I grew up reading many Formula 1 fact books and encyclopedias. Despite their different sources, ages, and authors (all English language, I should mention), they told approximately the same story of Formula 1 history, with the same heroes and villains.

Drivers with two or more titles were usually considered the “true greats”, joined by a select few, such as Gilles Villeneuve and Stirling Moss, granted honorary greatness.

Drivers with a single title were usually distilled down to a single notable characteristic, making it easy to shelve them together: Hunt the playboy, Rindt the posthumous winner, Surtees the motorcycle champion, Jones the tenacious Australian, Keke the hard-charger. The obvious exception to the rule was Nigel Mansell, who was generally counted among the all-time greats following his 1992 championship.

Next in the hierarchy: drivers who served as reliable number twos, such as Patrese, or drivers who had near championship misses, such as Reutemann.

Finally, drivers who failed to make it to a top team were usually footnotes, unless they met a grisly end before they had a chance to prove themselves, such as Jean Behra or Stefan Bellof.

That is a slightly cynical synopsis of the sport’s most pervasive driver narratives, but only slightly. Almost every driver ranking list ever produced by experts or fans approximately follows the formula described above. Looking at the sport impassively, however, many of the clean categorizations begin to break down, leaving a more complicated (and perhaps unsatisfying) story. To quote a recent comic, “Truth, by its nature, is often a bit shit, and the human brain has evolved to work around that.”

In Formula 1, we have to contend with what I call “visibility bias”, which is the tendency to focus on drivers in front-running cars. There is a natural tendency to want to rank drivers in order of their accolades. However, this must be reconciled with the fact that results are principally determined by team performance. In most years, a driver is not realistically eligible for wins or poles if they are not in a top-three team. Button and Alonso may be out of the limelight this year, but they are not necessarily driving any better or worse than they were in their championship years. Of course, better drivers tend to find their way to better teams, so successes are correlated with driver performances, but that does not make success a reliable proxy for objective driver performance.

Driver rankings

Previously, I presented a mathematical model’s ranking list of drivers across the sport’s history. Rather than looking at the usual statistical metrics (wins, titles, poles), my model worked by estimating both team and driver performances to best fit the historical data. The model is not perfect, but probably better than any other existing method. Most importantly, the model is both transparent and objective. Any faults are therefore easily subject to scrutiny and possible future improvement (something I’m currently working on). The same cannot be said of mental models used to construct subjective ranking lists, which may be riddled with biases and hidden inconsistencies, and which are impossible to ever resolve with other contradictory subjective ranking lists.

In the model’s all-time rankings, many recognized greats appeared near the top, but there were also some significant surprises. In a few particular cases, these could be attributed to known limitations of the model. For example, the article noted that the surprisingly high rankings of Heinz-Harald Frentzen, John Watson, and Nico Rosberg were all largely dependent on their results against teammates who may not have been near their peak form.

In other cases, the model identified drivers who have been legitimately overrated or underrated. Even when these rankings were clearly corroborated by data, many fans found them unsettling. As someone who grew up knowing that the three-time champions all belonged above James Hunt, it was jarring to see Hunt above most of them. Yet a careful examination of his career reveals that he probably deserves a place near the top of the list. As a lifelong Ayrton Senna fan who used to wave the Brazilian flag in the grandstands with a Nacional cap on, it was equally disagreeable to see him outside the top 10. Yet this was not some quirk of the model. I tested a large variety of model specifications (including changes to the scoring function and competition function) before settling on the published model as the most parsimonious and best fitting. In other models, Senna was consistently outside the top 10 and never in the top 5, whereas Hunt was rarely outside the top 10.

Cases such as Senna and Hunt pose challenges to the subjective consensus and suggest that it is worth reconsidering some of the sport’s entrenched narratives.

Reconstructing history

Besides generating all-time driver lists, my model can be used to reexamine the results of each year in the sport’s history, much as I did for the 2014 season previously. Since the model estimates both driver and team performances, we can pose two hypothetical questions.

