# How do you solve a problem like Hispania? // The driver dance at the rear of the field continues to hurt the team

Published by Bridget Schuil

How do you find the clown (who’s choosing driver line-up) and take him down? We've been over the events a million times – two happy drivers in the car and two reserves, swapping one of the drivers out for a reserve, swapping the other driver out for a reserve, swapping one of the reserves out for a reserve – and the team never give us a straight answer.

No, I don't believe that it was food poisoning that took Yamamoto out in Singapore. Well, it's possible, but if he'd spend a bit of time on YouTube, he would've found this advice from Rosberg.

Yes, I really want Chandhok to be in the car; I'm a fierce loyalist, and it seems unjust to me that someone who is paying for his drive isn't in the car. As a dedicated scientist (well, a nerdy science student), I decided that I couldn’t find out who it was making the decisions, but I could use stats (as much as I hate doing stats) to prove that his choices were bad ones. (That, and, I need to practice ANOVAs [analyses of variance] for my botany project. I gave it a solid attempt with a stats textbook. However, meaningless numbers are prime targets for my dyslexia, and I wasn't getting anywhere. Thus, I practiced using F1 stats.)

Quick stats lesson: when analysing the variation between two groups of numbers, there are two equations.

- One (an unpaired ANOVA) is for comparing two general groups – for example, the combustion rates of grasses in different subfamilies (yes, that's my project. It has important ecological implications in light of climate change, I promise; it's not just a reason to burn stuff, as fun as randomly burning stuff is).
- The other (a paired ANOVA) for comparing two groups of related numbers – for example, the difference between a specific racing driver and the pace setter for every qualifying session and race over a season. If the P-value (the number that the computer spits out when it's finished doing the ANOVA) is lower than 0.05, there is a statistically significant difference between the two groups of numbers (that is, the probability of obtaining test statistics as divergent as the one observed is less than 5%). A post-hoc test is performed to obtain a Q-value, which allows you to see which group of numbers is larger/smaller.

I used published times of the fastest laps in qualifying and the race, average speeds during the race, top speed in qualifying to calculate the percent deficit to the pace setter (remember? That equation we were all doing furiously at the beginning of the season to find out whether the new teams would have qualified under the 107% rule). I calculated the mean and standard deviation of these results to see how, on average, each driver does in relation to the front of the field. These are presented as a graph (Fig. 1) with the standard deviations represented as error bars.

For the unpaired ANOVA (since we’re using percent difference as our performance marker, we don’t need to do a paired ANOVA, and can thus compare Chandhok and Yamamoto), percent deficits of the following data were used: the fastest laps in qualifying and the race, average speeds during the race, and speed trap results from each qualifying session, as published on the Formula 1 website. These were analysed in the following permutations: Pace Setter/Chandhok, Pace Setter/Senna, Pace Setter/Yamamoto, Chandhok/Senna, Chandhok/Yamamoto and Senna/Yamamoto. As Klien has only completed one race weekend, the ANOVA equation doesn't allow us to determine the significance of his performance. I then did a post-hoc test to determine which driver was the faster of the two in the pairing.

So, to recap, if the number is less than 0.05, there is a significant difference; if the number is close to 1, there is little to no difference. And now, sportsfans (drum roll, please), the results.

As you can see from the graph below, Chandhok is closest to the pace setters going through the speed trap, and consistently so. In contrast, his fastest laps are higher than Yamamoto with more variation. However, if you exclude Bahrain (which, I'm sure we all agree, was a rough weekend for the man, and we can’t really use someone’s second session in a Formula 1 car as a performance marker), his average is 107.04 (and, thus, the lowest of the three).

Senna, despite having the slowest and most variable lap time and average speeds in the race, is closest to the leaders in qualifying. The lap times and average speeds in the race may be affected by Melbourne – when he retired on lap 4 with a hydraulic problem – and Belgium – when he suffered a damaged front wing early on and then retired with suspension issues. As with Chandhok, if you exclude this race from his results, the graph looks very different (see Fig. 2).

Yamamoto is the most consistent throughout both sessions in relation to the pace setter – he hasn’t set a terrible quali or race time; he hasn’t had any major failures early on in the session, which would affect his recorded pace. However, his average performance is perilously close to 107%, and (when the results are corrected for mechanical hindrances to performance) consistently further off-pace than his team mates. One would expect him to be faster than the two rookies, simply because of his previous F1 experience, so this should be an entirely surprising result (but, let’s face it, we’ve all been watching him on track, so it’s not actually a shocker). This is especially pertinent, given Klien's recent stint in the car in which he noticeably out-paced Senna. (Unfortunately, because he's only spent one race weekend in the car, I couldn't include his results in the analysis. It would be interesting to see what the results would be if we had more to go on.)

