Abstract
Overtaking in Formula 1 was far more abundant during the 1980s than during the 2000s, but it is poorly understood what exactly caused this decline. This paper uses a negative-binomial model on overtaking data at the driver level from 1983 to 2010 to disentangle the effect of quantifiable factors, such as the number of cars and pit strategies, from the non-quantifiable overtake-friendliness of the tracks and the cars. It was found that overtaking was easiest at the beginning of the study period (1984 and 1985) and then declined until the late-1990s. While most of this decline was gradual, some abrupt downturns were discovered. These downturns seem to coincide with fuel-limit restrictions in the 1980s and the re-introduction of in-race refueling in 1994. The decline in overtaking during the 1990s may be attributed to the increased role of aerodynamics and technology, but their impact was more gradual and therefore harder to establish.
1 Introduction
Throughout most of its history, overtaking in Formula 1 has been relatively uncommon. Even so, overtaking was far more abundant during the 1980s than during the 2000s. There are various potential explanations for this decline in overtaking, such as the increased dependence on aerodynamic downforce (Mafi 2007; Perry and Marshall 2008), technological improvements and the increased role of pit strategies, but the extent to which they had an impact on overtaking is poorly understood. As a lack of overtaking leads to static and unexciting races, Formula 1 policymakers have continuously tried to boost overtaking levels.[1] Until the invention of DRS (Drag Reduction System) in 2011, which gives the attacking car a distinct advantage, most attempts had not been very successful. Therefore, a detailed analysis of overtaking in Formula 1 spanning multiple decades is needed to reveal the factors that either had a positive or negative impact on overtaking, so overtaking can be increased in a more natural way.
Accurate timing measurements made their appearance in Formula 1 in the early 1980s, which from then on made it possible to keep track of every driver throughout the race. The number of position changes on lap charts then give a reasonably good indication of the number of actual overtakes during the race, even though some scrutiny based on lap times and actual footage may still be needed in order to dismiss position changes caused by driver errors or car problems that do not lead to retirements (for example, a gearbox problem). The number of genuine on-track overtakes after the first lap is then counted for every dry race. This number declined steadily between the mid-1980s and mid-1990s, from about 40 to 50 in the mid-1980s to about 10–15 from the mid-1990s until 2009, but jumped to around 20 in 2010, the last year before the introduction of DRS (Clip the Apex. Formula One Overtaking Database n.d.).
There are several potential explanations for this predominantly downward trend in overtaking. Aerodynamics may be the most obvious culprit. The importance of aerodynamics in Formula 1 greatly increased after the turbo era (1977–1988). Teams were chasing more downforce, which not only reduced brake distances and thereby the ability to out-brake another car, but created severe wake turbulence as well. As this wake turbulence took away downforce from a following car, it became harder to follow another car closely, let alone pass it (Dominy 1990). During roughly the same period, in the late-1980s and the early-1990s, some spectacular technological developments took place. Perhaps the most important and long-lasting development was the large-scale adoption of the semi-automatic gearbox. Previously, drivers had to manually select gears, which was slower and had a greater margin for error. Drivers could mis-shift and engage the wrong gear or no gear at all, resulting in a temporary loss of power, which would make them vulnerable to a close pursuer.
Another important development was the increasing influence of pit strategy in the mid-1990s. During the 1980s, drivers would often (attempt to) complete the full race-distance without stopping for tires. However, tire stops were still a regular occurrence back then, and they slowly but surely became more prevalent until in-race refueling was (re-)introduced in 1994, after which pit-stops for tires and fuel became the norm. This then increased the opportunities for drivers to pass their rivals in the pits, rather than on the track, thereby (potentially) reducing on-track overtaking. During the late-1990s and most of the 2000s, various rule changes regarding the cars[2] or the race format[3] were made, but their impact on overtaking seems very limited. The ban on refueling in 2010 boosted overtaking, although it is unclear to what extent the entrance of three new (and therefore much slower) teams contributed to this increase.
In order to estimate the effect of the regulations on overtaking, we will analyze overtaking at the driver (micro) level between 1983 and 2010. By controlling for as many quantifiable variables at the driver or race level, such as the number of cars, position, pit strategies and speed differentials, the non-quantifiable overtake-friendliness of the tracks and the cars (for each year) can be estimated during this period. Significant year-to-year changes in overtake-friendliness can then be retrospectively linked to rule changes.
2 Theoretical framework
2.1 Introduction
As far as we are aware, overtaking in Formula 1 has not been studied before, unlike other indicators that have been found to contribute to the attractiveness and commercial success of the sport, such as competitive balance or uncertainty of outcomes. For example, Budzinski and Feddersen (2020) found several indicators for competitive balance, such as Gini coefficients of points scored, laps led, and qualifying times. Judde et al. (2013) and Mastromarco and Runkel (2009) show that changes in regulation can improve competitive balance, which may then lead to higher broadcasting revenues. Krauskopf et al. (2010), however, suggests that too high levels of competitive balance can also reduce viewing rates. Higher uncertainty of outcomes lead to higher viewership (Schreyer et al. 2016), and this applies to NASCAR as well (Berkowitz et al. 2016). Therefore, in this section, we are going to build intuition for what factors can contribute to overtaking and what factors actually hurt overtaking.
Overtaking in Formula 1 has always been relatively uncommon because of three factors. First, the fastest cars are usually ahead of the slower cars, second, wake turbulence prevents close racing, and third, the twisty nature of the tracks prevents large-scale slipstreaming. These factors alone are not unique to Formula 1, but their combination is uncommon among other racing series. For example, many racing series use reversed grids to boost overtaking. Overtaking is much more common among less aerodynamically-sophisticated vehicles, such as go-karts, touring cars, or motorcycles. Even in case of severe wake turbulence, its negative impact on overtaking can be overcome when the straights are long enough to enable slipstreaming. This is exactly the idea behind oval-track racing, as these ovals are essentially endless straights.
In Formula 1, overtaking normally only occurs when a significantly faster car is running behind a slower car. These situations are rare, as faster cars generally start ahead of the slower ones. Therefore, on a large scale the field will be gradually pulled apart, but there may be some clumping together of cars on a smaller scale. This clumping together of cars may then lead to on-track battles and even overtaking. The total amount of overtakes in a race then depends on the number of battles and the probability of overtaking.
The cars and the track layout will affect the probability of overtaking. For example, in Monaco overtaking will always be more difficult than at most other tracks. Conversely, overtaking may have been easier in the 1980s than in the 2000s, as the cars were less aerodynamically sophisticated. In order to construct an unbiased and reasonably accurate model of overtaking, it is therefore important to find quantifiable variables that affect the number of on-track battles. There are two such variables: the number of cars (and their reliability), and the degree to which the cars are out of position (how well mixed the field is) at the beginning of the race. The most straightforward way to compute this mixing is by comparing the actual position p of every car the end of the first lap to its rank r, which is based on its fastest lap of the weekend.[4] So, this mixing parameter is positive for a fast car at the back of the field and negative for a slow car at the front of the field.[5] The mixing parameter can then be standardized by dividing it by the number of cars c,
Pit-stops are more complicated, as they affect both the number of on-track battles and the probability of overtaking. They may reduce the number of on-track battles if a driver pits (or has to pit) before he can challenge another driver. On the other hand, pit-stops can also increase the number of on-track battles if a driver emerges from the pits behind a slower car.[7] Similarly, different strategies may either increase or decrease the likelihood of overtaking, depending on whether the attacking or defending car has a tire or fuel-load advantage. Furthermore, the presence of pit-stops might induce something that can only be described as driver laziness; when drivers patiently wait for the pit-stops to effortlessly pass another driver, reducing the likelihood of overtaking on track.
The influence of speed differentials on overtaking is also not very straightforward. Small speed-differentials may increase the number of on-track battles, as the field does not spread out much, but they may decrease the likelihood of overtaking, as it is less likely for any driver to have a large enough performance advantage to overtake. All in all, it is hard to predict which effect dominates, or if the two effects cancel out. Somewhat related to speed differentials is the appearance of the safety car. As the safety car eradicates the existing gaps between the cars, it likely increases the number of on-track battles.
Figure 1 shows the development of the aforementioned control variables; the number of cars, their reliability, the degree to which cars are out of position at the beginning of the race (mixing), the number of scheduled pit-stops, speed differentials and the likelihood of a safety car. The graphs show a decline in number of cars and speed differentials over time, and an increase in reliability, the number of pit-stops and the likelihood of a safety car, whereas the mixing of the cars does not show a very clear trend.[8]

Countable control variables. Top left: Average number of cars running at the end of the first lap. Top right: Average race-distance completed by the cars running at the end of the first lap. Middle left: Average degree to which cars are out of position (mixing) at the end of the first lap with respect to the maximum mixing possible, which is set at 100 %. Middle right: Average number of scheduled pit-stops per car per race. Bottom left: Average speed-differentials among the field. Bottom right: Percentage of races affected by the safety car; included are mid-race safety cars only.
2.2 Model
The amount of overtaking done by every driver in every race is count data and can therefore be modelled by either a Poisson or the negative-binomial model. Due to over-dispersion in the count data, the negative-binomial model is more accurate and we therefore use it.[9] In the analysis, the number of places gained and lost by a driver are estimated together in one regression.
The expected number of places gained by driver i on track j in season t (G ijt ) and the corresponding number of places lost (L ijt ), given race circumstances x ijt , are then:
where
c
ijt
is a vector including the number of cars and reliability and
Something similar applies to pit strategy, depicted by the vector
p
ijt
, with the vectors of coefficients
As the negative-binomial model is a multiplicative model, it requires a log transformation. As such, the exponents of the coefficients (the incidence-rate ratios) of dummy variables can be interpreted as the factor to which they increase overtaking. Moreover, continuous nonnegative variables, such as reliability, are log-transformed, as well as the number of cars, so their coefficients can then be interpreted as elasticities.
