A reconstructed history of Formula 1

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

This has made a lot of people very angry and been widely regarded as a bad move

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.

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39 comments

  1. Very good article. Would like to know why you went with 10-6-4-3-2-1 instead of the 9-6-4-3-2-1 system? The latter was in place longer, and is more reflective of the usual percentage spread between 1st and 2nd (It’s been 8-6, 9-6, 10-6, 10-8, and 25-18) through the years.

    Also, do the lower points near the bottom lead to bigger teammate spreads because of what could be termed ‘freak’ results? For example, you listed ALO, VET, and HAM as the top 3 drivers of 2015 so far. But without the Hungary result, where would Alonso rank in your model?

    As you alluded to, correcting for fading ability by age would be nice. I have no idea how you’d do this. Not every driver has a 12 year career in F1 starting at age 22, for example. Another possible avenue for refinement would be a corrective enhancement for rookies (and perhaps sophomores), and for the first year or half-year in a new team. Could then compare and contrast against a teammate with greater F1 experience, and/or one that’s been in the same team for longer.

    Lastly, would it help to use junior series results to establish greater teammate linkages between driver pairs with little data to go on?

    Thanks for your blog posts, and the apparent effort and dedication you put into them.

    1. Thank you for the message, I appreciate it.

      The choice of the points-scoring system to use is of course arbitrary. I have played around with all of them, and generally it doesn’t have much effect on the overall team and driver hierarchy.

      Any ratings based on a small number of races are susceptible to freak results, so I always take ratings this early in the season with a grain of salt. Before Hungary, Alonso was ranked 2nd overall, still ahead of Button owing to their different number of counting races. But for McLaren in particular, these ratings are not yet very reliable, for obvious reasons.

      I have tried rookie-year effects of the form you suggested (including excluding the rookie period altogether), but it does not perform well, presumably because drivers come into F1 with widely varying levels of prior racing experience and age. That’s why I think a function that accounts for all of these factors will need to be fitted to the entire dataset, but as you say, it’s a challenging problem that doesn’t have a clear analog in other statistical sports models.

      I think using junior results or other single-seater series, such as IndyCar, to establish relative ratings is an excellent idea. At present I don’t have the database for doing that, however.

      1. Regarding Junior results, is it appropriate to use most recent/available data and working backwards? Rather than finding a database with complete results from 19XX to the present or end of x series.

      2. You could do either. The problem is that most databases do not explicitly give the reason for DNFs (which is necessary for the model) or do not do so in a reliable fashion. It could be done, and I might indeed do it some day, but it would be a very time-consuming task.

      3. Fascinating research. It’s good that you are investigating how to incorporate fading ability due to age. It’s an important element when comparing team mates. For instance, the 3 year period that Rosberg is assessed on in your all times rankings list, he performed well against Schumacher, but unfortunately it was an ageing, declining Schumacher who promptly then retired. Although, the flip side of the coin is if you were to re-evaluate and base Hamilton’s peak 3 years as 2013-2015, if Hamilton goes on to become a triple world champion at the end of this year,Hamilton would be more favourably placed in the all time list as he would have beaten Rosberg, 3 years in a row, who in turn beat Schumacher 3 years in a row. I can’t help feeling that you have used the wrong peak years to assess Hamilton (2007 -2009). Although Hamilton beat Alonso in 2007, and won a title in 2008 while not driving the best car on the grid, Hamilton has now matured and is now reaching his prime.
        Ageing would potentially effect Vettel’s rankings in the all times ranking list too. During Vettel’s peak 3 years, he was teamed up with an ageing Webber who again promptly retired at the end of their pairing. Arguably, the same can be said of Alonso V RaikKonen in 2014. Alonso had the oldest man on the grid as is team mate during one of his peak period years, the oldest man of the grid who also had to contend with settling in to a new team. And the way Raikkonen is performing this year too, it’s arguable to many that he has been on the decline over the past few years..

        Quote from Nikki Lauda “You cannot go at it as you did when young” !

        Quote from Prost on Senna “….after 10 years, you can no longer go flat out”!

        Age matters…

  2. Interesting article but the whole thing seems too “pro-Alonso”…The Renault cars were in fact the best cars of 2005 and 2006 (winning the constructors’ title too) yet your model claims that Alonso, as a champion, never spent a year in the best ranked car? Or am i mis-interpreting your rather complex theory?.Surely Hamilton in 2008 is a truer case of winning in a car that is not the best. Also, with Alonso, his constant need to have de-facto number 1 status in a team and all the help that would have brought him needs to be factored in?

