By Ahaan Jindal '27
Introduction
The implementation of a range of regulatory changes by the FIA (Fédération Internationale de
l’Automobile) in 2022 endeavored to usher in a new era of competitive Formula 1 racing with cars stacked much closer to each other and more teams jostling for podiums and pole-positions than ever before. Whether or not that promise has materialized is yet up for debate, thanks in large part to Max Verstappen’s unprecedented and record-breaking 2023 World Championship-winning season.
What is undoubtedly clear, however, is the prevalence and degree of severity of first-lap incidents, which have manifested in 36 out of the 44, or 82 percent, of Grands Prix held in the past two seasons. From Silverstone’s 2022 scary multiple-car crash that sent Zhou Guanyu’s Alfa Romeo spinning into the crowd fencing to Lewis Hamilton’s Mercedes being sent airborne after contact with Fernando Alonso in Belgium, this first-lap drama has considerable implications for the World Championship. The ensuing research aims to use statistical methods and R to quantitatively analyze the conditions that influence first-lap incidents and their severity, looking at races held in the new ‘ground effect’ era of F1 racing (2022 onwards).
Data Collection and Analytical Methods
No substantive data regarding first-lap incidents - or incidents/contact between cars/crashes in
general - is made available by the FIA, Formula 1 Data Analytics websites, or independent researchers on motorsport forums. All data, therefore, needed to be manually scraped; this was done by going through a) the lap-by-lap reporting of each race in the 2022 and 2023 seasons provided by StatsF1; b) the race highlights released by the FIA on YouTube (each of which showed the entirety of the first lap of each race); and c) the official Formula 1 website, Formula 1 for official starting grids, for a total of 117 incident data points.
Note: for this research, an ”incident” is counted as any impact on a single car, so if a collision happened
between 2 cars, it would be counted as an incident for each. Additionally, in some instances, first-lap
incidents were clearly attributable more to driver error than any of the aforementioned factors. Yuki
Tsunoda crashed into a wall and subsequently could not finish the Azerbaijan Sprint Race owing to his AlphaTauri failing on the first lap; similarly, Liam Lawson lost the car on his own during the Qatar Sprint. These data points were therefore omitted.
A few main factors emerged as possible catalysts for first-lap drama - these included:
| Variable |
Description |
| position |
The drivers’ starting position on the grid (P1 to P20) |
| corner | Which corner the incident took place in |
| sprint | Race format - sprint (around 1/3rd the laps of a full race) or full-length |
| rain | Whether it rained on the day of the race |
| street | Whether the track was either a street circuit or a purpose-built circuit |
Table 1: Description of Variables
Another interesting area of exploration that emerged during the compilation of data was the degree of impact (hereinafter abbreviated as DoI) of each incident. Depending on the extent to which the driver’s race was impacted, a score of 0 to 4 was allocated as the DoI for each incident recorded. This was classified as follows:
0: no loss of position/significant impact to car
1: loss in track and race position
2: debris released/5 or 10-second time-penalty awarded by stewards/need for a pitstop to
change car parts/virtual safety car (VSC)
3: Did not finish (DNF) for driver/10+ second penalty/safety car
4: 2 or more DNFs/“major” crash with 3+ cars involved
A final data table with the aforementioned factors, DoI, as well as race details was compiled. This table was then uploaded and read into R Studio as a data.frame called f1data for further analysis. Bearing this in mind, the ensuing exploration starts by reviewing some preliminary results and visualizations obtained from the data in R (Section 3), paving the way for the statistical analysis of the extent to which each factor affects the DoI in section 4. A range of statistical methods were used for the same. In section 4.1, a Multiple Linear Regression Model with Interaction Variable (all variables linked to DoI) was applied; 4.2 used Welch’s Two-sample t-test to understand how binary variables (street, rain, sprint) impact DoI; finally, 4.3 applies the Kruskal-Wallis Test to understand the extent to which the non-binary variables (corner and position) affect DoI. 4.2 and 4.3 were utilized to confirm or deny the results found in 4.1, increasing the reliability of the conclusions found in section 5.
Preliminary Data Analysis
To first understand which predictor variables were the most likely to lead to first-lap incidents, basic data analysis in R was used; these results pave the way to understand the research in Section 4.
Firstly, using ggplot on R, a histogram was used to plot the frequency of incidents by corner. Figure 1 is sufficient to reveal that a lion’s share of first-lap incidents - 74 out of 117, or 63.2 percent - occur within the first 2 corners of the race. Corner 1 on its own constitutes nearly 36 percent of these incidents! Interestingly, incidents taking place after the 10th corner are nearly non-existent, bar one-off instances of contact on corners 14 and 19.