Table 1 shows the control variables by category, as well as a brief description. Apart from the track and year fixed effects, as well as the first category of control variables (number of cars and reliability), most variables are estimated separately on overtaking and being overtaken, so they will have different coefficients.
Control variables.
| Variable | Symbol | Description |
|---|---|---|
| Number of cars and reliability: | ||
| Number of cars |
|
Number of cars surviving the first lap |
| Overall reliability |
|
Average percentage of total race distance completed by cars surviving the first lap |
| Individual reliability |
|
Percentage of total race distance completed |
| Not in pack |
|
Dummy, 1 if driver is not in the pack (
|
| Safety car |
|
Dummy, 1 if there is at least a mid-race safetycar. |
| Position: | ||
| Better than expected |
|
|
| Worse than expected |
|
|
| Pit-stops: | ||
| Number of pit-stops |
|
Number of scheduled pit-stops per driver, interacted with in-race refueling |
| Unknown strategy |
|
Dummy, 1 if a driver retires before 75 % of the total race distance |
| Percentage pitting more often |
|
Percentage of drivers making more pit-stops than reference driver, interacted with in-race refueling and overtaking/being overtaken |
| Percentage pitting less often |
|
Percentage of drivers making fewer pit-stops than reference driver, interacted with in-race refueling and overtaking/being overtaken |
| Number of unscheduled stops |
|
Number of unscheduled stops in the race after the first lap (excluding penalties) on probability of being overtaken |
| Unscheduled stop × rank |
|
Dummy if a driver makes an unscheduled stop, interacted with rank based on its expected speed (0 is slowest, 1 is fastest) on probability of overtaking |
| Long repair stop |
|
Dummy, 1 if a driver makes a long, unscheduled stop, usually to fix a technical issue |
| Speed differences: | ||
| Speed deficit categories |
|
Driver’s gap to the fastest car in 6 categories (
|
| Average speed difference |
|
Race-average speed deficits, interacted with overtaking/being overtaken |
The position controls consist of an upper and a lower branch in order to account for possible nonlinearities. If position p is better (lower) than the expected position r,
The pit-stop variables have some interactions with in-race refueling as well. Long repair stops (for example, to fix an engine problem or a broken rear wing, processes that take minutes rather than seconds) and unscheduled stops (usually to replace a flat tire or a broken front wing) are included as well, except for unscheduled stops at the end of the first lap or during an early safety-car period, as these stops directly affect the order of the field at the end of the first lap, and are therefore captured by the position controls. As faster cars are more likely to recover from unscheduled stops, the unscheduled-stop dummy is interacted with the driver’s expected speed R,
Speed differences are measured at an individual level (speed deficit to the fastest car) by six categories (ranging from less than 1 % slower to over 5 % slower). The average speed difference among the field per race is included as well. Both the dummy variables and the average speed difference are again estimated separately on overtaking and being overtaken.
3 Data
We combine micro-level overtaking data with position and lap-time data. In the analysis, each driver in each race is treated as one observation, resulting in over 10.000 observations across 28 seasons. The detailed overtaking data are provided by Clip the Apex, with some manual deviations based on lap-time analysis and actual race footage.[11] Included are all contested overtakes after the first lap. In the analysis, we focus on dry races only, as wet-weather races are harder to analyze. Changeable weather conditions, in which drivers have to repeatedly switch back and forth from dry tires to wet tires, may boost overtaking, whereas in a monsoon-hit race overtaking may even be reduced due to poor visibility. Therefore, wet-weather races are ignored in the analysis.[12] Out of a total of 466 races from 1983 to 2010, 401 were included in the analysis. Table 2 shows the number of dry races per track.
Number of dry races per track.
| Track | Number of dry races | Period |
|---|---|---|
| A1-Ring | 7 | 1997–2003 |
| Adelaide | 9 | 1985–1995 |
| Aida | 2 | 1994–1995 |
| Albert Park | 13 | 1996–2010 |
| Brands Hatch | 4 | 1983–1986 |
| Buenos Aires | 4 | 1995–1998 |
| Catalunya | 17 | 1991–2010 |
| Circuit Gilles Villeneuve | 23 | 1983–2010 |
| Dallas | 1 | 1984 |
| Detroit | 6 | 1983–1988 |
| Dijon | 1 | 1984 |
| Donington | 0 | 1993 |
| Estoril | 12 | 1984–1996 |
| Fuji Speedway | 1 | 2007–2008 |
| Hermanos Rodríguez | 7 | 1986–1992 |
| Hockenheimring (old) | 16 | 1983–2001 |
| Hockenheimring (new) | 7 | 2002–2010 |
| Hungaroring | 24 | 1986–2010 |
| Imola (old) | 10 | 1983–1994 |
| Imola (new) | 11 | 1995–2006 |
| Indianapolis | 6 | 2000–2007 |
| Interlagos | 15 | 1990–2010 |
| Istanbul Park | 6 | 2005–2010 |
| Jacarepaguá | 7 | 1983–1989 |
| Jerez | 7 | 1986–1997 |
| Kyalami | 5 | 1983–1993 |
| Long Beach | 1 | 1983 |
| Magny-Cours | 15 | 1991–2008 |
| Monaco | 23 | 1983–2010 |
| Monza | 26 | 1983–2010 |
| Nürburgring | 12 | 1984–2009 |
| Paul Ricard (old) | 2 | 1983–1985 |
| Paul Ricard (new) | 5 | 1986–1990 |
| Phoenix | 3 | 1989–1991 |
| Sakhir | 7 | 2004–2010 |
| Sepang | 10 | 1999–2010 |
| Shanghai | 3 | 2004–2010 |
| Silverstone | 22 | 1987–2010 |
| Singapore | 3 | 2008–2010 |
| Spa-Francorchamps | 15 | 1983–2010 |
| Suzuka | 19 | 1987–2010 |
| Valencia | 3 | 2008–2010 |
| Yas Marina | 2 | 2009–2010 |
| Yeongam | 0 | 2010 |
| Zandvoort | 3 | 1983–1985 |
| Zolder | 1 | 1984 |
| Österreichring | 5 | 1983–1987 |
Figure 2 shows the average number of overtakes per dry race for every year in the dataset. 1984 was the peak year, with around 47 overtakes per dry race, after which overtaking declined very steadily until it hit a low of around 10 overtakes per dry race in 1998. From then on, the season averages were usually in the 10 to 15 range until 2010, when three new teams joined the grid and in-race refueling was banned, and it suddenly increased to slightly over 20 overtakes per dry race. In order to get a better understanding of what may have caused this decline, it is useful to map all potentially important rule changes during the study period. Figure 3 shows the different engine specifications, fuel limitations, tire rules and the qualifying format between 1983 and 2010.

Number of overtakes per dry race from 1983 to 2010.

Rules per year. Note: The grey cells indicate that something was allowed or existed. The capitals refer to the following tire manufacturers: (G) Goodyear, (P) Pirelli, (M) Michelin and (B) Bridgestone.
Up until 1988 turbo engines were allowed. Throughout most of this period, some teams still elected to run a normally-aspirated engine (the exception being the all-turbo 1986 season). The turbo engines were subject to strict limitations regarding engine and fuel-tank capacity, as well as maximum allowed turbo boost, in a bid to prevent them from completely outcompeting the normally-aspirated engines. After banning in-race refueling in 1984, the fuel limit for turbo engines was reduced step by step from 220 L in 1984 and 1985 to only 150 L in 1988.
Furthermore, in 1983 and 1984 there were three active tire manufacturers: Goodyear, Pirelli and Michelin. This tire war did not last very long and from 1985 onward at most two tire manufacturers were active at the same time, creating a few tire wars alternated by tire monopolies.
In-race refueling was re-introduced in 1994, while at the same time some advanced technology such as active suspension, ABS and traction control got banned. In 1996 the qualifying format was changed to one one-hour session instead of two, which likely increased the likelihood of qualifying upsets, as drivers did not get a second chance to recover from a poor session. More unpredictability was added in 2003 with the introduction of the single-lap shootout. Moreover, drivers had to qualify with the fuel load they wanted to start the race, which further mixed up the grid and influenced race strategy as well.
2006 saw the introduction of the current three-session qualifying format, albeit with limited freedom to refuel the cars between qualifying and race. Tire changes were disallowed for the 2005 season only, while from 2007 onwards drivers were required to run both dry-weather tire compounds in the race. After eleven seasons of grooved tires, slick tires were re-introduced in 2009. Then in 2010 in-race refueling got banned.
While some of these regulation changes may seem to coincide with changes in overtaking frequencies, it is important to rule out other inter-season heterogeneity that may have affected overtaking as well. Therefore, a statistical analysis is required.
4 Results
4.1 Baseline results
Table 3 shows the year effects and Table 4 shows the other controls. Table A1 shows the track fixed effects. In all cases, the incidence-rate ratios (the exponent of the coefficients) rather than the coefficients are displayed.
