The secret of a good race

When is a Formula 1 race a good race? A lot of overtaking and a nice battle for the lead are generally appreciated, but what other factors do play a role?

Although qualitative labels like “good” or “bad” are highly subjective, they can be made a lot more objective if they are collected in a large-scale survey. For this I’ve used the rate-the-race results from F1 Fanatic. This wonderful site allows readers to give their verdict on the races from 2008 onwards and with about 600 votes per race the average ratings should be quite accurate. The ratings vary strongly from race to race, but the season averages show that some seasons were rated higher than others. The average rating of the best season was more than one point higher than the average rating of the worst season (7.37 to 6.32 on a scale from 1 to 10).

Average race ratings from 2008 to now.

It’s interesting to determine the root cause of these per-season differences and therefore I’ve analyzed the ratings of the individual races. There are many factors that will affect the race ratings. I came up with these factors:

• Number of overtakes

• Number of retirements

• Track

• Weather conditions

• World Championship situation

• Whether or not there is a battle for the lead

• Whether or not the winner is the same as the previous race

Most of this data is easy to obtain, except for the overtaking data. The per-season averages can be found at Clip the Apex, while the figures per race are only available for members. So let’s first focus on the season averages.

Average number of overtakes per race per season from 2008 to now.

Clip the Apex shows the average number of overtakes per season for all races (blue) and the dry races only (orange). The number of overtakes increased substantially with the introduction of DRS and Pirelli tires in 2011, but since then the number of overtakes has decreased again. Indeed there is some correlation between the per-season number of overtakes and the average race ratings, but it’s clear that more factors play a role.

Retirements per race per season from 2008 to now.

Retirements add unpredictability and are therefore likely to raise the race rating. The reliability of the cars shows, however, a fairly predictable pattern: the number of retirements generally decreases, except for 2010 (3 new and inexperienced teams) and 2014 (complex hybrid turbo engines).

Frequency of races on Tilke tracks from 2008 to now.

The so-called “Tilkedromes” are not really liked by the fans, as they share common traits like long straights and a lot of boring constant-radius corners. However, the frequency of Tilkedromes races per season has remained more or less constant during the test period.

Frequency of wet and variable weather races from 2008 to now.

Although the weather should be pretty much random (this timescale is not long enough for climate change to play a role), the graph shows a clear trend. 2008 had by far the most wet (dark blue) races and a substantial amount of partly wet races (blue), while the fateful 2014 Japanese Grand Prix was the only wet race of the last 5 seasons. As wet races induce more unpredictability, they are usually rated higher.

Average championship lead in wins from 2008 to now.

If one driver dominates the championship, viewers may lose interest in the race. In the recent years, 2011 saw the biggest dominance by one driver, when Vettel led the championship from the first race. In 2008 (with Hamilton only winning the title in the last corner), 2010 (four title contenders in the last race) and 2012 (where Vettel won the title from a seemingly hopeless position) the championship was much tighter and more interesting, which may have led to higher race ratings.

Frequency of back-to-back wins from 2008 to now.

A bit correlated to the championship lead is the back-to-back wins frequency. However, there is a difference between seasons when only one driver dominates the season (Vettel in 2011 and 2013) or when one team dominates the season (2014 and 2015). While both cases result in many back-to-back wins, the championship lead is of course much bigger in the former case. The frequency of back-to-back wins shows how predictable the championship is. Indeed, the unpredictable 2012 season (with 7 different winners in the first 7 races) has the lowest percentage (15%) of back-to-back wins.

Frequency of races with a battle for the lead from 2008 to now.

Another important factor is whether or not there was a fight for the lead, which I define as whether or not there was a pass for the lead. Fights for the lead have always been rare in modern Formula 1, but the introduction of DRS has increased this frequency. This year, however, only in the US Grand Prix there was a genuine fight for the lead, as in Malaysia and Bahrain there was a pass for the lead because of different strategies.

Analysis

So now it’s time to estimate the combined effect of the different factors on the race rating. I’ve done several analyses in order to obtain robust results. First, I’ve tested the influence of overtaking on the race rating. As overtaking has become much easier because of DRS, it makes sense to distinguish between the number of overtakes between non-DRS and DRS years. It appears that every overtake in the non-DRS years added 0.030 points to the race rating, while in the DRS years this value was “only” 0.021 points. However, this reduction may well be caused by the higher number of overtakes in the DRS years, which may decrease the additional value of one extra overtake. In order to circumvent this problem, I’ve used the logarithm of the number of overtakes. In this case, the coefficient for the DRS years in actually higher than for the non-DRS years, which suggests that overtaking actually has become more important.

The estimated effect of the number of overtakes on the race rating with and without DRS.