    1. That may be your subjective perception, but the model contains no biases towards any particular drivers and comes to different conclusions regarding the Renault cars. 2005, 2006, and 2008 are all rated similarly in terms of the difference between the best and second-best cars.

      The point regarding preferential treatment of some drivers is certainly an important caveat (I discussed it in the original article), which applies to many other drivers too, including Schumacher, Senna, and indeed most multiple champions in the sport’s history. Today, with the exception of direct team orders (which don’t usually account for many points alone), the effects are surely much less than in the past, when teammates often ran with different parts, different access to the T-car, etc.

      1. The Scuderia have an ingrained systematic number 1 de-facto/supporting number 2 driver system in place. It’s no coincidence that the points difference between Ferrari team-mates is often larger than at other teams. This is a serious factor that should affect any ranking of Alonso during that period. Alonso is a driver that will insist on de-facto number 1 status in his contract. Afrer all, isn’t that one of the reasons why he left McLaren? Questions have to be asked if Alonso would have achieved such results if he had to battle with his team-mates on an equal footing…..

  3. Officer · · Reply

    I have taken the time to read most of your articles and rankings. Your articles are well put together and dare i say, even “innovative”…so well done on that.
    However, i have serious reservations. For me, in all of your models, there seems to be an over strong attempt to emphasise data that tends to particularly “lift” Alonso’s rankings. For instance, in your greatest ever driver rankings, you do not take into account qualifying performance. Alonso has never been particularly known for his 1 lap speed and he has never been known as an outstanding qualifier, unlike say Hamilton or Senna so i suppose for you to include that would detract from Alonso’s scores. As i have mentioned above, we all know that Alonso has benefited from de-facto number 1 status and team orders and again, this information is conveniently excluded from the rankings, which is unfair on those drivers who fight their team-mates on an equal footing? Also for this model here, we all know that the Renaults of 2005/2006 were the best cars but you fail to include this, thus further “boosting” Alonso. For me, that’s a fundamental flaw in these models. Because they are “mathematical” it would be easy to deduce that they are totally impartial, but surely, a certain amount of bias is there in deciding what stats, information, criteria goes into making up these models, There is an element of “picking and choosing” what criteria the model is based upon-picking and choosing criteria that you know will elevate the rankings of a particular driver. I sense this is a common theme that runs through all your articles and i am sorry to say that you continually seem to be including information that tends to favour Alonso in particular.

    Going forward, i would like to see more objectivity when choosing the criteria upon which to base your models and rankings…

    1. I have no particular interest in elevating Alonso or any other driver. If I could be charged with any particular driver bias as a fan of Formula 1, it would be a strong pro-Senna bias, given I was an obsessive Senna fan when he was racing. You seem to have some misguided ideas about how models are constructed and what factors could reasonably be incorporated in an objective model. The only picking and choosing with respect to the factors that go into the model is the requirement that any such factors be 100% objective and easy to apply in a 100% consistent fashion to all data going back to 1950. If you think you can do a better job, I welcome you to try.

      1. I can certainly appreciate the time and effort that you have put into your model/rankings. I am no statistician or mathematician so maybe i do not fully understand all aspects of your model/data and i certainly do not think that i could do any better. To be honest, i probably would not know where to even begin! I can see what you are trying to achieve. You are trying to remove all aspects of subjectivity and use data that is easily quantifiable/measurable and thus can be easily consistently applied. But for me, that’s a fundamental flaw of a model simply based on maths/stats. F1 is rarely black and white, it has lots of variables and sometimes, you have to take these variables into account to get a truer picture of an overall performance. Even if these variables cannot always easily be defined or measured, surely some attempt needs to be made to consider them.