Baseline results: year effects. Incidence-rate ratios. Standard errors are in brackets and clustered at race level. 1983 is the reference year.
| Dependent variable: number of overtakes per driver per race (log-transformed) | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Year | (1) | (2) | (3) | (4) | (5) | (6) | ||||||
| 1984 | 1.139 | (0.126) | 1.260** | (0.132) | 1.344*** | (0.131) | 1.321*** | (0.121) | 1.368*** | (0.138) | 1.450*** | (0.135) |
| 1985 | 1.017 | (0.129) | 1.135 | (0.114) | 1.221 | (0.114) | 1.300 | (0.110) | 1.321 | (0.123) | 1.412 | (0.129) |
| 1986 | 0.892 | (0.125) | 1.024 | (0.135) | 1.093 | (0.139) | 1.094* | (0.125) | 1.091* | (0.132) | 1.215 | (0.151) |
| 1987 | 0.842 | (0.115) | 0.971 | (0.123) | 0.997 | (0.118) | 1.008 | (0.100) | 0.970 | (0.097) | 1.183 | (0.123) |
| 1988 | 0.704 | (0.104) | 0.805 | (0.107) | 0.805* | (0.101) | 0.769*** | (0.082) | 0.819** | (0.087) | 0.809*** | (0.081) |
| 1989 | 0.799 | (0.109) | 0.93 | (0.123) | 0.961 | (0.128) | 0.953* | (0.123) | 0.981 | (0.132) | 0.846 | (0.111) |
| 1990 | 0.724 | (0.119) | 0.803 | (0.101) | 0.800 | (0.096) | 0.827 | (0.090) | 0.829 | (0.096) | 0.735 | (0.087) |
| 1991 | 0.659 | (0.096) | 0.756 | (0.107) | 0.754 | (0.098) | 0.763 | (0.089) | 0.780 | (0.094) | 0.715 | (0.088) |
| 1992 | 0.535 | (0.083) | 0.601 | (0.086) | 0.598 | (0.086) | 0.566** | (0.072) | 0.576** | (0.074) | 0.559* | (0.072) |
| 1993 | 0.623 | (0.105) | 0.815* | (0.142) | 0.776 | (0.130) | 0.709 | (0.117) | 0.701 | (0.114) | 0.685 | (0.107) |
| 1994 | 0.491 | (0.080) | 0.597* | (0.084) | 0.592 | (0.084) | 0.544 | (0.068) | 0.560 | (0.074) | 0.504* | (0.067) |
| 1995 | 0.365* | (0.058) | 0.436** | (0.063) | 0.436** | (0.062) | 0.453 | (0.061) | 0.463 | (0.064) | 0.463 | (0.061) |
| 1996 | 0.342 | (0.059) | 0.385 | (0.058) | 0.367 | (0.066) | 0.351 | (0.060) | 0.359 | (0.064) | 0.314** | (0.061) |
| 1997 | 0.472 | (0.093) | 0.529 | (0.103) | 0.467 | (0.100) | 0.448 | (0.086) | 0.468 | (0.092) | 0.408 | (0.085) |
| 1998 | 0.301* | (0.057) | 0.346** | (0.059) | 0.312* | (0.060) | 0.302** | −0.051 | 0.323** | (0.054) | 0.280** | (0.047) |
| 1999 | 0.391 | (0.092) | 0.429 | (0.077) | 0.395 | (0.077) | 0.362 | (0.063) | 0.36 | (0.060) | 0.305 | (0.053) |
| 2000 | 0.363 | (0.091) | 0.416 | (0.081) | 0.372 | (0.078) | 0.342 | (0.068) | 0.361 | (0.071) | 0.308 | (0.065) |
| 2001 | 0.326 | (0.055) | 0.391 | (0.058) | 0.355 | (0.057) | 0.33 | (0.048) | 0.362 | (0.053) | 0.319 | (0.051) |
| 2002 | 0.367 | (0.071) | 0.403 | (0.068) | 0.362 | (0.065) | 0.318 | (0.056) | 0.322 | (0.057) | 0.278 | (0.051) |
| 2003 | 0.448 | (0.112) | 0.544 | (0.133) | 0.455 | (0.123) | 0.368 | (0.083) | 0.409 | (0.095) | 0.322 | (0.076) |
| 2004 | 0.433 | (0.070) | 0.495 | (0.073) | 0.405 | (0.077) | 0.323 | (0.057) | 0.365 | (0.065) | 0.288 | (0.055) |
| 2005 | 0.342 | (0.060) | 0.383 | (0.068) | 0.305* | (0.064) | 0.250** | (0.047) | 0.283* | (0.053) | 0.235 | (0.047) |
| 2006 | 0.422 | (0.082) | 0.453 | (0.076) | 0.379 | (0.069) | 0.311 | (0.050) | 0.349 | (0.055) | 0.291 | (0.047) |
| 2007 | 0.326 | (0.057) | 0.341* | (0.050) | 0.275** | (0.050) | 0.245* | (0.042) | 0.273* | (0.045) | 0.221** | (0.040) |
| 2008 | 0.351 | (0.067) | 0.343 | (0.061) | 0.27 | (0.060) | 0.214 | (0.043) | 0.235 | (0.047) | 0.201 | (0.043) |
| 2009 | 0.338 | (0.070) | 0.386 | (0.067) | 0.299 | (0.064) | 0.254 | (0.051) | 0.283 | (0.057) | 0.246 | (0.055) |
| 2010 | 0.544* | (0.107) | 0.620** | (0.129) | 0.502*** | (0.107) | 0.377* | (0.096) | 0.413* | (0.087) | 0.351* | (0.077) |
| Controls: | ||||||||||||
| Year | Yes | Yes | Yes | Yes | Yes | Yes | ||||||
| Track | Yes | Yes | Yes | Yes | Yes | |||||||
| No. cars | Yes | Yes | Yes | Yes | ||||||||
| Mixing | Yes | Yes | Yes | |||||||||
| Pit-stops | Yes | Yes | ||||||||||
| Speed diff. | Yes | |||||||||||
| Obs. | 17,756 | 17,756 | 17,756 | 17,756 | 17,756 | 17,756 | ||||||
| Log llh. | −23,331 | −23,023 | −22,576 | −21,696 | −21,442 | −21,157 | ||||||
| AIC | 46,720 | 46,182 | 45,297 | 43,546 | 43,065 | 42,523 | ||||||
| BIC | 46,946 | 46,712 | 45,857 | 44,145 | 43,773 | 43,332 | ||||||
| α | 1.323 | (0.045) | 1.212 | (0.038) | 1.052 | (0.037) | 0.736 | (0.031) | 0.669 | (0.029) | 0.602 | (0.028) |
-
Asterisks depict year-to-year significance levels. *10 % significance level, **5 % significance level, ***1 % significance level.
Baseline results: control variables. Incidence-rate ratios. Standard errors are in brackets and clustered at race level.
| (3) | (4) | (5) | (6) | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Number of cars (log) |
|
0.934 | (0.345) | 1.144 | (0.366) | 1.028 | (0.324) | 1.054 | (0.337) |
| Overall reliability (log) |
|
1.321* | (0.314) | 1.620*** | (0.341) | 1.675*** | (0.339) | 1.599** | (0.337) |
| Individual reliability (log) |
|
1.758*** | (0.034) | 1.757*** | (0.033) | 2.032*** | (0.056) | 2.101*** | (0.058) |
| Not in pack |
|
1.082 | (0.096) | 0.523*** | (0.061) | 0.510*** | (0.055) | 0.444*** | (0.046) |
| Safety car |
|
1.472*** | (0.156) | 1.446*** | (0.149) | 1.460*** | (0.160) | ||
| Being overtaken | |||||||||
| Better position than expected |
|
0.029*** | (0.005) | 0.034*** | (0.006) | 0.104*** | (0.019) | ||
| Worse position than expected |
|
0.383*** | (0.057) | 0.332*** | (0.054) | 0.359*** | (0.065) | ||
| Overtaking | |||||||||
| Better position than expected |
|
2.123*** | (0.445) | 1.964*** | (0.450) | 2.663*** | (0.650) | ||
| Worse position than expected |
|
24.789*** | (2.546) | 25.288*** | (2.674) | 32.147*** | (3.529) | ||
| Number of pit-stops | |||||||||
| No refueling |
|
0.907 | (0.078) | 0.953 | (0.091) | ||||
| Refueling |
|
0.927* | (0.042) | 0.928 | (0.043) | ||||
| Unknown strategy |
|
1.389*** | (0.101) | 1.339*** | (0.098) | ||||
| Being overtaken | |||||||||
| No refueling: | |||||||||
| % of drivers pitting more often |
|
1.797*** | (0.229) | 1.484*** | (0.200) | ||||
| % of drivers pitting less often |
|
1.361 | (0.198) | 1.239 | (0.189) | ||||
| Refueling: | |||||||||
| % of drivers pitting more often |
|
2.307*** | (0.228) | 1.882*** | (0.198) | ||||
| % of drivers pitting less often |
|
0.661*** | (0.102) | 0.664** | (0.101) | ||||
| Overtaking | |||||||||
| No refueling: | |||||||||
| % of drivers pitting more often |
|
1.148 | (0.178) | 1.120 | (0.174) | ||||
| % of drivers pitting less often |
|
1.940*** | (0.278) | 1.841** | (0.292) | ||||
| Refueling: | |||||||||
| % of drivers pitting more often |
|
0.818*** | (0.102) | 0.780** | (0.100) | ||||
| % of drivers pitting less often |
|
2.383*** | (0.324) | 2.536*** | (0.353) | ||||
| Being overtaken | |||||||||
| Number of unscheduled stops |
|
1.051*** | (0.010) | 1.038*** | (0.011) | ||||
| Overtaking | |||||||||
| Unscheduled stop × rank |
|
2.870*** | (0.324) | 3.319*** | (0.369) | ||||
| Long repair stop |
|
0.813*** | (0.042) | 0.782*** | (0.042) | ||||
| Being overtaken | |||||||||
| 1–2 % |
|
1.654*** | (0.115) | ||||||
| 2–3 % |
|
2.064*** | (0.151) | ||||||
| 3–4 % |
|
2.428*** | (0.182) | ||||||
| 4–5 % |
|
2.656*** | (0.214) | ||||||
| 5 % or more |
|
3.027*** | (0.247) | ||||||
| Average speed difference in % |
|
0.817*** | (0.028) | ||||||
| Overtaking | |||||||||
| Speed deficit <1 % |
|
0.873*** | (0.069) | ||||||
| 1–2 % |
|
1.282*** | (0.108) | ||||||
| 2–3 % |
|
1.584*** | (0.139) | ||||||
| 3–4 % |
|
1.626*** | (0.146) | ||||||
| 4–5 % |
|
1.705*** | (0.167) | ||||||
| 5 % or more |
|
1.457*** | (0.147) | ||||||
| Average speed difference in % |
|
0.885*** | (0.028) | ||||||
-
Asterisks depict significance levels. *10 % significance level, **5 % significance level, ***1 % significance level.