The difference between the estimated coefficients is, however, not statistically significant and as there is no good reason why the DRS coefficient should be higher, I chose not to distinguish between the non-DRS and DRS years. The average effect of the logarithm of the number of overtakes on the race rating is 0.810, which means that an increase from 1 to 10 overtakes increases the race rating by almost 1.9 points (races with no overtakes cannot be analyzed in this way, but there is only one race without overtakes in the dataset), while 40 overtakes boost the rating by about 3 points.

Other factors

The analysis clearly shows that unpredictability and uncertainty in appreciated. A battle for the lead is rewarded with 0.7-0.8 points, while the ratings drop by about half a point when the championship is decided. The championship decider is generally awarded with half a point, though. Back-to-back wins cost about 0.3 points, but every car that retires boosts the race rating by 0.14 points.

The tracks are a bit difficult to control for. Firstly, I distinguished between Tilke and non-Tilke tracks. Tilke tracks do 0.3 points worse on average. When controlling for all individual tracks, the results are similar. The most notable change is that overtaking becomes more important (the coefficient increases to 0.9), which probably means that tracks where overtaking is difficult have intrinsically higher ratings than overtaking-friendly tracks.

Wet races are usually rated quite highly. Variable weather increases the race rating by 0.8-0.9 points on average and wet races add 0.6-0.8 points.

Improving the sport?

Since 2009, Formula 1 has tried to improve the show. The return of slick tires in 2009 was one step, but the most important changes where the introduction of DRS and rapidly-degrading tires in 2011. Did they improve the show? According to the race ratings, they did, but how would every season be rated if all factors (number of overtakes, championship situation, reliability, weather…) had been equal? Interestingly, it seems that 2009, the season with the lowest actual ratings, is the clear winner, followed by 2008.

Average race ratings per year the individual contributions of the most important factors.

Due to a lack of overtakes (yellow), a relatively boring championship (grey) and relatively few wet races (light blue) 2009 was not rated very highly, but apparently its structural rating was quite high. This may have to do with the extreme competitiveness of the field (as Luca Badoer found out when he replaced Massa at Ferrari). Also, compared to 2008, there were fewer weird green-table decisions. The structural values also suggest that 2010 was not as good as many people make out, possibly because the refueling ban tended to make the races more predictable, or because the reduced competitiveness of the field. The drop of the structural value was compensated by an increase in the number of overtakes and the number of retirements, though. Since 2010 the structural rating has been quite low, but interestingly, the introduction of DRS in 2011 (easy overtakes) and the change to hybrid turbo engines in 2014 (lack of noise) have not influenced the structural value a lot, even though many fans didn’t like those changes. Interestingly, the championship situation, battles for the lead and weather conditions only explain a small part of the race ratings. Tilke tracks (grey), teamorders, prematurely red flagged races and races started from behind the safety car (red) had a negative influence on the race rating.

So it seems that the secret of a good race is a nice track, a battle for the lead, variable weather, a lot of overtakes, retirements, no back-to-back winners, and, if possible, the race should also be a championship decider. This sums up the 2012 Brazilian Grand Prix.

It's the engine, stupid!

Even though Mercedes were dominating the 2014 season, there was some hope that the other teams would catch up in 2015. Williams, for example, were very strong at the end of 2014 and Red Bull were likely to perform better in 2015 with an upgraded Renault engine, so the future looked promising. In the end these predictions did not materialize and Mercedes were dominating again in the 2015 season, which was a big disappointment. Where did it all go wrong and why did Ferrari suddenly become Mercedes's closest rivals?

In 2014 Mercedes had by far the best car-engine combination. Williams had more or less the same engine, but a relatively poor chassis, while Red Bull had possibly the best chassis, but a much weaker engine. Apparently, neither Williams, nor Renault managed to make much progress over the winter, which left a much improved Ferrari as the only real threat for Mercedes, even though they still lacked a considerable amount of single-lap pace.

Although Ferrari had improved on all areas, only the improvements on the powerunit really stood out. In fact, the Ferrari chassis was even worse compared to Mercedes's in 2015, as an analysis on pure relative pace (based on the fastest lap by every team) shows.

Data (from F1 Fanatic):

• Outright pace in 2014 and 2015
• Track characteristics

I've used the relative pace of the teams (except Caterham, which was not included in the dataset and Manor for various reasons) for all races in the past two seasons. As the pace is relative to the fastest time, I think it makes sense to compare the pace to the mean pace-deficit of the field. In this way the relative performance of the frontrunners can be estimated. I've removed the outliers in the data and then I've correlated these relative performances to track characteristics.

Track characteristics:

• Number of corners per kilometer to test the performance of the car's chassis
• Percentage full throttle to test the performance of the engine

I've estimated the relative performance of each chassis and each engine for both seasons. These were the results:

Chassis performance in 2014 (red) and 2015 (green).