        For example, teams orders. Certain drivers have undoubtedly benefited from these more than others. Out of all the current drivers, Alonso has arguably been the greatest beneficiary of preferential treatment and team orders. We all know about Korea, USA, and Brazil 2012. There was the team order in Germany 2010 – “Massa, Alonso is faster than you”..Singapore 2009 where NPJ was ordered to crash to help out Alonso, with Alonso actually going on to win the race. Japan 2013 teams orders to help Alonso out, but ignored by Massa etc etc etc etc etc There is no denying that such orders would have in reality helped Alonso achieve better race results, and at the same time, unfairly be detrimental to Alonso’s team-mates, and indeed the rest of the field who were battling on an equal footing. Yet under your model, it would not harm Alonso’s scores because the model does not consider team orders. So in effective, your model has an inherent bias towards drivers that have been de-facto number 1 or had team orders in their favour. The Scuderia in particular have a clear policy of de-facto number 1 and supporting number 2 and this perhaps is more of a legitimate reason as to why the points gap between Ferrari team-mates is often the largest out of any team-mate pairings on the grid. For me, this can not be comfortably excluded from consideration and for me, puts a sizeable doubt on the accuracy of your driver rankings. I understand WHY you do not consider things like team orders, de-facto number 1 etc–it’s not easily quantifiable or measured– but i don’t agree with it. It may sound silly but perhaps a separate model should be done to measure the performances of exclusively those drivers who have been known to be de-facto number 1 or regular beneficiaries of team orders, such as Schumacher and Alonso. It’s unfair that their performances are measured against performances where no team orders have been at play and against drivers who are willing and capable of battling on an equal footing.

        You have stated yourself that the model has limitations and you don’t claim it to be perfect.. For me, the biggest limitation on anything based purely on maths and stats is that while aiming to remove subjectivity, it can fail to reflect what’s actually happened on the track. For me, pure stats can never quite capture the essence of a race weekend and what’s actually happened that can affect a driver’s overall performance.

      2. Officer raises an important point about the effect of team orders on the model results, but unfortunately it seems there is no way to accurately incorporate these since we just do not know the status and extent of team orders in every team in every year, even just among the top teams. We do however know that they existed and that there are many cases of No.1 drivers benefiting from them (and consequently of No.2 drivers ‘suffering’ poorer race outcomes). There is no doubt that this will effect the model results since a major factor in the model is comparative performance between team-mates.

        Arguably the better the driver the more likely they are to be given No.1 status and therefore the more likely they are to be the beneficiary of team orders. One circumstance where that may not be the case would be when a team has two exceptional drivers and therefore does not operate team orders, or the drivers refuse to yield to them.

        Alonso has undoubtedly been a beneficiary of team orders, more than anyone else it’s hard to say, but I suspect not (perhaps more than any current driver, but not than all previous ones).
        Andretti and Peterson, Sheckter and Villeneuve, Hakkinen and Coulthard, Fangio and Collins, Regazzoni and Jones, Schumacher with Barrichello, Irvine and Massa, Alonso and Massa or Piquet (Jr), and Surtees and Bandini are just a few of the more frequently talked about instances of team orders influencing outcomes, but I would suggest that where there is an obviously top driver/world champion paired with a rookie or lesser driver then team orders have probably been the norm since the beginning of the championship. Stewart (the model’s second top driver) himself has indicated that Cevert clearly could have won some races (e.g. Germany 1973) but appeared to hold back in deference to his more experienced team-mate (presumably knowing that Stewart would soon retire leaving him as No.1 driver and the beneficiary of future team orders or driver deference).

        Perhaps someone should consider trying to do some separate assessment of team orders to see if it is possible to gather enough information to make an attempt at adjusting the model to partially account for them. It would be particularly interesting to see if any of the top 10 or 20 drivers have overly benefited or not from them compared to each other.

      3. @P STOP

        “perhaps someone should consider trying to do some separate assessment of team orders to see if it is possible to gather enough information to make an attempt at adjusting the model to partially account for them”

        Great suggestion.

        Regular use of team-orders and/or de-facto number 1/supporting number 2 status has the potential to have such a HUGE impact on performance that to me, it almost seems unthinkable to not some how try to take them into account – not just here, but on ANY kind of driver rankings attempt. I think we can all appreciate the difficulties involved in attempting to do this but to just ignore them seems most unsatisfactory and indeed unfair.

        “Arguably the better the driver the more likely they are to be given No.1 status and therefore the more likely they are to be the beneficiary of team orders”.

        Agreed. .Those drivers who have been de-facto number 1 or were in regular receipt of favourable team orders, in all honesty, would still have probably gone on to beat their respective team-mates or out perform them over a entire season even WITHOUT favourable team orders. But perhaps the MARGINS by which they beat their team-mates, would have been more NARROW or REDUCED, without favourable teams orders in their favour…….