As the table below demonstrates, there is a significant difference in lap times, average speeds on the fastest lap in the race and speed trap readings between the front runners and the Hispania drivers. The exception to this is Senna’s lap times during a race, which are not significantly different to the pace-setters.

Table 1: P-values comparing Chandhok, Senna and Yamamoto to the pace setter and each other.

PS/CHD | PS/SEN | PS/YAM | CHD/SEN | SEN/YAM | CHD/YAM | |
---|---|---|---|---|---|---|

Lap Times - Quali | 0.0001 | 0.0001 | 0.0001 | 0.1989 | 0.2518 | 0.8557 |

Lap Times - Race | 0.0001 | 0.5463 | 0.0001 | 0.2709 | 0.8895 | 0.4945 |

Speed Trap - Quali | 0.0001 | 0.0001 | 0.0001 | 0.4522 | 0.3045 | 0.0642 |

Average Speeds - Race | 0.0001 | 0.0052 | 0.0001 | 0.2607 | 0.4489 | 0.4945 |

To put the above table in context, I have made the Q-values into a table. Quick guide to decoding it: if the number is negative, the first group of numbers was smaller; if the number is positive, the converse is true.

It would appear that Senna’s race pace is terrible. Although, if one factors in Melbourne and Spa, these results would probably look a bit different, and it is possible that, if these results were excluded, Yamamoto would have consistently performed worse than Senna. Likewise, if we excluded Bahrain from the equation, Chandhok’s qualifying pace would be closer to the pace-setter and he may even be faster than Senna. Yamamoto has done better than Senna in terms of race pace since joining the grid. However, it is interesting to note that the difference between Yamamoto and Senna is insignificant on this count, despite Senna’s high average.

So, after all that, what have we learned? In an ideal world, I would have much larger data sets in order to get a more accurate picture. However, all we have is the figures published on the internet. From the numbers that I have access to, a few things occur to me:

- The car is rubbish. Or all three drivers are rubbish, and I don't think that's the likely explanation, given their performances in other series. However, Klien’s recent performance in the car could be an indicator of the difference between how a rookie handles the (particularly unwieldy) car compared to how a skilled, experienced driver handles the car.
- It would appear that, with the exception of lap times in qualifying, Chandhok is getting the most out of the car.
- On average, all three drivers are closer to the leaders in qualifying. Whether this is because of race reliability issues or simply because all three are pushing harder at that time would be an interesting study. How one would go about investigating that evades me, but it is an interesting question.

In conclusion, perhaps Yamamoto isn’t as bad of a driver as we all think he is. Alternatively, the two other drivers on the team are still rookies with reliability issues (or, at least, have been on track more, and so have had more bad luck). In addition, Yamamoto makes silly mistakes than the others don’t (anyone remember the fire switch incident?), which affect his results. So, in terms of on-track performance (and I hate that I have to admit to this), each driver has his weaknesses. But F1 isn’t all about on-track performance: a fair part of it is playing the game.

The team suffers a general lack of performance and reliability, which is hampering everyone who drives for them.

Yes, Yamamoto is consistently out-performed, but the team mate performance comparison data is statistically insignificant. The team suffers a general lack of performance and reliability, which is hampering everyone who drives for them. Thus, drivers must be picked on earning potential. Is it possible that Chandhok got put on permanent PR duty, because he’s the best to raise the visibility of the brand off-track? Chandhok is the clear winner in terms of public support and twitter proficiency. Senna, while not as eager of a tweeter as Chandhok, still has an interesting feed. On the other hand, Yamamoto tweets infrequently and usually in Japanese. Fair enough, Bruno tweets in Portuguese fairly often, but he usually provides a translation.

If you think about it, it’s genius – Senna in the car, keeping the fans happy; Yamamoto in the car, keeping the sponsors happy; Chandhok in the commentary box, which I assume is earning the team TV royalties (since coverage time usually translates into royalty cheques) to bring in extra cash. In addition, the wave of public sympathy for Chandhok is going to mean more coverage when (if?) he returns. He seems to think that he’ll be back in the car at least once before the end of the season, but the team have remained quiet. If he does return (and I hope he does), we’ll see if his stint on publicity has had any effect on the amount of coverage and sponsorship, and thus the team.