Engine performance in 2014 (red) and 2015 (green).

The chassis performance indicates how much the relative performance of a car improves with the number of corners per kilometer (which ranges from 1.9 in Monza to 5.7 in Monaco). As expected, Mercedes and Red Bull have the highest chassis performance (around 0.3% per corner per kilometer), followed by Ferrari. The chassis performances did not change too much between 2014 and 2015. The weaker teams did not really catch up. Only McLaren (different design philosophy), Force India and Toro Rosso managed to slightly improve their chassis compared to Mercedes. Mercedes's closest contenders actually all dropped back.

Interestingly, the Mercedes engine had on average the same edge over its rivals in 2015 as in 2014, as the engine performance shows. Their relative advantage was about 0.01% per percentage full throttle per lap (which is between 34 and 76%). Ferrari, however, made huge gains (which probably explains why Sauber did much better in 2015, as their chassis performance was still quite bad), while Renault was even less competitive than in 2014.

The combined effect of chassis and engine performance meant that Williams and Red Bull dropped away compared to Mercedes, as their loss of chassis performance was not compensated by a gain in engine performance. Ferrari, however, were the only of the three teams to gain a lot of horsepower, which meant that the prancing horse was the only top team to gain on Mercedes. This is clearly visible when the estimated average relative performances of 2014 and 2015 are plotted against each other:

The team average performance-level in 2014 and 2015.

On an average circuit Mercedes were 1.5% faster than the average car in both seasons, while Ferrari improved from 0.4 to 0.9%. Williams dropped from nearly 0.6% to nearly 0.4%, while Red Bull went from 0.6% to 0.2%. The other teams were quite consistent, and their relative performances did not change more than 0.2% from one year to another. Lotus and McLaren were, however, the exceptions. That was no coincidence, as they were the only teams to switch engine supplier. Lotus switched from Renault to Mercedes and benefited, while McLaren switched from Mercedes to Honda and instantly became a backmarker. With the aerodynamic development going relatively slowly, a good powerunit is more important than ever.

2015: the true standings

The 2015 season probably was not the most exciting F1 season in history. One important reason was Hamilton's dominance in the first part of the season, which enabled him to decide the championship fairly early in the season. He was, however, also helped by Rosberg's misfortune. Could Rosberg have threatened Hamilton without his bad luck? And how would other drivers have performed without luck intervening? Let's find out!*

Australia

A race to forget as only 13 cars survived the first lap, while two more cars retired shortly after their pitstops. Räikkönen lost a likely 5th place, which drops Nasr and Ricciardo to 6th and 7th. The Toro Rossos of Sainz and Verstappen would have been 8th and 9th without a lengthy pitstop (Sainz) or a blown engine (Verstappen). Hülkenberg would then drop back to 10th place and Ericsson and Pérez would have dropped out of the points.

Malaysia

An interesting, yet rather straightforward race, with only a few mutations outside the points, where Button and Maldonado were on their way to finish in 12th and 13th place.

China

A much more difficult race. Maldonado was ahead of Grosjean when his brakes started to fail, so let's give him 7th place. Verstappen retired at the end of the race in 8th place, so let's give him 9th place (as Maldonado would still be ahead of him). Hülkenberg and Kvyat had to retire early in the race, but they were unlikely to score points anyway. Sainz lost some time due to a gearbox glitch, but it did not significantly affect his final position.

Bahrain

The first race in the season with some true battles at the front. Rosberg lost 2nd place to Räikkönen in the penultimate lap due to a brake problem, but Räikkönen was faster than him anyway, so this is a tough call. Let's assume for simplicity sake that Rosberg's problem didn't affect the final result. Ericsson lost a lot of time in the pits. His pace appeared to be good enough to beat the Pérez-Kvyat-Massa tussle, so an 8th place went begging. Maldonado also lost a lot of time during his last pitstop, but as he received a 5-second time penalty, he was likely to be classified behind Massa (who would have finished 11th) anyway.

Spain

A weird accident caused Maldonado to make another stop, which dropped him out of contention. He was 7th after a very strong opening phase and he may very well have finished there. Alonso was the other retirement, but he only lost a 14th place.

Monaco

Hamilton deserved to win this race, even though he was partly to blame for the decision to make that fateful second pitstop. In the midfield there were more unhappy drivers. Maldonado retired early in the race with yet again a brake failure. There is not enough data to determine his race pace, but given the impossibility of overtaking in Monaco, even with a disappointing pace he could have finished 8th. Verstappen would (at least) have finished in 9th place without his 30-second stop (and subsequent crash), while Alonso would likely have finished in 11th place behind Button.

Canada

Only some mutations at the back, where Merhi and the McLaren drivers retired towards the end of the race.