    2. I don’t understand the point to penalize drivers or promote based on qualifying rankings. After all, you don’t gain any points for winning pole, and the benefit of starting higher where you should should be reflected in the final race finishing order. The problem with simply rewarding qualifying performances is that you forget that cars that qualified on a lighter fuel load or drivers that would explicitly concentrate on qualifying setup at the expense of race trim would suffer accordingly in the races. So it’s appropriate that the rankings should purely be based on the quality of race finishes because it circumvents a load of biases in and of itself.

      As to the point raised about preferential treatment, absolutely narrative has to factor in when considering results. But unless you were intimately involved with every team dating back to 1950, it’s impossible to conclude which teams were and weren’t utilizing that policy. For example, we couldn’t positively conclude/appropriately account for the fact that vettel had number 1 status at red bull, even though webber himself, and mechanical discrepancies would certainly indicate that.

  4. Andrew M · · Reply

    Thanks again for this article, it’s always interesting to hear F1 analysis supported by strong facts and analysis, even if I don’t agree with it 100%.

    Am I correct in thinking that Alonso’s results in 2008-09 are very weakly correlated to the rest of the grid, as they are based off of Piquet Jr (who has no other reference point) and a few races of Grosjean? (Not to mention Singapore of course).

    Also, a relatively random question, how well does the model rate Toyota’s cars? I’ve often suspected they could get have gotten better results with better drivers (although probably not won a race).

    Finally, could you tell how the model rates Brawn vs Red Bull in 2009?

    1. You’re absolutely correct regarding 2008-2009. Piquet Jr.’s ranking is necessarily somewhat uncertain, and by extension Alonso’s in those years.

      Regarding Toyota, their predicted rankings are 2002-10th, 2003-8th, 2004-9th, 2005-3rd, 2006-6th, 2007-9th, 2008-4th, 2009-3rd.

      Regarding 2009, the Red Bull and Brawn are ranked very close together. With equal drivers, the model predicts 169 points for Brawn and 154 points for Red Bull.

      1. Andrew M · ·

        Great, thanks a lot!

  5. I appreciated the use of your model to determine your “Greatest F1 Driver” article (excluding the positions of Hunt, Nico Rosberg, Senna, Prost, Frentzen & Watson).

    However, I just cannot comprehend how your model slots Jordan into 4th on your 2003 season teams’ standing. The Jordan EJ13 was an Okay car in qualifying trim, but its race performances were dreadful. It only won the very wet Brazilian Grand Prix due to a combination of flukes- otherwise it was seen as the second-worst car throughout 2003 (exactly where it finished) due to lack of funding. The Renault R23 was a far better car throughout the season, mainly due to having more drivability and being more user-friendly despite its engine lacking horsepower. In spite of Alonso’s future prowess as the master of bad machinery, it probably helped him having an easy (but not always fast) car in what was only his second F1 season.

    It seems your ranking of Jordan is elevated far too much by the under-performing Firman (21st/last). Your ranking of Firman is fairly accurate, as I recall pundits rating him out of his depth in F1. However, I just don’t see how that should lift Jordan that far high up. It was clear to see that in a decent (but not great) driver’s hands such as Fisichella’s, the EJ13 was simply an awful car.

    My conclusion is that your model is in a need of some fine-tuning (which I’m sure you’re working upon). It perplexes me to see the Ferrari 126C (1982) appear on your most dominant team ranking, when Renault had a fast (but unreliable) car in the RE30B. On the other hand it’s pretty bizarre not seeing the Lotus 79 when it’s regarded as a car that allowed Andretti and Peterson to speed away early and cruise to easy 1-2 finishes.

    1. Regarding 1982, reliability is taken into account. The Renault was indeed very quick, but as an overall package it was obviously greatly inferior to the Ferrari. The Lotus 79 is up there (25th of all time), but remember that in 1978 Brabham, Ferrari, and Tyrrell all provided credible challenges at some races. It wasn’t a car that always just streaked into the distance, and it also had some reliability issues.

      Regarding 2003, I’m inclined to agree that the Jordan is somewhat overrated by virtue of the “lucky” win at Brazil. After the top three teams in 2003, everyone was a long way back, so it’s difficult to confidently order the other teams.

