Jerez 1997 Qualifying — Analyzing the Three Way Tie
What is the first thing you think of when you see the above results? An incredible three-way tie for pole at Jerez 1997 is certainly a compelling story. That said, it’s also an incredibly unlikely story. It is perhaps due to my software engineering background but when I see the above graphic the first thing I think of is that it’s a hardware or software bug.
Following this line of thinking, I wondered to myself whether anyone had done a post-analysis of these qualifying laps. I didn’t look extremely hard but I didn’t find anything obvious; so I decided to do some rudimentary analysis myself.
I’ll try to keep this relatively concise though I would like to make clear that I’m not trying to claim anything with this analysis. I am more than willing to accept that there are flaws in the analysis and I’ll try to point some of them out myself. Still, I felt it was an interesting enough topic to discuss and I’m curious if anyone else has additional info/ideas for further analysis.
Source videos
So starting from nothing I started looking for videos of the qualifying lap from both perspectives.
Schumacher: https://www.youtube.com/watch?v=xsjCmZrGZg8
Villeneuve: https://www.youtube.com/watch?v=pSE3xWCqQBY
We are about to analyze a comparison of the two videos above, here is the video of the two side-by-side and synchronized:
Synchronizing the start
The videos were synced by attempting to have the frame in which the cars cross the line play at the same time. Here are the video frames before and after the line is crossed on both videos:
Comparing the end
Once the start is synchronized, all that really needs to be done is to analyze the end. What follows are the relevant side-by-side frames at the end of the lap.
Judging simply by this, it would certainly appear that Schumacher was faster by about 5 frames. Given that this video is a 25 FPS video, that would mean Schumacher was faster by about (1 / 25) * 5 = 0.2 seconds, or 2 tenths. Even if we are off by one frame the wrong way in both directions, that would still mean Schumacher was faster by 1.2 tenths.
The next question though is: do we trust the videos? Is it possible that somehow the video with Schumacher is faster or lost some frames along the way?
The fact is these videos are old, were recorded on dated technology, were likely re-encoded a bunch of times. It’s tough to trust them. Let’s see if we can get an indication that there might be an issue with comparing them?
Video issues
Here we actually appear to have a problem. On the videos there is a timer which shows up in the bottom right.
It turns out that after having synced the start, the two clocks tick from 0.0 to 0.1 on exactly the same frame. So how do they look towards the end of the lap?
Uh-oh. Why is the timer on Schumacher’s video ahead? And why is it ahead by almost exactly 2 tenths, the exact amount we thought he was faster by?
If we assume that the on-screen timer is accurate, we can no longer trust our previous analysis as this completely undoes the time difference we calculated.
The best thing we could do to test this would be to find more videos of the laps and do the same analysis to see if our results are consistent.
More videos
Luckily there are more than only two drivers involved in the tie: thus far we have ignored Frentzen. I did find one video of Frentzen’s lap as well as a second recording of Villeneuve’s.
Source videos (side-by-side videos linked later):
Frentzen:
https://www.youtube.com/watch?v=9umbp_2rVkw
Villeneuve #2:
https://www.youtube.com/watch?v=KVpi5IhzBDY
Comparing Villeneuve #2 with the Schumacher lap gives roughly the same result. Likely the issue lies with the video of Schumacher’s lap, unfortunately I was unable to find a different recording of that lap. Does anyone know where to find one?
Since that didn’t work, let’s try comparing Frentzen’s lap with Villeneuve’s.
It looks like Frentzen crosses the line one frame before Villeneuve. Unfortunately I would say this is not super conclusive as synchronizing the videos is not a perfect art.
Here are the links to the videos used in this section if you would like to analyze them yourself. I recommend downloading them and using a video player which allows stepping through videos frame by frame.
Probability analysis
Unfortunately the evidence from the videos turned out not to be extremely conclusive. So I was curious: what is the probability that this actually could have happened?
Now I’m no statistician, just a measly software engineer, but I figured I’d give a go at calculating a minimum baseline probability that it could have happened. If a real statistician wants to take a crack at calculating this more comprehensively than I did, I’d love to hear about it.
Solving the actual problem is very complicated, so let’s solve a problem hopefully more within my capabilities:
What is the highest probability that a single person driving 48 qualifying laps will have 3 of those laps finish in the same thousandths place?
I picked 48 laps because the 1997 F1 season had 24 cars on the grid and I gave each car two laps. This is a major oversimplification; the odds naturally get much worse if you consider different drivers driving different cars. The idea behind this is to give us a lower bound to try and gauge whether if what actually happened is at all plausible.
So the first assumption I’m going to make is that a person’s lap performance fits a gaussian distribution.
I tuned the variance to give our driver about a 95% chance of finishing a lap within a range of 5 tenths. This seems pretty generous but again, we are looking for a baseline. The center-point (zero) is going to be our target lap time which would be the driver’s mean time. We use this point as it’s the most likely to have duplicates.
Now then, what is the probability that our driver finishes a single lap within 1 thousandth of their mean time?
Looks to be about a 0.31% chance. Now to solve our actual question — we need 3 of these laps out of 48.
This is the formula to calculate the probability of this. Our values are p = 0.00312, r = 3, and n = 48. nCr then equals 17296. (Smart people please tell me if I made any mistakes here)
After plugging everything in we get a probability of: 0.0004564, 0.046%, or a 1 in 2191 chance. Certainly unlikely… but not enough for me to think it’s absolutely impossible.
As a note: the probability would be very slightly higher if we allowed 3 or more tied times instead of exactly 3. I ignored this because the increase in probability would be fairly negligible. One would simply calculate the same formula for r = 4, 5, 6, etc and then add them all together.
In closing
As a final note, does anyone know how the speed in the graphic at the start of the article was calculated? If it was some kind of speed trap it seems especially unlikely the three cars all had exactly the same speed. If it’s calculated from the lap time, then it being the same value makes complete sense.
So what are your thoughts? Did it really happen or was there some sort of glitch?
Personally I feel like I want to believe but I’m still not sure. I would love to hear from anyone that has additional footage of the qualifying laps or new ideas for analyzing it further.
In either case, it’s an absolutely fascinating story and it boggles the mind that it happened. Thanks for reading!