Specification (1) in Table 3 is the most basic specification, as it only uses year fixed effects. As such, it can be used to look for significant year-to-year changes in overtaking in the raw data. Therefore, the asterisks depict year-to-year significance levels. Despite the decreasing trend in overtaking, which went from 1.14 times the 1983 overtaking levels in 1984 to 0.33 in 2007, only the 1995 and 1998 season show a somewhat (at the 10 % level) significant decline compared to the previous season, while 2010 shows a somewhat significant increase.
The inclusion of track fixed effects in Specification (2) and groups of control variables in Specifications (3) to (6) yields further significant year-to-year changes in overtaking. With controls, the long-term decline in overtaking becomes more pronounced, and as a result, more seasons see a statistically significant decline in overtaking. The analyses rather consistently imply overtaking got harder in 1988, 1998 and 2007. Furthermore, there is some evidence that overtaking got harder in 1986, 1992, 1994, 1996 and 2005 as well, but the results are not as conclusive. On the other hand, overtaking got easier in 1984 and 2010.
Table 4 shows the coefficients of the control variables from Specification (3) to (6). In Specification (3) the logarithm of the number of cars and reliability are added, while in Specification (4) the position variables are added as well. Pit-stop variables are then included in Specification (5), and finally, in Specification (6), the preferred specification, speed differentials are added as well. Overall, the coefficients do not change much between the different specifications, so only Specification (6), which has the lowest AIC and BIC values, will be discussed.
The number of cars does not seem to impact the amount of overtaking per car, as the incidence-rate ratio of its logarithm does not statistically significantly differ from one. Therefore, the coefficient, which is the logarithm of the incidence-rate ratio, is not significantly different from zero. Reliability does, however, positively affect overtaking. As the variables are log-transformed, the coefficients can be interpreted as elasticities. A 1 % increase in overall reliability increases overtaking by about 0.47 % (1 % × ln(1.599)), whereas the same increase in individual reliability increases overtaking by about 0.74 % (1 % × ln(2.101)). As these elasticities are below one, they suggest that overtaking is more likely at the beginning of the race, which seems right.[13] Furthermore, if a car that is not in the pack at the beginning of the race is half as likely to be involved in any overtaking, ceteris paribus. Conversely, the deployment of the safety car increases overtaking by almost 50 %.
The coefficients of the position controls are a little hard to interpret. As the ‘better position than expected’ variable is always non-positive, this means that in the most extreme case (the slowest driver leading the race) a driver is ten ((0.104)(−1) ≈ 9.6) times more likely to be overtaken than the average driver. In the exact opposite case, that is, the likelihood of overtaking in case the fastest driver is at the back of the field, is even higher at about 32.
The direct effect of pit-stops on overtaking appears slightly negative for both tire and fuel stops, but is not statistically significant. Strategic variation, on the other hand, seems to have a profound effect on overtaking as well. As expected, a driver is more likely to be overtaken when the opposition pits more often than he does, and is less likely to overtake. The opposite is true if the opposition pits less often. Interestingly, the influence (both positively and negatively) of strategic variation is higher with in-race refueling.
The number of unscheduled stops has a small but significant positive effect on the probability of being overtaken, whereas fast cars pass over thrice as many cars after an unscheduled stop. A long repair stop, on the other hand, seems to reduce overtaking. Furthermore, the ‘unknown strategy’ coefficient is only used to balance the model and has no real interpretation.
Finally, speed differentials have a clear effect on overtaking. As expected slower drivers are more likely to be overtaken. Interestingly, they are, to some extent, also more likely to overtake, which is consistent with the fact that overtaking tends to be more common towards the back of the field. However, the likelihood of overtaking decreases with overall speed differentials, as they cause the field to spread out more quickly and this affects every driver in the race. This means that the impact of speed differentials is not very straightforward, but it seems that average speed differentials of around 2–3 % are best for overtaking.
4.2 Sensitivity analysis
The results of the baseline model seem reasonable, yet there is reason to believe that the model suffers from some systematic biases. For example, the model tends to underestimate overtaking in races with high tire degradation, such as the 1997 Spanish and Hungarian Grand Prix, as well as the 2010 Canadian Grand Prix. The 2010 season as a whole might not be modelled accurately, as the impact of strategy on overtaking is largely determined by the other non-refueling seasons in the 1980s and early-1990s, when race strategies were less sophisticated and speed differentials were larger.[14] It is quite possible that back then the larger speed differences reduced overtaking in multiple-pit-stop races, as the field would have spread out too much by the time the first tire stops were made. Not accounting for the effect of speed differences on strategy possibly biased the coefficient of the 2010 season. For the same reason the coefficient of the 1983 season may be biased, as it is linked with the other refueling seasons over a decade later.
Furthermore, the number of pit-stops may have a nonlinear effect on overtaking. For example, the effect may be negative in case of few stops, but positive in case of many stops, as many stops indicate high tire degradation, which may induce overtaking. Zero-stop strategies, on the other hand, may increase overtaking as well, as the drivers adopting such a strategy cannot be passed in the pits. Another potential bias not accounted for in the main analysis is the timing of pit-stops. First, the distribution of fuel strategies among the field is likely non-random, and depends on grid position and the driver’s expected race-pace. In order to avoid time losses in ‘traffic’ a driver who is expected to do well in the race compared to qualifying may start with a relatively heavy fuel-load, thereby substituting (potential) on-track overtakes with pit-lane overtakes. Second, the earlier a driver stops, the more places he will lose, which increases his potential of overtaking.
In order to check the robustness of the main analysis, we conduct four sensitivity analyses regarding pit strategies, based on Specification (6) of the baseline analysis. In the first specification, we interact the number of stops with the average speed difference. In the second specification, we include a dummy for zero-stop strategies. In the third specification we include the timing of a driver’s first fuel stop compared to the median stop. The variable is then capped at plus or minus 10 % of the race distance.[15] Lastly, in the fourth specification, we include the timing of the first stop using six categories.[16] Table 5 shows the year effects, while Tables 6 and A2 show the control variables. The track fixed effects can be found in Table A3. The year effects are very robust and the year-to-year significance levels remain largely the same. The most significant changes are from 1983 to 1984 and 1987 to 1988. Less significant changes can be seen throughout the 1990s and from 2006 to 2007 and 2009 to 2010. These findings are very similar to the findings of the baseline analysis, even though according to the AIC and BIC values the goodness of fit has improved.
Incidence-rate ratios. Standard errors are in brackets and clustered at race level. 1983 is the reference year.
| Year | (1) | (2) | (3) | (4) | ||||
|---|---|---|---|---|---|---|---|---|
| 1984 | 1.414*** | (0.132) | 1.432*** | (0.132) | 1.443*** | (0.134) | 1.403*** | (0.154) |
| 1985 | 1.379 | (0.127) | 1.398 | (0.126) | 1.407 | (0.129) | 1.362 | (0.142) |
| 1986 | 1.185 | (0.148) | 1.220 | (0.150) | 1.209 | (0.151) | 1.209 | (0.159) |
| 1987 | 1.148 | (0.119) | 1.176 | (0.121) | 1.179 | (0.123) | 1.158 | (0.137) |
| 1988 | 0.790*** | (0.079) | 0.794*** | (0.078) | 0.805*** | (0.081) | 0.780*** | (0.091) |
| 1989 | 0.830 | (0.109) | 0.841 | (0.111) | 0.843 | (0.110) | 0.825 | (0.117) |
| 1990 | 0.724 | (0.086) | 0.734 | (0.086) | 0.732 | (0.087) | 0.727 | (0.092) |
| 1991 | 0.700 | (0.086) | 0.719 | (0.087) | 0.711 | (0.087) | 0.710 | (0.093) |
| 1992 | 0.547* | (0.070) | 0.553* | (0.071) | 0.556* | (0.072) | 0.548* | (0.077) |
| 1993 | 0.668 | (0.105) | 0.686 | (0.106) | 0.682 | (0.107) | 0.688 | (0.109) |
| 1994 | 0.513* | (0.068) | 0.509* | (0.068) | 0.500* | (0.067) | 0.493** | (0.067) |
| 1995 | 0.482 | (0.063) | 0.465 | (0.061) | 0.460 | (0.061) | 0.452 | (0.064) |
| 1996 | 0.317** | (0.061) | 0.316** | (0.061) | 0.310** | (0.060) | 0.311** | (0.061) |
| 1997 | 0.407 | (0.085) | 0.412 | (0.085) | 0.405 | (0.084) | 0.405 | (0.084) |
| 1998 | 0.283* | (0.048) | 0.284** | (0.048) | 0.276** | (0.047) | 0.278** | (0.047) |
| 1999 | 0.306 | (0.053) | 0.310 | (0.054) | 0.303 | (0.053) | 0.304 | (0.053) |
| 2000 | 0.306 | (0.065) | 0.313 | (0.066) | 0.306 | (0.064) | 0.306 | (0.064) |
| 2001 | 0.321 | (0.051) | 0.325 | (0.051) | 0.317 | (0.050) | 0.319 | (0.051) |
| 2002 | 0.278 | (0.051) | 0.282 | (0.052) | 0.276 | (0.051) | 0.278 | (0.052) |
| 2003 | 0.320 | (0.075) | 0.320 | (0.075) | 0.321 | (0.075) | 0.307 | (0.074) |
| 2004 | 0.288 | (0.055) | 0.282 | (0.054) | 0.288 | (0.055) | 0.276 | (0.057) |
| 2005 | 0.239 | (0.048) | 0.236 | (0.047) | 0.236 | (0.047) | 0.236 | (0.048) |
| 2006 | 0.293 | (0.048) | 0.292 | (0.048) | 0.288 | (0.047) | 0.288 | (0.048) |
| 2007 | 0.219** | (0.040) | 0.223** | (0.040) | 0.221** | (0.040) | 0.223** | (0.041) |
| 2008 | 0.196 | (0.042) | 0.203 | (0.043) | 0.200 | (0.043) | 0.200 | (0.043) |
| 2009 | 0.237 | (0.053) | 0.248 | (0.048) | 0.246 | (0.055) | 0.246 | (0.055) |
| 2010 | 0.332* | (0.069) | 0.352* | (0.076) | 0.349* | (0.076) | 0.334 | (0.074) |
| Controls: | ||||||||
| Stops × speed diff. | x | |||||||
| Zero stops | x | |||||||
| Timing of fuel stops | x | |||||||
| Timing of first stop | x | |||||||
| Observations | 17,756 | 17,756 | 17,756 | 17,756 | ||||
| Log likelihood | −21,155 | −21,155 | −21,142 | −21,110 | ||||
| AIC | 42,519 | 42,519 | 42,495 | 42,475 | ||||
| BIC | 43,336 | 43,337 | 43,320 | 43,463 | ||||
| α | 0.601 | (0.027) | 0.601 | (0.027) | 0.598 | (0.027) | 0.588 | (0.027) |
-
Asterisks depict year-to-year significance levels. *10 % significance level, **5 % significance level, ***1 % significance level.