      1. Great post again! I was also a little surprised to read the sentence “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.” I don’t know exactly how the model works, but apparently that freak win in Brazil only served to raise the expectations in the other races, while that result was due to mixed weather conditions, safety car periods, having more suitable tyres when it mattered, a good strategy, a red flag, combined with superb driving. I know it’s impossible to model so many variables, but as the Jordan was a really poor car in 2003, that 4th place doesn’t make sense. Perhaps, as a sensitivity analysis, it might be interesting to see what happens to the outcomes if you remove races from the sample randomly (or maybe not randomly, but only the “weird” races, like wet races). That will show how volatile the rankings are.
        Another issue might be some circular reasoning. For example: Rosberg was doing very well in 2010 because he was beating Schumacher. On the other side, Schumacher’s 2010 performance was inflated because he did do relatively well against the great (and probably “inflated”) Rosberg. Again, I do not fully understand the model, so I may be wrong, but it seems that the model is biased towards good drivers. It’s hard to tell how good the 2010 Mercedes was, but it seemed to be the 4th-fastest car, occasionally beating the McLarens or Ferraris and sometimes it was outpaced by the Renaults, but it is really unlikely to be just the 7th-best car. One weakness of the model is that it cannot assign a “target score” (if you drive in that car, given so many retirements in front of you, you should finish in …th position”). So it is possible that a 6th place is regarded as a perfect score (if the driver’s teammate did worse or retired), while in fact the driver should have been capable of scoring a 3rd place. So, a very good driver, who beats his teammate and scores a very good 3rd place is not rewarded more by the model than a driver who scores a modest 6th place. Instead, the improved performance is then only captured by the team dummy and not by the driver dummy (on the contrary, for example the 1999 McLaren was probably one of the more dominant cars ever, but due to bad driving, it doesn’t show up in the model). This problem is, of course, also very hard to tackle. The model does punish crashes and collisions, so crash-prone drivers (like Maldonado and last year the Sauber drivers) will perform significantly worse. This makes it even more surprising that Schumacher’s 2010 season is rated so highly.
        Furthermore, I find HRT’s “expected score” for 2010 weird (14 points, While Lotus was expected to score no points, which seems much fairer). HRT were extremely lucky to beat Virgin in the constructors’ championship, because the car was generally the slowest of the three new teams. Probably they didn’t have the best drivers too, but given their hopeless pace and the very low attrition rate, there was no way that even Vettel or Alonso could score a single point with that car. I also think the model is a little harsh on the Sauber drivers in 2012. Possibly they are punished by the rather irregular performances of the car (sometimes they qualified on the front row or took a podium and sometimes they were nowhere, possibly due to the car “liking” certain circuits and disliking others. The same probably applies to Ricciardo’s 2014 season in a car that didn’t like fast tracks), while I think they actually did a great job in a few races. Admittedly, if it was just a set-up issue, then they should have peaked in every race, but in 2012 no team had really discovered the secrets of the Pirelli tyres and only the Lotus and Sauber teams had mastered the art of tyre preservation, so I think they were ahead of their time.
        Still, I really like the model. Has there, for example, been made any progress in tackling the difference in performances during the driver’s “career arc”? That would probably significantly increase the model’s predictive power. Is there a way to test the rise and decline of drivers’ abilities by including dummy variables for age (and or experience) in order to roughly estimate the average driver’s peak?
        Good luck!

  6. Whiteshore · · Reply

    Thank god that F1 isn’t a spec formula like Indycar or GP2, for Alonso and Schmacher would dominate F1 with a 20 of the last 22 WDCs being won by these two according to the calculations

  7. Another brilliant article with loads of great info but it was far FAR too long!
    The article covers some very distinct areas, and I think it would make much more sense (and be much easier to read) if it were split into, say, 3 separate articles.
    Keep up the good work though.

    1. Thanks for the feedback! A number of readers contacted me asking for an even MORE detailed version of this article(!), so I made a compromise. I will consider splitting up articles of this length in future though.

  8. Hi again F1Metrics,

    This time I want to ask some questions about 2001 season. I actually never watched any of the races that year due to only taking an interest in F1 a year later as an 11 year old.

    I want to know your ranking positions for the rookies Montoya, Alonso and Raikkonen. I could remember reading the (non-mathematical) ranking list on the defunct F1 Rejects website (shame it was shut down) where they ranked Alonso 4th! TBF it was well justified as he managed outqualify the Benettons, Jaguars, Prosts and Arrows throughout the season. I would also like to know the ranking positions of Jacques Villeneuve (his last truly competitive season IMO before declining), Jarno Trulli (never quite fulfilled his potential), but last but not least Jenson Button (was he ranked the lowest of the full-time drivers? He was badly lampooned for his efforts that year).