Figure 1: Histogram plot of frequency distribution of corners where incidents took place
Most on-track battles for position (and hence incidents) therefore take place within the
first 2 corners of the first lap; drivers appear to get significantly more cautious as the lap goes
on, presumably valuing race endurance than a potentially costly overtake at the outset.
Secondly, plotting a simple histogram of the frequency of first-lap incidents by grid position
(P1-P20) using ggplot reveals:
Figure 2: Histogram plot of frequency distribution of number of incidents by grid position
P5 appears to be the most prone to first-lap incidents, with drivers at P5 present in 12
first-lap incidents - or 10.3 percent of the total 117. P4 and P8 are also risky, with 10 incidents
apiece; P15 and P16 were involved in 9 incidents each. Overall, however, since these results do
not seem to show a conclusive trend, looking at the number of incidents by row number on the
grid could perhaps prove more fruitful:
| Grid Row | # of Incidents |
| 1 (P1, P2) | 3 |
| 2 (P3, P4) | 16 |
| 3 (P5, P6) | 18 |
| 4 (P7, P8) | 15 |
| 5 (P9, P10) | 13 |
| 6 (P11, P12) | 11 |
| 7 (P13, 14) | 14 |
| 8 (P15, P16) | 18 |
| 9 (P17, P18) | 7 |
| 10 (P19, P20) | 2 |
Table 2: Frequency of Incidents by Grid Row on the First-lap
Table 2 reveals a couple of key trends. First, it is relatively rare for those positioned on the extremes (i.e., rows 1 and 10) to be involved in first-lap incidents. However, rows 3 and 8 suffered 18 incidents apiece. Interestingly, the cars positioned on these rows, P5/6 and P15/16, are squarely in the middle of the front and back halves of the grid respectively. This could indicate that battles between cars seeking to gain track position are the most competitive in the middle of each half of the grid; this effect tapers off at the extreme front and back of the grid.
Other conditions, such as rain, whether the track is a street circuit, and the format of the race (sprint or full-length) also lead to incidents and collisions. It could therefore be useful to find the proportions of incidents that take place when these conditions exist:
Figure 3: Track Conditions Causing Proportions of Incidents, 2022 and 2023 F1 Seasons
Overall, each of the 3 track conditions had extremely variable implications for causing incidents. Even though street circuits had just above 30% of the total incidents recorded (the highest of the 3), nearly a third of races over the past 2 years have been on street tracks. Predictably, rain-hit races had a proportionally higher amount of recorded incidents (17.1%) than rain-hit races themselves (5 out 44, or 11.4%). The quicker sprint format seemed to have negligible impacts on causing more first-lap incidents, with only 8.5% of the incidents caused during sprint races, even though 9 out of the 44 races (20.45%) ran in the 2022-23 seasons featured sprint races.
How Factors Affect Degree of Impact
Armed with the preliminary data obtained in Section 3, this section seeks to analyze what factors magnify the degree to which an incident impacts a driver’s race. To do this, it is essential to test each prediction factor’s statistical impact on the ordinal DoI scale (0-4 points) twice to confirm our results and thus draw meaningful conclusions. Therefore, multiple regression testing was used as the first step in order to analyze each factor’s numerical bearing on a linear model; this was then complemented by different types of hypothesis testing (Welch’s two-sample t-test for binary and Kruskal-Wallis rank sum test for non-binary factors).