Sensitivity analysis: control variables. Incidence-rate ratios. Standard errors are in brackets and clustered at race level. <1 % speed difference on the probability of being overtaken is the reference category.
| (1) | (2) | (3) | (4) | |||||
|---|---|---|---|---|---|---|---|---|
| Number of cars (log) | 1.042 | (0.334) | 1.047 | (0.335) | 1.053 | (0.336) | 1.062 | (0.338) |
| Overall reliability (log) | 1.605*** | (0.338) | 1.600*** | (0.337) | 1.585** | (0.334) | 1.569*** | (0.327) |
| Individual reliability (log) | 2.103*** | (0.058) | 2.101*** | (0.058) | 2.105*** | (0.058) | 2.098*** | (0.058) |
| Not in pack | 0.445*** | (0.046) | 0.443*** | (0.046) | 0.449*** | (0.047) | 0.437*** | (0.045) |
| Safety car | 1.461*** | (0.157) | 1.472*** | (0.156) | 1.460*** | (0.159) | 1.477*** | (0.152) |
| Being overtaken | ||||||||
| Better position than expected | 0.104*** | (0.018) | 0.104*** | (0.019) | 0.101*** | (0.018) | 0.104*** | (0.019) |
| Worse position than expected | 0.358*** | (0.064) | 0.359*** | (0.065) | 0.354*** | (0.064) | 0.368*** | (0.066) |
| Overtaking | ||||||||
| Better position than expected | 2.673*** | (0.649) | 2.663*** | (0.648) | 2.828*** | (0.690) | 2.830*** | (0.688) |
| Worse position than expected | 32.006*** | (3.514) | 32.179*** | (3.537) | 32.806*** | (3.616) | 31.788*** | (3.509) |
| Number of pit-stops | ||||||||
| No refueling | 1.106 | (0.162) | 1.031 | (0.121) | 0.954 | (0.091) | 1.101 | (0.130) |
| Refueling | 1.014 | (0.078) | 0.973 | (0.058) | 0.930 | (0.042) | 0.903 | (0.072) |
| No. of stops × av. speed difference | 0.965* | (0.019) | ||||||
| Zero stops | 1.157* | (0.094) | ||||||
| Unknown strategy | 1.338*** | (0.096) | 1.477*** | (0.155) | 1.343*** | (0.099) | ||
| Timing of fuel stop compared to median | ||||||||
| Being overtaken | 1.125** | (0.059) | ||||||
| Overtaking | 0.785*** | (0.043) | ||||||
| Being overtaken | ||||||||
| No refueling: | ||||||||
| % of drivers pitting more often | 1.480*** | (0.194) | 1.391** | (0.177) | 1.485*** | (0.200) | 1.477*** | (0.204) |
| % of drivers pitting less often | 1.216 | (0.186) | 1.230 | (0.188) | 1.236 | (0.189) | 1.145 | (0.182) |
| Refueling: | ||||||||
| % of drivers pitting more often | 1.890*** | (0.199) | 1.955*** | (0.216) | 1.660*** | (0.198) | 1.752*** | (0.244) |
| % of drivers pitting less often | 0.671*** | (0.102) | 0.650*** | (0.099) | 0.735* | (0.117) | 0.686** | (0.106) |
| Overtaking | ||||||||
| No refueling: | ||||||||
| % of drivers pitting more often | 1.114 | (0.167) | 1.044 | (0.146) | 1.126 | (0.175) | 0.984 | (0.152) |
| % of drivers pitting less often | 1.807*** | (0.285) | 1.824*** | (0.287) | 1.844*** | (0.293) | 1.624*** | (0.266) |
| Refueling: | ||||||||
| % of drivers pitting more often | 0.786** | (0.101) | 0.811 | (0.108) | 0.978 | (0.134) | 0.829 | (0.139) |
| % of drivers pitting less often | 2.567*** | (0.355) | 2.479*** | (0.350) | 2.020*** | (0.296) | 2.384*** | (0.363) |
| Being overtaken | ||||||||
| Number of unscheduled stops | 1.038*** | (0.011) | 1.037*** | (0.011) | 1.038*** | (0.011) | 1.041*** | (0.012) |
| Overtaking | ||||||||
| Unscheduled stop × rank | 3.318*** | (0.369) | 3.305*** | (0.366) | 3.123*** | (0.349) | 3.036*** | (0.353) |
| Long repair stop | 0.781*** | (0.042) | 0.780*** | (0.041) | 0.780*** | (0.042) | 0.805*** | (0.046) |
| Being overtaken | ||||||||
| 1–2 % | 1.656*** | (0.115) | 1.653*** | (0.114) | 1.651*** | (0.115) | 1.654*** | (0.114) |
| 2–3 % | 2.073*** | (0.152) | 2.062*** | (0.150) | 2.054*** | (0.149) | 2.073*** | (0.150) |
| 3–4 % | 2.441*** | (0.184) | 2.427*** | (0.182) | 2.425*** | (0.182) | 2.431*** | (0.181) |
| 4–5 % | 2.670*** | (0.216) | 2.652*** | (0.213) | 2.650*** | (0.213) | 2.666*** | (0.214) |
| 5 % or more | 3.021*** | (0.247) | 3.015*** | (0.245) | 3.020*** | (0.246) | 3.054*** | (0.249) |
| Average speed difference in % | 0.835*** | (0.028) | 0.818*** | (0.028) | 0.817*** | (0.028) | 0.811*** | (0.028) |
| Overtaking | ||||||||
| Speed deficit <1 % | 0.865* | (0.067) | 0.870* | (0.068) | 0.868* | (0.068) | 0.852* | (0.082) |
| 1–2 % | 1.274*** | (0.106) | 1.276*** | (0.107) | 1.277*** | (0.107) | 1.239*** | (0.119) |
| 2–3 % | 1.578*** | (0.138) | 1.574*** | (0.138) | 1.580*** | (0.139) | 1.527*** | (0.154) |
| 3–4 % | 1.621*** | (0.145) | 1.619*** | (0.146) | 1.616*** | (0.145) | 1.576*** | (0.159) |
| 4–5 % | 1.699*** | (0.165) | 1.693*** | (0.165) | 1.702*** | (0.166) | 1.646*** | (0.178) |
| 5 % or more | 1.440*** | (0.144) | 1.447*** | (0.146) | 1.451*** | (0.146) | 1.396*** | (0.155) |
| Average speed difference in % | 0.907** | (0.029) | 0.887*** | (0.028) | 0.885*** | (0.028) | 0.893*** | (0.028) |
-
Asterisks depict significance levels. *10 % significance level, **5 % significance level, ***1 % significance level.
The controls in Table 6 behave as predicted. Specification (1) shows that higher average speed-differentials increase the negative effect of pit-stops on overtaking. In case of low speed differentials, tire stops may actually slightly increase overtaking, whereas the effect of fuel stops is virtually nonexistent. However, the coefficients are not statistically significant.
Specification (2) shows that zero-stop strategies are associated with an increase in overtaking by around 16 %, indicating that overtaking becomes (slightly) more common when there is no way of overtaking in the pits. Interestingly, overtaking does not seem to depend on the number of pit-stops.
The timing of the first fuel-stop in Specification (3) affects overtaking as well. Pitting late is associated with an increase in the probability of being overtaken, and a decrease in the probability of overtaking. This makes perfect sense, as the relatively heavy fuel-load slows the car down. Interestingly, the analysis suggests the effects are not symmetric, as the negative effect on the probability of overtaking is larger (up to 20 % less overtaking) than the positive effect (up to 12.5 % more overtaking). This implies a net reduction in driver aggressiveness due to different strategies.
Controlling for the timing of the first stop in Specification (4) increases the tire-stop coefficient, but leaves the fuel-stop coefficient unaffected (see Table 2). As expected, later pit-stops are generally associated with higher probabilities of being overtaken, and lower probabilities of overtaking. However, at an aggregate level its impact on overtaking is very limited.
The sensitivity analysis shows that the year effects are fairly robust, which suggests there are no large systematic biases in the model. The most significant changes in overtaking took place between 1983 and 1984 and between 1987 and 1988.
5 Discussion of the results
The decline in overtaking was likely triggered by the cars, and not through other inter-season differences, such as tracks, reliability, pit strategy and speed differences. Had the cars remained the same, overtaking actually should have increased over time, as shown in Figure 4. The counterfactual analysis shows that with the 1984 cars, overtaking would have hovered around 50 overtakes per race in the 1980s and 1990s, and climb to about 80 overtakes per race in 2010. In contrast, with the 2008 cars, there would be about 10 overtakes per race in every season on average, as, under the same conditions, overtaking was over seven times more abundant in 1984 than in 2008. Most of the negative effect of the cars on overtaking took place in the 1980s and 1990s, with a few large, statistically significant year-to-year changes. Many of these year-to-year changes in overtaking correspond with major regulation changes.