    I also would like to know where you ranked Alonso for 2004, where he was outpaced by Trulli in the first half of the season. It seems a lot of readers have an issue with Alonso’s consistently high rankings on your mathematical model, possibly due to his perceived prima donna persona (leaving McLaren after a tumultuous 2007 and use of team orders at Ferrari).

    Of course I understand your model is based partly on team-mate comparisons. Politics and favouritism is not really something that can be measured accurately and it will remain a fact that many will have variable theories on how well two drivers, who have never been team-mates, would compare against each other if such a scenario emerged (i.e. Vettel vs. Alonso, Vettel vs. Hamilton, Raikkonen vs. Button).

    Right now I just a brain scan of the team mates the current 5 world champions have had:

    ALONSO (Marques, Yoong, Trulli, Villeneuve, Fisichella, Hamilton, Piquet Jr., Grosjean, Massa, Raikkonen & Button). 11
    HAMILTON (Alonso, Kovalainen, Button & Rosberg), 4
    VETTEL (Heidfeld, Liuzzi, Bourdais, Webber, Ricciardo & Raikkonen), 6
    BUTTON (R Schu, Fisichella, Trulli, Villeneuve, Sato, Davidson, Barrichello, Hamilton, Perez, Magnussen & Alonso) 11
    RAIKKONEN (Heidfeld, Coulthard, Montoya, de la Rosa, Wurz, Massa, Badoer, Fisichella, Grosjean, Alonso & Vettel) 11

    Although this may bear little relevance to your lists, it does seem noticeable that Vettel & Hamilton have not only have had less than half of the team-mates Alo/But/Rai have had, but I feel this is down having spent a higher proportion of their careers in competitive machinery. It also struck me both started in 2007 (both currently in their 9th season of F1- Alo 14th, Rai 13th, But 16th).

    Having just thought of this, I wonder whether it could be possible to formulate a mathematical model to take into account the eras of F1. Hamilton and Vettel never drove in old V10 3 litre era, so there’s a sort of semi-generation gap between them and the other 3 world champions.

    Something like this:
    1950-53: The old 4.5 N/A + 1.5 S/C /// F2 engine regs
    1954-60: 2.5 N/A regs (front engined cars) fuel addictives banned
    1961-65: 1.5 N/A regs (mid-engined cars)
    1966-70: 3.0 N/A regs (Ford Cos V8s) experimentation of wings
    1971-75: 3.0 N/A regs (increasing chassis design sophistication/higher death rates/slick tyres)
    1976-80: 3.0 N/A regs (airboxes banned/ground effects+ Renault turbo/Tyrrell six wheeler)
    1981-85: 1.5 T/C + 3.0 N/A regs (numerous rule changes/ very poor reliability)
    1986-88: 1.5 T/C + 3.5 N/A regs (money hugely increasing gaps between teams)
    1989-93: 3.5 N/A regs (electronics developed/ huge expansion of grid/ reliability still very poor)
    1994-99: 3.5 N/A reduced to 3.0 (electronics banned/endless rule changes/reliability gradually improving)
    2000-05: 3.0 N/A (electronics return/huge costs/increasing aero sophistication/gimmicks- one lap qualifying)
    2006-10: 2.4 N/A (Bridgestone control tyres (excl. 06), testing limits, customer cars, engine freeze)
    2011-now: 2.4 N/A – 1.6 T/C hybrids (Pirelli control tyres, fuel restrictions, engine tokens)

    Finally I would like to know where the Japanese drivers ranked on your greatest drivers list. I’d be interested in who is ranked highest of them all, plus the positions of Sato, Katayama & Kobayashi.

    Apologies for the long post, but keep up the good work!

  9. Actually, can you please ignore my previous post altogether.

    I understand there’s a real difficulty in creating a mathematical model to order the “greatest drivers of F1 history”. In all honestly, it stumps me to see Mika Hakkinen ranked down in 56th (but that’s not what I’m here to talk about).

    The one question I really want to ask is how Nico Rosberg is ranked 2nd on your 2012 model ranking, but yet it shows a real drop below the 0.5 line on his performances relative to Schumacher during the same season on a graph you displayed on the “Fernando Alonso” section of your 2014 model-based driver rankings. Thanks.

