Experiment 2: order 2 and it seems to fit correctly, as we can see after 25 laps most of the yellow dots are to the upper extreme and our reg plot shows the loss of pace. Physical reason is after tires lose certain amount of threads degradation drops off the cliff. I previously saved the plot that shows the drop off, but couldn’t find it yesterday and today, that I wanted to add to the article to support the model.
Experiment 3: order 3 shows the inverse effect, so I abandoned it.
Seems like if you are going to be assigning a specific order polynomial fit, then there needs to be some kind of external justification (such as the rubber is known to change properties with a measured mathematical relationship) otherwise it’s guesswork. It’s hard to look at either relationship and say it “looks” second order. It’ll always tend to get you a better Rsquared value than linear and indeed the more you increase the order the better fit you’ll have so there needs to be some kind of logical reason for choosing a given order.
Spline interpolation seems to make a lot more sense in that the way tires degrade (and they will degrade differently at different weekends and different tracks) is (probably to my mind) not linear or tied to a specific order but very much piecewise which this takes into account. I don’t know enough about spline interpolation and its drawbacks to have a firm opinion on it either way though.
I’m working on developing a tire degradation model of my own and specifically trying to separate it from the effects of a changing fuel load so I’m curious to see what others have done, why they’ve chosen their given approach, and what works.
Update on this: Tweet author answered to my question. "It looks like you discovered something like polynomial regression, which is definitely an option—the higher order polynomial you use, the more “curvy” the line will be. I generally use something similar, called locally weighted scatterplot smoothing, which you could look into as well; there are several python implementations, like sklearn, scipy, or statsmodels. Hope that helps!"
This is guesswork, since I don't know the exact function OP tweet used. I've asked everywhere I possible could, and was unable to arrive at a solution, so I figured publishing my article to get more eyes who can help me, figure out the correct function. Now that I know, I'll improve the model next time, hopefully we get drivers starting on all 3 different tire sets at Spanish GP.
What was your justification for using a second order regression?
Tyre Degradation chart is inspired by this tweet: [https://twitter.com/rowsofthree/status/1514954946021670914](https://twitter.com/rowsofthree/status/1514954946021670914)
I couldn’t figure out what function OP used, firstly I tried by trail and error to find out
Experiment 1: Use linear regression of order 1. It looks like this: [https://i.postimg.cc/wv35smyf/miami-tyredeg.png](https://i.postimg.cc/wv35smyf/miami-tyredeg.png)
Experiment 2: order 2 and it seems to fit correctly, as we can see after 25 laps most of the yellow dots are to the upper extreme and our reg plot shows the loss of pace. Physical reason is after tires lose certain amount of threads degradation drops off the cliff. I previously saved the plot that shows the drop off, but couldn’t find it yesterday and today, that I wanted to add to the article to support the model.
Experiment 3: order 3 shows the inverse effect, so I abandoned it.
In the meantime, I asked the OP, and on several help channels to figure out what function is originally used. A user of r/f1technical answered here: [https://www.reddit.com/r/F1Technical/comments/urhcid/tyre_degradation_analysis_pace_difference_between/i8yh5i1/](https://www.reddit.com/r/F1Technical/comments/urhcid/tyre_degradation_analysis_pace_difference_between/i8yh5i1/) that it is probably a spline interpolation, which seems about right ([https://www.delftstack.com/howto/python/python-spline/](https://www.delftstack.com/howto/python/python-spline/))
What are your thoughts on this?
Excuse any typos/formatting, I’m on mobile.
Seems like if you are going to be assigning a specific order polynomial fit, then there needs to be some kind of external justification (such as the rubber is known to change properties with a measured mathematical relationship) otherwise it’s guesswork. It’s hard to look at either relationship and say it “looks” second order. It’ll always tend to get you a better Rsquared value than linear and indeed the more you increase the order the better fit you’ll have so there needs to be some kind of logical reason for choosing a given order.
Spline interpolation seems to make a lot more sense in that the way tires degrade (and they will degrade differently at different weekends and different tracks) is (probably to my mind) not linear or tied to a specific order but very much piecewise which this takes into account. I don’t know enough about spline interpolation and its drawbacks to have a firm opinion on it either way though.
I’m working on developing a tire degradation model of my own and specifically trying to separate it from the effects of a changing fuel load so I’m curious to see what others have done, why they’ve chosen their given approach, and what works.
Update on this: Tweet author answered to my question. "It looks like you discovered something like polynomial regression, which is definitely an option—the higher order polynomial you use, the more “curvy” the line will be. I generally use something similar, called locally weighted scatterplot smoothing, which you could look into as well; there are several python implementations, like sklearn, scipy, or statsmodels. Hope that helps!"
This is guesswork, since I don't know the exact function OP tweet used. I've asked everywhere I possible could, and was unable to arrive at a solution, so I figured publishing my article to get more eyes who can help me, figure out the correct function. Now that I know, I'll improve the model next time, hopefully we get drivers starting on all 3 different tire sets at Spanish GP.
Since you're also working on a tire degradation model, you might find this post helpful: https://www.reddit.com/r/formula1/comments/tmwnb4/oc_an_attempt_at_comparing_performance_gaps/
Here the user tried to separate out the fuel load to estimate tire performance.
Thank you very much for the feedback and contributions, hope to see your model soon.
Please leave your feedback here. Let me know if you have new ideas, or want to know anything particular about formula1.