Austria

A bad pitstop cost Vettel 3rd place. Grosjean was on his way to at least a 9th place. Sainz, however, was unlikely to finish in the points.

United Kingdom

Ricciardo was just ahead of Sainz, who was in 9th place after the pitstops, so they would likely have finished in 9th and 10th position, barring mistakes when the rain came down.

Hungary

Räikkönen was the biggest victim of this chaotic race, as he lost an almost certain 2nd place. Rosberg and Ricciardo then had a race incident, which cost them 3rd and 4th place. Hamilton was perhaps a bit more to blame in his accident with Ricciardo and without the lost time in the pits he would have been 5th. Bottas also suffered a flat tire, which then cost him a 6th place. This then drops Kvyat to 7th and Verstappen to 8th place, while Sainz was good enough to claim 9th place without his issues. Alonso's strong drive should have earned him only one point.

Belgium

Vettel was on his way to 3rd place when his tire blew unexpectedly in the penultimate lap. Ricciardo then lost a 5th place when his car died in the Busstop Chicane, while Bottas lost a 6th place because of a weird tire mix-up.

Italy

Rosberg lost a 3rd place when his "old" engine finally gave up.

Singapore

Kvyat was hugely unlucky with the pitstops. He should have been 4th. Without his problems Hamilton would then have been 5th. Hülkenberg and Massa would have been 8th and 9th had they not collided.

Japan

Not much to say. Sainz was driving well until he damaged his front wing after a very late call, which cost him a 9th place.

Russia

Rosberg retired early in the race. which cost him a likely win. Bottas and Räikkönen then lost fourth and fifth place when Räikkönen crashed into his compatriot in the last lap. Ricciardo and Sainz were on their way to 7th and 8th place until their cars gave up the ghost in the final stages of the race.

United States

Many drivers eliminated themselves in the damp conditions at the beginning of the race. Hülkenberg was a bit unlucky when he crashed into Ricciardo after a front-wing failure, which cost him a 5th place. Alonso was unlucky at the start, but he was lucky with the safety cars. Without engine problems he may have finished in 6th place ahead of Pérez.

Mexico

Vettel was unlucky at the start, otherwise he was likely to finish in 3rd place. Räikkönen was a bit unlucky when Bottas ran into him as a retribution for what happened in Russia, but his pace was disappointing anyway.

Brazil

Nothing much happened. As he was quite slow compared to his teammate, it seems that Massa did not really benefit from his under-inflated tires, so let's give him that 8th place back.

Abu Dhabi

Kvyat lost engine power towards the end of the race, which cost him two places. Bottas was 10th before he ran into the back of Button in the pits, so let's give him 10th place.

Conclusion

Due to reliability problems and collisions there is a tendency for points to flow from the front to the back of the grid. This season Rosberg was the biggest net loser. He scored 40 points less than in the ideal-world situation. The Ferrari drivers lost 27 points each, while Hamilton only lost 15 points. The difference in lost points between the Mercedes drivers was not nearly enough for Rosberg to claim the title, but the gap would at least have shrunk from 59 to 34 points, enough to make the championship battle go on for two more races.

Points scored per driver and the ideal-world scenario.

The ideal-world scenario allows us to more accurately determine the relative strength of the drivers. The Williams drivers, for example, were seemingly very close (Bottas scored 136 points, Massa 121), but as Bottas lost 16 points due to bad luck, while Massa gained 21, the true difference should have been a much more substantial 52 points. Although he was outscored by his teammate, Ricciardo was the better Red Bull driver, as he lost a couple of points, while Kvyat was one of the biggest net gainers. Also Hülkenberg should have outscored Pérez, while Maldonado was much closer to Grosjean than the standings would suggest.

The team scores show that the top teams lost some and that these points were gained by the midfield teams like Force India (+27) and Red Bull (+20). Sauber (+22) made the highest relative gains, which suggests that the team really had to depend on other teams' misfortune to score points. The high relative gains of the weaker teams is illustrated in the graph below, which uses a logarithmic scale to highlight relative gains.

Actual points and ideal-world points per team on a logarithmic scale.

McLaren (grey-black) and Sauber (yellow-blue) scored well above their ideal-world points, the relative gains and losses were much less for the other teams. Ferrari (red) and Mercedes (grey) were the only net losers.

* I try to correct only for factors that are outside the drivers' control, like mechanical problems, botched pitstops and unforeseen consequences of wheel-to-wheel battles. Note that this is no rocket science. I only try to establish the true potential of all drivers.

Welcome

Hi folks, welcome to my site F1 in Figures! This site will of course be all about Formula 1, with a lot of data analyses. I hope you will enjoy it and I hope to initiate some interesting discussions about the sport we love, so feel free to leave a reply in the comment section below.