cars. 

Hence, this "Best-of-all-time" ranking is a combination of speed, guts, tactics and, above all, making the right choice at the right time. Choices on-track and off-track alike.

A top driver with a lesser car will never be a world champion; a lesser driver with a top car can. That explains the car's dominant share in F1. As an example below the performance of

• • Vettel- with Red Bull, Ferrari, Aston Martin

  • Button- with BAR Honda, Brawn Mercedes, McLaren Mercedes.

Another indication of the dominant role of the car is the rise of most top drivers into the top 10. 

In their first three years Ickx, Rindt, Lauda, Andretti, Prost, Senna and Hamilton all jumped from low positions into the Top 10 once they got a seat in a competitive car. The only exception to this is Fangio, who won his titles with 4 different cars or engines.

Lewis Hamilton achieved his 100th pole and victory in 2021. As usual, all kinds of All-time rankings appeared around that time. Most of those lists use absolute numbers as criteria. 

There are also more scientifically based lists with new criteria, such as the difference between two teammates. This removes the variable of differences between cars from the calculation. But that list does not take into account team orders, strategy or competition between teammates: 

Criteria

FIA uses only one criterion for its championship: points. OneFormula's model is based on 4 criteria:

1.  Wins %

2.  Poles %

3.  Podiums %

4.  Level of competition

Weighting factors are applied; it goes without saying that winning a Grand Prix is not the same as a finishing on the podium. That is why we need weighting factors. Here we enter the subjective part of statistics. We have tested dozens of combinations of weighting factors; the differences between various combinations had a minimal influence on the final ranking.  I therefore use the most logical weighting factors:

• Wins factor 3

• Poles factor 2

• Podiums factor 1

Result in Figure 1:

The OneFormula format is better than most existing rankings in a number of ways:

1.  Percentages vs. numbers

2. One standard points system 

3. Exclusion of reliability factor 

4. Including level of competition

Hamilton leads in terms of number of wins. He needed almost 300 Grand Prix to reach his 100th victory.  If we express that in percentages, the top ten list looks like this:

2. Points system

FIA has used six different points systems troughout the history of formula 1:

Apples to apples here too:
To make a correct comparison, OneFormula uses a standard points system for the entire period. On top of this, points can also be earned in shootouts and qualifications.

3. Reliability

Eliminating the role of the car is the biggest challenge in making a best-of-all-time list, but the reliability of the car can be removed from the calculation by excluding races or qualifications in which a driver does not make it to the finish -DNF- due to technical- or team related issues After all, this is about the Driver Championship, not the Constructors Championship. 

The chart below shows how important these DNF's are. In 1967, only half of all cars reached the finish due to technical problems (blue). In comparison, driver-related DNF's in red.

Example DNF-T

The above formula results in following ranking:

4. Competition

As a last criterion to the ranking the level of competition is added:

The level of competition -C-level- for a particular season is defined by 

• Applying a standardized points system for all seasons. 

• Calculating the standard deviation of average points per race of the first 6 finishers in a season. 

• Dividing 1 by standard deviation*

*The higher the deviation, the lower the level of competition. Hence the inversion.

See Figure 4

Example C-levels

Example C-factors

The average of C-levels of seasons in which a driver has been active yields a personal C-factor. See Figure 5

The C-factor is now divided by the average C-level of all seasons in Formula One ( 1950 - 2023 ). This alters the original scores of drivers in figure 3 and in some cases their ranking as well.
See Figure 6

The result of the formula above is multiplied by a driver's C-factor, yielding a final score. See OneFormula Stats

References

• Stats F1 is used as the preferred database for the OneFormula model.

• Bell, A., Smith, J., Sabel, C. E., and Jones, K. (2016). Formula for success: multilevel modeling of formula one driver and constructor performance, 1950–2014. Journal ofQuantitative Analysis in Sports, 12(2):99–112.

• Bol, R. (2020). How to win in formula one: is it the driver or the car? The Correspondent.

• Budzinski, Oliver and Feddersen, Arne, Measuring Competitive Balance in Formula One Racing (March 16, 2019). Available at SSRN: https://ssrn.com/abstract=3357687 or http://dx.doi.org/10.2139/ssrn.3357687

• Burkner, P.-C. (2017). brms: An R package for bayesian multilevel models using Stan. Journal of statistical software, 80(1):1–28.

• Eichenberger, R. and Stadelmann, D. (2009). Who is the best formula 1 driver? An economic approach to evaluating talent. Economic Analysis & Policy, 39(3).

• Elo, A. (1978). The rating of chess players, past and present. Arco, New York.

• Henderson, D. A., Kirrane, L. J., et al. (2018). A comparison of truncated and time-weighted Plackett–Luce models for probabilistic forecasting of formula one results. Bayesian Analysis, 13(2):335–358.

• Ingram, M. (2021). A first model to rate formula 1 drivers. https://martiningram.github.io/f1-model/ (accessed March 2022).

• Phillips, A. J. (2014). Uncovering formula one driver performances from 1950 to 2013 by adjusting for team and competition effects. Journal of Quantitative Analysis in Sports,10(2):261–278.

• Van Kesteren, E.-J. and Bergkamp, T. L. G. (2022). Code Repository: Bayesian Analysis ofFormula One Race Results.