    1. Sorry, it took me a while to appreciate what you were asking. The reason for the seemingly contradictory conclusions is that race results and points tell quite a different story at Mercedes in 2012. On points per counting race, which the model here uses to assess performance, Rosberg was well ahead, but when the cars were free of mechanical problems Schumacher was more often finishing ahead of Rosberg, which is what was graphed previously.

      It’s really a case of neither metric telling a fully accurate story of the whole season. Mercedes became generally less competitive across the 2012 season, and Schumacher had more problems in the early season, costing him many points. If you carefully analyze each race in 2012, accounting for lost results and lost points, the correct conclusion seems to be that Schumacher and Rosberg were actually fairly closely matched that year.

  10. […] This article was previously included in my article A Reconstructed History of Formula 1, but is now presented as a companion article for improved readability. The model rankings have also […]

  11. What a load of bullshit,you do know that teammate comparisons mean little as so much politics goes inside the team,especially with alonso who always gets team support and gets the car built around him,and how exactly do you find out which car is better than the other,such a biased bullshit attempt.

    1. Teammate comparisons are never perfect, as openly discussed and acknowledged in my articles. However, they evidently remain better than any other method of direct driver comparison.

  12. […] performances for drivers. It achieves this by finding the best fit to all race result data from 1950 to the present. As new races are completed, model rankings are continually […]

  13. >”Alonso, who has consistently found himself outperforming uncompetitive cars.”

    Any time you find yourself writing the deadly phrase “X outperformed his car”, STOP! You’d gone badly astray and are deceiving yourself.

    No driver can “outperform his car”. The very best drivers can get something approaching the maximum possible out of their cars on a consistent basis, but no mortal can wring 101 MPH out of a car which is mechanically capable of no more than 100 MPH. Notwithstanding Alonso’s oft-repeated claim to have driven at “120%” in some race!

    1. I’m always amazed by people who think this is a clever point that others have somehow overlooked!

      A driver “outperforming” their car has always simply been shorthand for the driver outperforming the car’s expected performance. Literally nobody who has ever used the phrase intended the meaning you have assumed.

  14. I don’t understand how you did this, but this is the first time that I’ve seen a list that makes sense to me.

    I’ve watched all the full races starting from the 80s because I was interested in knowing who was this Senna everyone talks about. I wanted to know why he was considered such a good driver. But while watching his races, I have to say I felt a tad disappointed. I could see Senna was a very strong driver, but not the god driver everyone hailed him to be. Race after race, it was Prost who was impressing me the most (Only races. I didn’t watch qualifying). The exact opposite happened with Schumacher. I’d always had the feeling he won too easily thanks to his car (I was too young to know better), until I watched his first years in F1, followed by his dominant years with Ferrari. Only then I saw clearly that the guy was in another level. He was so much faster than most of his rivals! Ferrari designed very good cars, but it was the combination of Ferrari + Schumacher what really made it so successful. And finally, just like your stats show, Alonso came along and took the baton from Schumacher.

    Again, I don’t know you made your models or how much time you put into this, but thank you. To me, your stats are more credible than a thousand lists made by the specialized press.

  15. […] undermines the ability to do per-season rankings (as I’ve presented using my model previously) and can lead to some peculiar driver rankings. For example, Lauda is ranked very low by the Bell […]

  16. […] I did for 2014 and 2015, as well as other seasons historically, I applied my model of driver and team performance to ranking driver performances in 2016. This […]

  17. andrewthun · · Reply

    Might be a dumb question, but it’s still not clear to me: are performances of past seasons changed dynamically and retroactively as new results and, with them, teammate comparisons are fed into the model? As an example, when the model rates Räikkönens 2007 seasonlong performance any time after 2007, does it take the data from only up to 2007, or from Räikkönens whole career, even after 2007? So do his recent relative performance against Alonso and Vettel change his previous season ratings? Or are teammate comparisons only the subject of whole career (3-years-peak) analyses and single-season performances are not including these?

    1. Yes, exactly, all years are fit simultaneously by the model, so new incoming data from current seasons also cause (slight) changes to retrospective ratings.

      1. andrewthun · ·

        Many thanks, now it’s clear.
        Another question, if I may: Do you have maybe a method to visualize teammate links of certain groups of drivers? I tried to sketch up manually the links of the 2017 grid (finally all of them will be linked), but even without the inactive connections, it looks pretty chaotic: http://i.imgur.com/mHi8pZe.png

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