Actual number of overtakes per dry race and the predicted number of overtakes in case of 1984 and 2008 cars.
Figure 5 shows the year coefficients from Specification (6) of the baseline analysis with respect to 2008. The graph shows that overtaking was more abundant during most of the turbo era and when there was no refueling, which suggests that the switch from turbo to normally-aspirated engines and the re-introduction of in-race refueling may have been the main contributors to the decline in overtaking. While this may seem correct, it is important to have an intuition as to why this is the case.

Overtaking compared to 2008. The black line shows the estimated year fixed effects and the shaded area depicts the 95 % confidence interval. The turbo era (until 1988) and refueling eras (1983 and 1994–2009) are highlighted as well.
There are two likely reasons as to why overtaking was so abundant during the turbo era. First of all, the cars were difficult to drive due to the infamous turbo lag, which likely induced (small) driver errors and could lead to drivers being more easily overtaken. The second potential explanation is the huge difference in power output between the qualifying and race engine. Differences in how much the engines had to be turned down on race day would then have created overtaking potential.
Furthermore, there is evidence that tight fuel-limits may have negatively affected overtaking, as the reduction of the fuel limit in 1988 coincided with a very statistically significant 30 % drop in overtaking. An obvious downside of tight fuel-limits and the need for fuel management is that it does not allow drivers to attack all race long. This reduction in driver aggressiveness may therefore have negatively affected overtaking.
The 1983 season suggests that in-race refueling fundamentally reduces overtaking as well. As this effect is not captured by the strategy controls, the reduction has to be through driver laziness. This pattern is also visible when refueling was introduced in 1994 and when it was banned in 2010. In-race refueling seems to reduce overtaking by around 30 %.[17] This also needs some explanation, however, as the analysis then implies that during the refueling era drivers may have been overly cautious, which may have negatively affected their performance.
First of all, it may have been perfectly rational for drivers to wait for the fuel stops to easily pass another car avoid a possible collision. This, however, does not explain why this behavior would be completely unique to refueling strategies and why this effect would not be picked up by the number of pit-stops in the analysis.
In-race refueling allows drivers to start on different fuel-loads, which affects their relative performances at the beginning of the race and may induce driver laziness when drivers overestimate their strategies and therefore rely too much on pit strategy to make up places.[18] Driver laziness may, however, not be counterproductive, as drivers may save fuel instead in order to increase the likelihood of making up places during the pit-stops. As such, this may have a negative impact on on-track overtaking.
Another explanation is the invisible sorting of strategies. The model uses relative qualifying pace as a crude proxy for relative race pace. In reality, drivers can be more competitive in the race than in qualifying. Fuel strategies can then be used to smoothen out these speed differentials and substitute potential on-track overtakes with pit-lane overtakes. As such, the different fuel strategies may reduce, not increase the speed differentials between the cars at the beginning of the race.
These considerations might explain why overtaking was relatively scarce during the refueling era. Both the transition to normally-aspirated engines and the introduction of in-race refueling explain a significant portion of the drop in overtaking between the mid-1980s and the mid-1990s. The role of aerodynamics on overtaking is not easy to determine, as this development was likely gradual. Aerodynamics became more important during the normally-aspirated engine era, when engine development became more incremental. This may have had an impact on overtaking in the early-1990s, but this decline was relatively small (around 20 % from 1989 to 1993, according to Specification (6) of Table 3) and may have been caused by the large-scale adoption of the semi-automatic gearbox during this period as well. Either development may have caused this decline, but it seems that neither aerodynamics, nor the semi-automatic gearbox had a very large impact on overtaking during this period.
The reduction of ground-effect downforce in 1994 and 1995 may have had a negative effect on overtaking. The 26 % reduction in overtaking from 1993 to 1994 can, however, be explained by the introduction of in-race refueling in 1994. Only the 8 % drop in overtaking in 1995 may be attributed to the reduction in ground-effect downforce, but as a much larger decrease (over 30 %) occurred from 1995 to 1996, when the rules largely remained constant, this further suggests that the reduction of ground-effect downforce was not the main factor in the decrease in overtaking in the mid-1990s. This finding is somewhat supported by Newbon et al. (2017), who claim that ground-effect downforce is actually detrimental to overtaking.
The introduction of narrower cars and grooved tires in 1998 seems to have reduced overtaking even further. Interestingly, with the exception of 2005, overtaking remained fairly constant between 1998 and 2006, despite rapid development in all areas, including aerodynamics and tires. This suggests the increase in downforce was not detrimental to overtaking. The decrease in 2005 may be attributed to the ban on tire changes, either because it facilitated pit-lane overtaking, or because it made drivers less aggressive as they had to protect their tires.
Overtaking dropped again in 2007. While it is tempting to attribute this decrease to the end of the Bridgestone-Michelin tire war, there is very little evidence that tire wars generally increased overtaking throughout the study period. The only exceptions are the outlier seasons 1992 and 1997. A possible explanation for the decline in overtaking in 2007 therefore is the requirement to use both tire compounds during the race (the ‘two-compound rule’). Prior to 2007, drivers could only use one tire compound for both qualifying and race, so they had to compromise between qualifying and race performance. From 2007 onward, drivers could use the optimal tire in qualifying and during most of the race, which may have contributed to a reduction in overtaking.
In this discussion, the role of tracks on overtaking cannot be neglected. On a year-to-year basis, their impact is limited as largely the same tracks are used. The Formula 1 calendar always consists of a few tracks unsuitable for overtaking, as well as a couple of tracks were overtaking is relatively straightforward. Generally, tracks with long straights and long braking zones perform better than narrow, twisty tracks.
In the analysis, Monaco is treated as the reference track. Interestingly, two tracks perform worse. One of them is the Valencia Street Circuit, a track that only made three appearances in the dataset. The other one is the post-1994 Imola (Autodromo Enzo e Dino Ferrari) circuit, a circuit infamous for its lack of overtaking possibilities.[19] Other poorly-performing tracks are Jérez, Circuit de Catalunya, the Hungaroring and Magny-Cours, four twisty tracks without really long straights. Interestingly, the equally twisty Autódromo Oscar Alfredo Gálvez (Buenos Aires, Argentine) is one of the better-performing tracks, even though this rating is based on only four races.
Perhaps unsurprisingly, the relatively new tracks designed by Hermann Tilke are the best-performing tracks, such as Istanbul Park and the Bahrain International Circuit. These tracks consist of long straights and long braking zones to promote overtaking. On top of the list is the Fuji Speedway, but this rating is solely based on the 2008 event (the 2007 event was a wet race). The relatively short track does possess a very long straight (of almost 1.5 km), which suggests the result may hold water.
Interestingly, not all Tilke-designed tracks perform well. For example, the Yas Marina Circuit (Abu Dhabi) is one of the worst-performing tracks, although this rating is based on only two races. The Shanghai International Circuit is also one of the weaker tracks, only barely outperforming the Marina Bay Street Circuit (Singapore). This suggests that the concept of long straights and long braking zones does not always promote overtaking. However, as the track coefficients in the analysis are a bit of a ‘black box’, it is hard to establish the exact reason as to why some tracks are good for overtaking and why other, similar tracks are not.
6 Conclusions
This paper has tried to find the factors that led to the decline in overtaking during the 1980s and 1990s by controlling for all sorts of quantifiable factors, such as the number of cars, position, pit strategies and speed differentials to accurately estimate the non-quantifiable overtake-friendliness of the tracks and the cars, by analyzing overtaking at the driver level.
Overtaking was highest during the turbo era at the beginning of the study period. Interestingly, a large (30 %) drop in overtaking during this era coincides perfectly with the fuel-limit reduction in 1988, strongly suggesting that fuel-saving reduces overtaking. Perhaps even more interesting is that overtaking did not go up again when normally-aspirated engines were mandated in 1989 and the fuel limit was lifted. This suggests that overtaking was especially abundant throughout most of the 1980s due to the use of turbo engines.
The analysis also strongly suggests that in-race refueling is associated with a reduction in overtaking. This can clearly be seen when comparing the transition seasons (1983–1984, 1993–1994 and 2009–2010). The refueling seasons in each case had about 30 % less overtaking than the adjacent non-refueling seasons, which was likely due to reduced driver aggression (‘driver laziness’).
Overtaking dropped in the 1990s, but it is hard to find the actual cause. The increased dependence on aerodynamic downforce, the impact of technological developments, and the reduction of ground-effect possibly all may have had a small but negative effect on overtaking. The introduction of narrower cars and grooved tires in 1998 likely reduced overtaking even more, but interestingly, overtaking remained roughly constant throughout most of the 2000s.
Furthermore, the effect of tire wars on overtaking seems limited. The one-off ban on tire changes in 2005 had a negative impact on overtaking by about 20 %, similar to the drop in 2007, which was likely caused by the requirement to use both tire compounds during the race.
The impact of tracks on overtaking at a season level is also seems limited, as the year-to-year changes to the calendar are usually quite small. The increased share of Tilke-designed tracks may have increased overtaking, although some of them are among the worst-performing tracks in terms of overtaking.
7 Policy recommendations and further research
We have tried to reveal the main causes of the decline in overtaking during the 1980s and 1990s. While Formula 1 has changed a lot since then, some findings may still be relevant today. Just as in the overtaking heydays in the 1980s, Formula 1 cars are nowadays powered by turbo engines. The analysis suggests that a tight fuel-limit is detrimental to racing. Indeed the fuel capacity was increased from 100 kg in 2014 to 105 kg in 2017 and 110 kg in 2019, which allowed drivers to push harder and may therefore have improved racing. It is unclear if a further fuel-capacity increase will increase racing. Similarly, increasing the number of power units a driver can use per season may increase overtaking as well, as the engines can be pushed harder for longer on race day. However, there may be a trade-off. If the engines can be pushed harder on race day, this reduces the difference in engine power between qualifying and race, one of the factors that may have made overtaking so abundant during the 1980s turbo era. This also suggests that revoking the 2020 ‘party mode’ ban could increase overtaking.