1. How would each season’s results have looked if all drivers had been in equal machinery?

2. How would each season’s results have looked if all teams had equally skilled drivers?

For the latter question, I assumed two cars per team in each race and used the rates of actual mechanical failures in computing predicted points. For direct comparison with history, I also linked the model’s points output system to the points systems used in each year.

Below is a table showing the model’s predicted winner of the World Drivers Championship (WDC) and the model’s predicted winner of the World Constructors’ Championship (WCC). These results incorporate all data up to and including the 2015 Hungarian Grand Prix. The model’s rankings for the actual WDC and WCC are shown as “Model rank”. Cases where the model’s predicted champion differs from the actual champion are highlighted in green.

Notably, there are 38 years with different WDCs from the historical winner, whereas there are only 14 years with different WCCs. This reflects the fact that the strongest team tends to win, due to team performance being the dominant factor in Formula 1. In several years, such as 1978 and 1996, it is pleasing to see an incredible driver performance in a much less competitive car rewarded with the title. In a few cases the actual WDC is rated outside the top 5 drivers in their championship year, suggesting their title was down to a dominant car, some good fortune, or both. There are also a few interesting new champions, including Elio de Angelis in the tumultuous 1982 season, Heinz-Harald Frentzen in 1999 (when Schumacher had a slow start to the season before his injury and Hakkinen was unusually error-prone), and Jean Alesi in 1992, who could well have been champion at Williams had he stuck with the 1991 contract he signed with them.

With differences in team performance taken out of the equation, new periods of driver dominance emerge, with the most deserving drivers winning many consecutive titles. In total, the model awards titles to 20 drivers, which is fewer than the 32 actual WDCs. Below is a table showing the number of championships awarded by the model to each driver.

The largest gains are made by Stirling Moss, who is awarded four titles by the model, and Fernando Alonso, who has consistently found himself outperforming uncompetitive cars. Two of the triple-world champions — Jack Brabham and Nelson Piquet — are no longer awarded titles. For now at least, the same is also true of quadruple-champion Sebastian Vettel.

The team hierarchy is less affected. Below is a table showing the number of championships awarded by the model to each team.

Looking at the drivers’ championship results, the importance of having the best car is evident. In 65% of years, the historical drivers’ champion was in what the model ranks the best car. Of course, there is having the means, and then there is capitalizing. The most successful drivers in history did both. Below is a table of drivers who spent at least three years in the model-ranked best car, and the number of championships they achieved.

By the model’s reckoning, only four of the historical drivers’ champions never spent a year in a best-ranked car. They are Jochen Rindt, James Hunt, Keke Rosberg, and Fernando Alonso. Renault are ranked a very close second to Ferrari in 2006, although it was really a season of two halves, with Renault generally superior before the mass-damper ban and Ferrari generally superior afterwards. Whether Alonso’s statistic is due to poor luck or poor planning is open to interpretation. If his latest McLaren venture goes nowhere, it will undoubtedly remain a contentious narrative for years to come.

Using the model, we can look more closely at results in specific years. At the midpoint of 2015, the model ranks Alonso, Vettel, and Hamilton the three top performing drivers. More detailed analysis will follow at the end of the season.

Next, let’s consider a few interesting recent years where there was a close championship fight between multiple teams.

Season reports

2003

Sandwiched between two years of total Ferrari domination, 2003 was a rare year where three teams fought closely for the WCC and three drivers fought closely for the WDC. Third-placed Williams finished the year with 89.9% of title-winner Ferrari’s points; no third-placed team has even done better. Given the different drivers on each team, it is difficult to say who had the best car. Williams had an unrivaled BMW engine, but McLaren and Ferrari had strengths in other areas.

By the model’s reckoning, the Williams was the overall best car of 2003 by a small margin. The model’s predicted points for each team with equal drivers versus the actual points scored by each team are listed below.