Multiple Regression Model
The advantage of running a multiple regression is that it becomes easier to quantify the relationship between an outcome variable (in this case DoI score) and multiple predictor variables (such as rain/corner/grid position) simultaneously. Additionally, the coefficients in multiple regression provide quantitative estimates of the strength and direction of the relationships between each predictor variable and the outcome variable. This allows for the comparison of the relative contributions of different factors in determining how damaging a first-lap incident is. Multiple regression models also can deal with the issue of ‘multi-collinearity’ - when predictor variables are correlated with each other - by implementing what is known as an ‘interaction effect.’ This effect is added as another variable in the regression that provides insights into how the impact of one variable changes in the presence of another. The model being run therefore accounts for the joint effect of two or more variables, captures
non-additivity, and addresses issues of non-constant variance as well. In this case, whether or not it rains would invariably affect the starting position of a car on grid and is therefore the interacting variable. Bearing this in mind, the multiple regression equation would look like this:
DoI = position ∗ β1 + rain ∗ β2 + street ∗ β3 + corner ∗ β4 + sprint ∗ β5 + position x rain ∗ β6 + ε
Using R, the estimated value of each of the ’beta-hats’ - or coefficients - can easily be plotted by running a summary of a linear model. This summary function - apart from the coefficient estimates - also plots the standard error, the t-value, and the Pr(> |t|) value. This aids with further statistical analysis, as the t-value is a measure of how many standard deviations our coefficient estimate is away from 0, while Pr(> |t|) relates to the probability of observing any value equal to or larger than t. It thus follows that if a t-value is high and Pr(> |t|) is low, we can reject the null hypothesis, i.e. that the coefficient is effectively 0 and there is no statistically significant relationship between the predictor and outcome variable. When run in R, the above model yields the following results:
Table 4: Multiple Regression Coefficients
Analyzing the coefficient estimates reveals that whether the circuit is a street circuit considerably impacts the DoI score. This is because the absolute value of the estimate (0.796) is the highest of all estimates provided. What further justifies this is the relatively low Pr(> |t|) of 1.78 × 10−4, which - since it is well below the 0.05 significance level - conveys that there is a statistically significant relationship between street and DoI. If the track is a street circuit, the DoI score on average decreases by approximately 0.80 points. Factors like rain (-0.147) and sprint (-0.129) also appear to mathematically impact DoI to an extent compared to other variables; however, their Pr(> |t|) scores of 0.805 and 0.704 are nowhere near the 0.05 or even 0.1 significance levels. Corner has a Pr(> |t|) of 0.086, which approaches 0.05 and thus significance. However, its coefficient of merely -0.048 fails to impact DoI much on its own. These apparent dichotomies - high coefficient estimates and high Pr(> |t|) values and vice-versa - could, unfortunately, be a consequence of an insufficient sample size (leading to large standard errors), outliers, nonlinear relationships, or simply a lack of a relationship.
Hypothesis testing - Race Conditions (binary)
Another method that can be used to better understand the relationship between variables and DoI and confirm or deny findings from the regression model is hypothesis testing. For binary variables - in this case, street, sprint, and rain - a simple Welch two-sample t-test would suffice, owing to the fact that the data meets the conditions for causal inference:
• Randomization: the 117 data points of incidents on the first-lap collected, although observational, can be assumed to be randomly selected and representative of the population in the sense that they represent a broad range of incidents.
• Normality of Populations: Sample size of at least 30 (117 > 30) ensures that the sample will be normally distributed, as per the Central Limit Theorem (CLT).
• Independent Sampling: The samples collected are independent of each other, as the selection of incidents in one group (rain happens, sprint race, etc) does not affect the selection of incidents in the other group.
• Sample size of 117 is less than 10 percent of the infinite number of incidents that could take place on the first-lap of future F1 seasons.
Bearing this in mind, this hypothesis test was run using the t.test() function in R for three different binary track conditions - whether it rained or not; whether the race was a sprint race or not; or whether the circuit is a street circuit or a normal race circuit. The 95% confidence intervals obtained, including the actual difference-in-means values, were plotted; p-values were used for further analysis:
Figure 4: Confidence Intervals for different track/race conditions, 2022 and 2023 Seasons
For context, the 95% confidence interval indicates that 95% of difference-in-means values will fall within the upper and lower bounds of the interval, and the p-value demonstrates the probability of observing a difference-in-means value as extreme as, or more extreme than the one obtained. As Figure 4 shows, the street vs. normal confidence interval of (-1.16, -0.47) did not include 0 and was therefore statistically significant; this is backed up by an extremely small p-value of 8.254 × 10-6, significantly less than the conventional 0.05 significance level. There is thus sufficient evidence to refute the null hypothesis, i.e. that the difference-in-means for DoI for whether or not the race was conducted on a street circuit or not was equal to 0. Races conducted on street circuits had incidents that were 0.815
points less risky than those conducted on race circuits. This, fortunately, reinforces the significance proved by the multiple regression as well, cementing incidents on street circuits as less damaging than those conducted on purpose-built tracks.
When looking at rain and race format (sprint or full-length), neither of the two were statistically significant, with p-values of 0.1276 and 0.9569 respectively. Whether or not the race was a sprint or not was overwhelmingly insignificant - the average treatment effect/difference-in-means was a mere 0.015 DoI points. However, the p-value of 0.1276 for rain can nearly be said to be approaching significance at a 0.10 significance level, perhaps demonstrating that incidents in races without rain are riskier. The results for rain and sprint therefore affirm those found in the multiple regression.