The analysis further suggests that aerodynamic developments had a strong negative effect on overtaking during the 1990s, but that the negative effect leveled off around the turn of the century, despite the cars getting more aerodynamically advanced every year. This suggests that more aerodynamic downforce may not necessarily be detrimental to overtaking. Anecdotal evidence for this statement from more recent times is the 2018 British Grand Prix, where the leaders were able to follow each other closely through the ultra-fast Maggotts-Becketts section because of, not in spite of, their cars’ extremely high downforce levels. Furthermore, the analysis suggests that reverting to manual transmissions and more ground-effect downforce may improve overtaking to some extent, but not by very much. Overtaking reportedly increased by 30 % with the return of the ground effect in 2022 (Smith 2022), but in recent years overtaking seems to have become harder again. There is also little evidence that a tire war will increase overtaking in the long run, although it is unclear if this finding still holds true in the current high-degradation tire era. The same goes for the ‘two-compound rule’, which may have been detrimental to racing when it was introduced back in 2007.
There are still a few loose ends in the analysis that may require further research. For example, the impact of turbo engines compared to normally-aspirated engines, semi-automatic gearboxes compared to manual transmissions, and different tire suppliers on overtaking has only been determined indirectly. It may be useful to analyze their impact on the driver level. Will the estimated effects explain year-to-year differences in overtaking? Furthermore, the analysis may be improved by feeding it with data from the current DRS era. This may improve the estimation of the track fixed effects, especially for the more recent additions to the Formula 1 calendar. Furthermore, including races from the high-degradation tire era may increase our understanding of the impact of pit-stops on overtaking.
Acknowledgments
We thank Clip the Apex and Ergast Developer API for the providing me with the data to conduct this research. I would also like to thank Claudia Sulsters for her helpful comments and suggestions.
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Research ethics: Not applicable.
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Informed consent: Not applicable.
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Author contributions: The author has accepted responsibility for the entire content of this manuscript and approved its submission.
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Use of Large Language Models, AI and Machine Learning Tools: None declared.
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Conflict of interest: The author states no conflict of interest.
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Research funding: None declared.
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Data availability: The data that support the findings of this study are available at the Clip the Apex website. Restrictions apply to the availability of these data, which were used under license for this study. Data are available at https://cliptheapex.com/ with the permission of Clip the Apex.
Baseline results: track effects. Incidence-rate ratios. Standard errors are in brackets. Monaco is the reference track.
| Track | (2) | (3) | (4) | (5) | (6) | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| A1-Ring | 3.492*** | (0.643) | 3.386*** | (0.633) | 2.756*** | (0.442) | 2.856*** | (0.432) | 2.917*** | (0.447) |
| Adelaide | 1.976*** | (0.352) | 1.978*** | (0.321) | 2.021*** | (0.317) | 2.126*** | (0.316) | 2.088*** | (0.325) |
| Aida | 1.589*** | (0.247) | 1.447** | (0.213) | 1.452*** | (0.185) | 1.689*** | (0.210) | 1.739*** | (0.211) |
| Albert Park | 2.600*** | (0.614) | 2.757*** | (0.637) | 2.071*** | (0.371) | 2.131*** | (0.356) | 2.250*** | (0.379) |
| Brands Hatch | 2.073*** | (0.485) | 1.934*** | (0.408) | 1.880*** | (0.332) | 1.873*** | (0.299) | 1.940*** | (0.331) |
| Buenos Aires | 3.604*** | (0.651) | 3.681*** | (0.705) | 2.807*** | (0.462) | 2.843*** | (0.477) | 2.858*** | (0.464) |
| Catalunya | 1.385* | (0.279) | 1.354* | (0.263) | 1.360* | (0.240) | 1.475** | (0.250) | 1.526** | (0.259) |
| Circuit Gilles Villeneuve | 2.193*** | (0.364) | 2.152*** | (0.354) | 1.987*** | (0.320) | 1.861*** | (0.261) | 1.867*** | (0.273) |
| Dallas | 1.917*** | (0.279) | 1.820*** | (0.239) | 1.638*** | (0.205) | 1.605*** | (0.196) | 1.529*** | (0.202) |
| Detroit | 2.111*** | (0.295) | 2.175*** | (0.271) | 2.234*** | (0.268) | 2.034*** | (0.234) | 1.895*** | (0.226) |
| Dijon | 2.244*** | (0.326) | 2.091*** | (0.286) | 2.123*** | (0.272) | 2.428*** | (0.313) | 3.096*** | (0.425) |
| Estoril | 2.017*** | (0.323) | 1.789*** | (0.288) | 1.699*** | (0.255) | 1.759*** | (0.256) | 1.775*** | (0.264) |
| Fuji Speedway | 5.208*** | (1.004) | 5.501*** | (1.054) | 5.806*** | (1.000) | 5.220*** | (0.870) | 5.499*** | (0.953) |
| Hermanos Rodríguez | 3.175*** | (0.515) | 3.073*** | (0.474) | 2.759*** | (0.391) | 2.893*** | (0.393) | 2.933*** | (0.412) |
| Hockenheimring (old) | 2.028*** | (0.298) | 2.014*** | (0.274) | 2.031*** | (0.265) | 2.105*** | (0.248) | 2.131*** | (0.249) |
| Hockenheimring (new) | 2.863*** | (0.558) | 2.737*** | (0.518) | 2.967*** | (0.468) | 3.043*** | (0.524) | 3.084*** | (0.511) |
| Hungaroring | 1.529*** | (0.251) | 1.471** | (0.243) | 1.490*** | (0.230) | 1.591*** | (0.225) | 1.613*** | (0.236) |
| Imola (old) | 2.467*** | (0.335) | 2.325*** | (0.299) | 2.136*** | (0.247) | 2.298*** | (0.247) | 2.382*** | (0.273) |
| Imola (new) | 0.780 | (0.162) | 0.780 | (0.167) | 0.834 | (0.169) | 0.899 | (0.189) | 0.933 | (0.205) |
| Indianapolis | 2.396*** | (0.460) | 2.321*** | (0.420) | 2.384*** | (0.359) | 2.478*** | (0.364) | 2.490*** | (0.378) |
| Interlagos | 2.814*** | (0.470) | 2.880*** | (0.465) | 2.872*** | (0.451) | 2.943*** | (0.435) | 3.007*** | (0.479) |
| Istanbul Park | 3.284*** | (0.662) | 3.117*** | (0.652) | 2.905*** | (0.501) | 3.167*** | (0.519) | 3.337*** | (0.574) |
| Jacarepaguá | 2.659*** | (0.394) | 2.612*** | (0.360) | 2.352*** | (0.321) | 2.576*** | (0.383) | 2.836*** | (0.413) |
| Jerez | 1.474** | (0.230) | 1.381** | (0.208) | 1.357** | (0.192) | 1.400*** | (0.185) | 1.393** | (0.192) |
| Kyalami | 1.853** | (0.475) | 1.919*** | (0.378) | 1.821*** | (0.298) | 1.960*** | (0.312) | 2.133*** | (0.353) |
| Long Beach | 4.079*** | (0.622) | 3.911*** | (0.580) | 3.453*** | (0.467) | 3.470*** | (0.466) | 3.197*** | (0.438) |
| Magny-Cours | 1.568*** | (0.259) | 1.481** | (0.245) | 1.626*** | (0.246) | 1.710*** | (0.257) | 1.654*** | (0.252) |
| Monza | 2.040*** | (0.290) | 2.002*** | (0.279) | 1.946*** | (0.247) | 2.025*** | (0.240) | 2.068*** | (0.245) |
| Nürburgring | 2.009*** | (0.386) | 1.854*** | (0.334) | 1.756*** | (0.293) | 1.859*** | (0.300) | 1.862*** | (0.297) |
| Österreichring | 1.938** | (0.563) | 1.820** | (0.475) | 1.562*** | (0.308) | 1.587*** | (0.283) | 1.742*** | (0.362) |
| Paul Ricard (old) | 2.047*** | (0.314) | 1.928*** | (0.265) | 1.859*** | (0.245) | 1.953*** | (0.229) | 2.074*** | (0.241) |
| Paul Ricard (new) | 2.102*** | (0.269) | 1.940*** | (0.250) | 1.751*** | (0.221) | 1.818*** | (0.213) | 1.810*** | (0.229) |
| Phoenix | 2.028*** | (0.448) | 2.000*** | (0.412) | 1.984*** | (0.431) | 1.965*** | (0.459) | 2.029*** | (0.499) |
| Sakhir | 2.995*** | (0.637) | 2.893*** | (0.569) | 3.208*** | (0.589) | 3.408*** | (0.611) | 3.701*** | (0.689) |
| Sepang | 2.550*** | (0.473) | 2.570*** | (0.444) | 2.625*** | (0.423) | 2.635*** | (0.373) | 2.798*** | (0.412) |
| Shanghai | 2.324*** | (0.421) | 2.184*** | (0.392) | 1.898*** | (0.255) | 1.862*** | (0.226) | 1.898** | (0.294) |
| Silverstone | 2.293*** | (0.337) | 2.133*** | (0.303) | 1.919*** | (0.244) | 1.990*** | (0.235) | 2.133*** | (0.268) |
| Singapore | 1.966** | (0.556) | 1.974** | (0.537) | 1.608** | (0.427) | 1.573** | (0.402) | 1.603** | (0.401) |
| Spa-Francorchamps | 2.286*** | (0.355) | 2.154*** | (0.326) | 1.924*** | (0.267) | 2.102*** | (0.275) | 2.106*** | (0.300) |
| Suzuka | 2.039*** | (0.372) | 1.886*** | (0.320) | 1.786*** | (0.268) | 1.919*** | (0.267) | 1.972*** | (0.281) |
| Valencia | 0.845 | (0.356) | 0.779 | (0.329) | 0.801 | (0.292) | 0.849 | (0.319) | 0.883 | (0.330) |
| Yas Marina | 1.321 | (0.231) | 1.205 | (0.207) | 1.291 | (0.250) | 1.458** | (0.273) | 1.409 | (0.288) |
| Zandvoort | 2.517*** | (0.490) | 2.522*** | (0.488) | 2.075*** | (0.322) | 2.150*** | (0.314) | 2.121*** | (0.317) |
| Zolder | 2.109*** | (0.307) | 2.196*** | (0.293) | 1.939*** | (0.246) | 2.038*** | (0.258) | 1.993*** | (0.254) |
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Asterisks depict significance levels. *10 % significance level, **5 % significance level, ***1 % significance level.