From this perspective, Juan Pablo Montoya and Ralf Schumacher blew an excellent chance at a title. Among the other teams, Renault (with Alonso and Trulli) are ranked the greatest overachievers and Jordan (with Fisichella and Firman) are ranked the greatest underachievers.

Simulating the championship with all drivers in equal teams, the model predicts that the historical winner, Schumacher, would have beaten Raikkonen and Montoya, as occurred in reality. However, a new name emerges as the year’s best performing driver for the first time in this alternate history: Alonso. Frentzen also appears as a top driver in 2003; he outscored teammate Heidfeld 13-6.

In 2003 Alonso returned to Formula 1 from a full year of testing. He scored his first race win, outscored one of the McLarens (Coulthard), and finished within ten points of a Ferrari (Barrichello) and three points of a Williams (Ralf Schumacher). Across the season, he outscored teammate Trulli 55-33. Interestingly, this advantage over Trulli did not persist into 2004, when the model again awards the championship to Schumacher. In 2005, Alonso is ahead again. Their relative performances over time are graphed below.

Going by the model’s results, the mantle of greatest current driver therefore passed between Schumacher and Alonso somewhere in the period 2003-2005.

2007

2007 was one of the most fascinating seasons in the sport’s history. While the racing on track was not always enthralling, the stories off track were irresistible, as the reigning double world champion Alonso found himself struggling to beat an unbelievably talented and well-prepared rookie, Hamilton. McLaren’s dream team imploded and Ferrari ultimately picked up the pieces, winning both titles by a single point (before McLaren were altogether excluded for cheating).

The Ferrari F2007 is ranked the superior car in 2007 by a significant margin over the McLaren and this is discussed in the companion article on the sport’s most dominant teams. The model considers Hamilton and Alonso a much stronger driver line-up than Raikkonen and Massa. Recent results between Alonso-Massa and Alonso-Raikkonen at Ferrari lend obvious support to that view.

BMW Sauber (Kubica and Heidfeld) clearly overperformed compared to model predictions, while Renault (Fisichella and Kovalainen), Red Bull (Webber and Coulthard), and Super Aguri (Sato and Davidson) were significant underperformers.

The 2007 season is often remembered for McLaren’s drivers taking points from one another, ultimately costing each other the title. However, it is worth remembering the same was true to a lesser extent at Ferrari, with the team supporting title bids for both Massa and Raikkonen until late in the season. With team orders on their side (swapping positions in any races where they finished just behind their respective teammates), Alonso could have scored an extra 7 points, Hamilton 11 points, Raikkonen 3 points, or Massa 7 points.

With equal machinery, Hamilton is crowned champion as a rookie, just ahead of his teammate. This makes him the second rookie champion in the model’s alternate history after Hunt in 1973 (not counting 1950, when all drivers could be considered rookies in the championship). The Ferrari drivers descend into the rest of the pack, with the gap between Raikkonen and Massa extended due to Raikkonen suffering one more mechanical DNF than Massa, and due to greater predicted point spread between drivers when they are in midfield than when they are in a dominant car (a fact confirmed by simulation).

Vettel is another rookie ranked extremely highly, while Heidfeld’s impressive season for BMW Sauber is rewarded with 3rd in the championship.

2010

Like 2003, this was a fascinating season with chances for drivers at three different teams. None of the title contenders drove a perfect year. Alonso made costly mistakes at Monaco and Belgium. Hamilton did the same at Italy and was several times outpaced by teammate Button. Meanwhile, the Red Bull drivers created their own myriad problems, with Webber crashing in Korea and Valencia, and Vettel crashing into Button in Belgium and into teammate Webber in Turkey. In the end, Vettel clinched the title in dramatic fashion in Abu Dhabi, after strategic blunders from his two main competitors.