Kruskal-Wallis Hypothesis Test - Position and Corner (non-binary)
T-testing would not be applicable for numeric and non-binary variables like incident corner and starting grid position. Therefore, to determine whether there is a statistically significant relationship between the two non-binary variables (position/corner and DoI), some variant of the Analysis of Variance (ANOVA) test can be utilized. ANOVA is applicable in this context as it analyzes the differences in means for more than two groups; this works because variables like position and corner have more than two groups. However, what is critical to realize is that for ANOVA to be applied, the variances of the dependent variable (DoI) must be similar across the predictor variable’s multiple levels (Positions 1-20/Corners). To counter this issue, a non-parametric statistical method - used when distributional assumptions like variance or normality are violated or in question - like the Kruskal-Wallis Test, can be applied. This test is apt for the given situation since the dependent variable DoI is inherently ordinal but not normally distributed.
Running this test in R using the kruskal.test() function, the following results are obtained:
Table 4: Results of the Kruskal-Wallis rank sum test for DoI by position.
Table 4: Results of the Kruskal-Wallis rank sum test for DoI by position.
The results shown in tables 3 and 4 justify the results obtained in 4.1 - at the 0.05 significance level, position’s p-value of 0.9366 yet again clearly fails to reject the null hypothesis, which is that the medians of DoI are equal across all levels of car grid position. Corner quite clearly passes the test, with a p-value of 0.00081 (less than 0.05) proving sufficient to reject the null hypothesis, showing that there are statistically significant differences in the distribution of DoI across different corners.
Discussion by Factor
• Rain: Somewhat Significant - although perhaps not as much as one would expect, given historically dramatic races like the soaked 4-hour-long 2011 Canadian Grand Prix. The multiple regression analysis coefficient of -0.147 was relatively higher than other factors but failed the t-test with a p-value of 0.1276. Interestingly, the data analysis - the negative sign on the coefficient as well as the 95% CI being mostly below 0 - showed that incidents in dry races were more risky than those in rain-hit races. This could be due to any number of reasons: either drivers are more cautious and focused on finishing a race than getting into a deadly crash, or the limited number of rain-hit races (only 5 out of 44 races) analyzed leads to sample-size insufficiency.
• Street: Highly Significant, with the highest regression coefficient absolute value (0.796),
lowest Pr(> |t|), and lowest p-value of 8.254 × 10-6. However, this was in the opposite direction as well, with first-lap incidents on purpose-built circuits 0.82 points riskier than those on street circuits. This could be attributed to the high degree of precision needed on such circuits thanks to the lack of tarmac/grass runoff areas and higher-speed corners; this perhaps compels drivers to focus on preserving their current position rather than making risky moves on the first lap. Additionally, street circuits like Monaco and Singapore have been known to be notoriously difficult to overtake on, reducing the propensity for not only severe/major crashes early on, but crashes in general.
• Sprint: Insignificant, with a low coefficient in the multiple regression and high p-value of 0.9569 - this meant that statistically there was no difference in DoI if the race was a shortened sprint. This is a logically sensible conclusion: sprint races (normally 1/3rd the length of a full race) are worth only 8 championship points for the victor compared to 25 for the full race. The incentive to possibly be involved in an exorbitantly expensive crash and be out of Sunday action (where a majority of points are to be scored) could thus explain why there is no substantial difference in first-lap strategy.
• Incident Corner: Highly Significant, with the higher of the two non-binary coefficients in the regression, and rejecting the null hypothesis of the Kruskal-Wallis test with a 0.00081 p-value. Predictably, the statistical analysis posited that the most severe incidents took place in the earlier stages of the lap, aligning with the preliminary finding shown in Figure 1 that most incidents took place in the first two corners of the race.
• Starting Grid Position: Insignificant, with a negligible coefficient in the regression and a high p-value of 0.9366 as per the Kruskal-Wallis test; this indicates that the starting grid position has no significant bearing on how severe a first-lap incident is. However, the preliminary research revealed that those in the middle of each ‘half’ of the starting grid probabilistically have the highest chance of being involved in a first-lap crash, while those at the extreme positions (first 2 and last 4) have the lowest. These findings coincide with those found by a 2013 Seton Hall University study (McCarthy and Rotthoff, 2013).
Conclusion
Overall, the type of circuit (street or purpose-built) and incident corner appear to statistically have the highest bearing on the degree of impact of a first-lap incident. Interestingly, factors like rain and sprint races are not as significant. If the results of this study are to be followed, F1 teams should encourage their drivers to proceed with particular caution during the first corners of opening laps - and especially so on purpose-built tracks.
In this new and thrilling era of F1 racing, cars are only expected to become more and more equally competitive, (hopefully) leading to entertaining championship battles. In any case, analyzing first-lap incidents will become an increasingly noteworthy component of team strategy, spelling championship glory for some and the anguish of costly crashes for others.
Bibliography
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