Sensitivity analysis: pit-stop timing controls. Incidence-rate ratios of the pit-stop timing controls of specification (4) of the sensitivity analysis. Standard errors are in brackets. Unknown strategy is the reference category.
| (4) | ||||
|---|---|---|---|---|
| Being overtaken | ||||
| No refueling: | Refueling: | |||
| First stop within 20 % of total race distance | 0.534*** | (0.076) | 0.707* | (0.139) |
| First stop 20–30 % of total race distance | 0.495*** | (0.071) | 0.824 | (0.138) |
| First stop 30–40 % of total race distance | 0.601*** | (0.084) | 0.730** | (0.117) |
| First stop 40–50 % of total race distance | 0.630*** | (0.081) | 0.840 | (0.122) |
| First stop 50–90 % of total race distance | 0.830 | (0.099) | 0.817 | (0.115) |
| First stop after 90 % of total race distance | 0.798*** | (0.064) | 0.752 | (0.151) |
| Overtaking | ||||
| No refueling: | Refueling: | |||
| First stop within 20 % of total race distance | 1.000 | (0.128) | 1.010 | (0.203) |
| First stop 20–30 % of total race distance | 0.665** | (0.127) | 0.919 | (0.162) |
| First stop 30–40 % of total race distance | 0.622*** | (0.096) | 0.761* | (0.125) |
| First stop 40–50 % of total race distance | 0.579*** | (0.074) | 0.732** | (0.116) |
| First stop 50–90 % of total race distance | 0.613*** | (0.077) | 0.709** | (0.100) |
| First stop after 90 % of total race distance | 0.806** | (0.068) | 0.653** | (0.125) |
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Asterisks depict significance levels. *10 % significance level, **5 % significance level, ***1 % significance level.
Sensitivity analysis: track effects. Incidence-rate ratios. Standard errors are in brackets. Monaco is the reference track.
| Track | (1) | (2) | (3) | (4) | ||||
|---|---|---|---|---|---|---|---|---|
| A1-Ring | 2.907*** | (0.445) | 2.957*** | (0.451) | 2.920*** | (0.444) | 2.913*** | (0.437) |
| Adelaide | 2.072*** | (0.323) | 2,075*** | (0.320) | 2.089*** | (0.326) | 2.084*** | (0.318) |
| Aida | 1.780*** | (0.216) | 1.700*** | (0.208) | 1.741*** | (0.212) | 1.741*** | (0.216) |
| Albert Park | 2.258*** | (0.382) | 2.248*** | (0.376) | 2.251*** | (0.379) | 2.242*** | (0.372) |
| Brands Hatch | 1.919*** | (0.321) | 1.943*** | (0.330) | 1.946*** | (0.333) | 1.948*** | (0.321) |
| Buenos Aires | 2.852*** | (0.471) | 2.850*** | (0.466) | 2.871*** | (0.471) | 2.860*** | (0.471) |
| Catalunya | 1.533** | (0.263) | 1.510** | (0.255) | 1.534** | (0.260) | 1.534** | (0.253) |
| Circuit Gilles Villeneuve | 1.850*** | (0.266) | 1.859*** | (0.267) | 1.875*** | (0.275) | 1.839*** | (0.255) |
| Dallas | 1.560*** | (0.206) | 1.533*** | (0.201) | 1.532*** | (0.203) | 1.526*** | (0.199) |
| Detroit | 1.898*** | (0.225) | 1.905*** | (0.226) | 1.901*** | (0.227) | 1.900*** | (0.223) |
| Dijon | 3.082*** | (0.422) | 3.169*** | (0.426) | 3.096*** | (0.425) | 3.154*** | (0.429) |
| Estoril | 1.769*** | (0.263) | 1.781*** | (0.266) | 1.780*** | (0.265) | 1.796*** | (0.263) |
| Fuji Speedway | 5.474*** | (0.950) | 5.571*** | (0.948) | 5.533*** | (0.960) | 5.465*** | (0.924) |
| Hermanos Rodríguez | 2.929*** | (0.416) | 2.898*** | (0.405) | 2.938*** | (0.413) | 2.865*** | (0.393) |
| Hockenheimring (old) | 2.115*** | (0.248) | 2.148*** | (0.250) | 2.129*** | (0.250) | 2.146*** | (0.246) |
| Hockenheimring (new) | 3.082*** | (0.498) | 3.066*** | (0.502) | 3.098*** | (0.512) | 3.066*** | (0.506) |
| Hungaroring | 1.615*** | (0.235) | 1.602*** | (0.234) | 1.620*** | (0.237) | 1.620*** | (0.232) |
| Imola (old) | 2.363*** | (0.271) | 2.382*** | (0.270) | 2.386*** | (0.275) | 2.384*** | (0.270) |
| Imola (new) | 0.929 | (0.205) | 0.927 | (0.204) | 0.936 | (0.204) | 0.939 | (0.207) |
| Indianapolis | 2.464*** | (0.372) | 2.512*** | (0.381) | 2.512*** | (0.380) | 2.495*** | (0.374) |
| Interlagos | 2.978*** | (0.477) | 3.017*** | (0.478) | 3.015*** | (0.481) | 3.021*** | (0.473) |
| Istanbul Park | 3.297*** | (0.570) | 3.339*** | (0.567) | 3.361*** | (0.577) | 3.326*** | (0.547) |
| Jacarepaguá | 2.849*** | (0.414) | 2.828*** | (0.401) | 2.827*** | (0.410) | 2.853*** | (0.402) |
| Jerez | 1.382** | (0.193) | 1.401** | (0.194) | 1.395** | (0.192) | 1.424** | (0.192) |
| Kyalami | 2.118*** | (0.351) | 2.144*** | (0.355) | 2.130*** | (0.354) | 2.121*** | (0.351) |
| Long Beach | 3.134*** | (0.429) | 3.157*** | (0.430) | 3.189*** | (0.437) | 3.181*** | (0.464) |
| Magny-Cours | 1.635*** | (0.250) | 1.639*** | (0.252) | 1.661*** | (0.252) | 1.656*** | (0.252) |
| Monza | 2.060*** | (0.243) | 2.081*** | (0.245) | 2.063*** | (0.244) | 2.061*** | (0.240) |
| Nürburgring | 1.778*** | (0.269) | 1.792*** | (0.270) | 1.798*** | (0.271) | 1.804*** | (0.274) |
| Österreichring | 1.730*** | (0.358) | 1.753*** | (0.366) | 1.745*** | (0.363) | 1.746*** | (0.361) |
| Paul Ricard (old) | 2.045*** | (0.237) | 2.093*** | (0.242) | 2.063*** | (0.240) | 2.090*** | (0.243) |
| Paul Ricard (new) | 1.782*** | (0.227) | 1.838*** | (0.231) | 1.813*** | (0.230) | 1.851*** | (0.229) |
| Phoenix | 2.039*** | (0.500) | 2.025*** | (0.503) | 2.032*** | (0.498) | 1.997*** | (0.496) |
| Sakhir | 3.638*** | (0.680) | 3.701*** | (0.683) | 3.686*** | (0.689) | 3.687*** | (0.665) |
| Sepang | 2.773*** | (0.408) | 2.803*** | (0.408) | 2.808*** | (0.415) | 2.849*** | (0.407) |
| Shanghai | 1.850*** | (0.287) | 1.900*** | (0.299) | 1.908*** | (0.299) | 1.914*** | (0.296) |
| Silverstone | 2.111*** | (0.262) | 2.127** | (0.265) | 2.136*** | (0.268) | 2.134*** | (0.262) |
| Singapore | 1.601* | (0.403) | 1.592* | (0.399) | 1.607* | (0.405) | 1.530** | (0.374) |
| Spa-Francorchamps | 2.085*** | (0.297) | 2.107*** | (0.298) | 2.104*** | (0.300) | 2.115*** | (0.300) |
| Suzuka | 1.963*** | (0.281) | 1.976*** | (0.281) | 1.974*** | (0.282) | 2.002*** | (0.281) |
| Valencia | 0.871 | (0.325) | 0.890 | (0.331) | 0.885 | (0.332) | 0.835 | (0.298) |
| Yas Marina | 1.412* | (0.280) | 1.431* | (0.284) | 1.418* | (0.288) | 1.327 | (0.239) |
| Zandvoort | 2.112*** | (0.314) | 2.150*** | (0.316) | 2.118*** | (0.316) | 2.173*** | (0.320) |
| Zolder | 1.993*** | (0.254) | 2.033*** | (0.256) | 1.991*** | (0.255) | 2.031*** | (0.256) |
-
Asterisks depict significance levels. *10 % significance level, **5 % significance level, ***1 % significance level.
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Articles in the same Issue
- Frontmatter
- Research Articles
- NHL aging curves using functional principal component analysis
- Aerodynamics, technology or pit strategy: why did overtaking in Formula 1 decline during the 1980s and 1990s? A micro-level analysis
- Analyzing and forecasting success in the Men’s Ice Hockey World (Junior) Championships using a dynamic ranking model
- FIVB ranking: misstep in the right direction
- Analyzing key factors influencing IPL cricket scores using explainability and multimodal data