The model thinks it should have been plain sailing for the Red Bull drivers. Given the quality of the RB6, it’s difficult to argue against that. In Adrian Newey’s opinion, the RB6 was the pinnacle of aerodynamic development, unmatched before or since,

“The RB6 was probably the car with the most downforce in the history of F1, more even than the legendary spoiler cars of the 1980s. We measured up to 5.5G of lateral acceleration. It could go flat out through Copse at Silverstone, and on the sharp bend on the back straight at Barcelona [Campsa].”

The model’s team rankings for 2010 are given in the table below.

Besides Red Bull’s advantage over title rivals McLaren and Ferrari, it is interesting to note how highly the model rates the 2010 Toro Rosso. This is related to how lowly the model rates the Toro Rosso drivers, Alguersuari and Buemi, which I would treat with some skepticism, as these drivers are among a small number of historical pairs who are only very weakly linked via teammates to the rest of the grid (the only connection is a half season with Bourdais). Their rankings are thus highly uncertain, as is the ranking for their car.

Once team differences are leveled out, Alonso and Hamilton emerge well ahead of Vettel and Webber. Other top performers are Nico Rosberg, who is perhaps over-rewarded for thrashing Schumacher (given the model does not account for the fact that Schumacher was likely well past his peak form) and Kubica, who outscored his rookie teammate Petrov 136-27.

2012

2012 is largely remembered as a year in which Alonso dragged his Ferrari kicking and screaming into the championship fight. However, there is significant disagreement among fans over the quality of the F2012, with some claiming its superior reliability and wet-weather handling made it a good match for the RB8, while others consider it a vastly inferior car. On raw pace, the quickest cars of 2012 were clearly the Red Bull and McLaren, which were on average about 0.5% quicker than the Lotus and Ferrari. As always, this is somewhat confounded by the drivers behind the wheel of each car, so a model is required to properly untangle this.

After accounting for differences in drivers, my model predicts that the Red Bull RB8 was indeed the year’s best car by a significant margin. Even with its poor reliability, the model thinks it should have won both championships relatively easily. McLaren are a distant second, with Ferrari and Lotus closely matched for the honor of third best car. Lotus’s results were certainly impressive considering that one of their drivers was returning from a two-year break and the other was in his first full season of Formula 1. They won only one race, but were within 4 seconds of the winner at 4 other races, suggesting better results were on offer.

The revivals of Sauber and Williams on the 2012 Pirelli tyres are also recognized by the model. Indeed, the model thinks both teams could have scored considerably better with more capable drivers. Meanwhile, Mercedes is seen as a team that punched significantly above its weight.

In the drivers’ championship, Alonso is considered the outstanding driver of the year. It’s worth noting that he benefited from team orders at Korea, USA, and Brazil, which the model does not consider. He is also penalized for crashes at Spa 2012 and Suzuka 2012, despite only the latter being his fault, since the model does not assign blame for crashes. Similarly, Vettel is affected by his result in Malaysia, where Karthikeyan punctured his tyre, knocking him out of the points. However, none of these factors could reasonably explain the predicted points difference between Alonso and Vettel or between Red Bull and Ferrari.

Nico Rosberg benefits in the analysis from his points lead over Michael Schumacher, but this should be considered in light of Schumacher’s 2012 misfortunes, which included several unfortunately timed reliability problems.

Interestingly, Vergne and Ricciardo both appear in the top 10, foreshadowing their future results. Perez is 12th and Hulkenberg 14th, suggesting neither was a particularly compelling option for McLaren in 2013, when they faced the sudden need to fill Hamilton’s seat.

Other applications of the model

There are many things we can do with this model, some of which will be explored in future articles. One application is generating yearly rankings, which I intend to continue doing. Another application is predicting how certain drivers would have performed if they had hypothetically signed for different teams. A third application is ranking the best teams in history, much as I previously ranked the best drivers in history. This article previously included a ranking list of the top 20 teams, but the list is now presented here as a companion article for improved readability.