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Thats about as much "specifics" as I can give.
There's driver smoothness stat, chassis tyre wear stat, chassis tyre heating stat, the actual temp gauge during testing, track grip, location ambient air temperature (Black Sea vs Dubai), different tyre compounds, different tyre suppliers and types (gma rules), race length settings etc. All these things and more affect tyre temp and tyre deg in some way and would need to be individually tracked or standardized in some way to get a good understanding what each variable does. Maybe a lot of them don't really affect the results but we won't know that until it's tested and shown that it doesn't. So it looks like a massive headache.
There's also different phases of tire wear in SingleSeaterDesignData. If memory serves, it goes by the compounds that are available at the race. So the softest available compound will be fresh for x laps, normal for x laps, and worn for x laps, not counting the cliff. Tire Wear and Smoothness apparently add more normal laps to a tire's life. And I assume all of this is somehow converted into the percentage you see. It probably spends like fuel, where if you're pushing you use up say 1.2 laps of tire life for one lap on the track. I could be wrong.
There are values listing the time penalties for fresh/normal/worn tires per available compound. The cliff is uniformly an 8 second penalty. The differences between fresh/normal/worn are subtle to the point that I don't think they actually make a difference when refueling is in play. For example, worn tires of the softest compound have a bigger penalty than normal tires of the middle compound, but when you take into consideration the softest tire's fresh and normal laps, while also considering the probable greater fuel load under the middle compound, the softest compound is still preferable. With no refueling, it probably matters more, but I've never had a chance to play with no refueling.
As for the temperature penalties, my best guess is that you get a very slight penalty to wear and lap time for being max temperature or min temperature, and anywhere in between carries no penalty. I don't believe this penalty gets worse for continuing at min/max temp, nor do I believe that your tires can get hotter than max temp or colder than min temp. In other words, once you hit max temp, you might as well keep pushing, and it's preferable to push than to hit min temp, because you get a tire wear penalty anyway and you're losing lap time while running neutral or conserve. Again, with no refueling this probably matters more.
Wouldn't this also explain why the ai sometimes keep going even though their tyres are under 25%? I remember seeing some cheating ai accusations being tossed around, can't be bothered to recall exact details but some where upset that the ai was able to keep their pace even though they're clearly below the critical 25%.
Fresh) 100-75%, fastest +0.0s/lap
Normal) 75-50%, average +0.5s/lap
Worn) 50-25%(varies), slow +1.0s/lap
Dead) 25 (varies for diff compounds)-0%, no grip +10.0s/lap
Preliminary results on a test run in Dubai (2.82mi laps) with optimal temperature on the option tyres (SS), track tyre wear is very low (so no adjustment needed for expected tyre deg). I compared later lap times with some reference lap times that had been done very early in the race (to ensure I'm comparing to fresh tyres). Somewhere between 66-63% tyre deg the delta changed from around +0.15s to 0.477s. The next lap, at ~60% deg, the delta changed again to around +1.3s/lap. This continued on until around 25% when the car came in to pit, so no confirmed lap time to determine the pace when tyres fall off. Simplifying into a chart:
Driver 1 (SS 23-25 laps expected)
Fresh) 100-64.5% (~10 laps), +0.164s/lap
Norm) 64.5%-60% (~1 lap), +0.477s/lap
Worn) 60%-25% (~12 laps), +1.350s/lap
Dead) 25% (pit end of 23/42), no data
Driver 2* (SS 25-27 laps expected)
Fresh) 100-64% (~11 laps), +0.907s/lap
Norm) 64-53% (~3 laps), +1.802s/lap
Worn) 53-14% (~15 laps), +2.471s/lap*
Dead) 14% (pit end of 29/42), +10.9s pace
*low accuracy data due to rough adjustments to account for different driving modes
Oh lawd was this tedious af. Had to find fair ways to factor slight mode changes and account for fuel weight difference. Needless to say the actual delta values are not super accurate (especially for driver 2) but it was a decent method to find a rough estimate of where the tyre transitions happen. Plus the error(s) is(are) probably small since the changes in tyre/engine mode (up/down 1-2) shouldn't cause massive deviations. So despite that there's probably some usefulness in the pace delta values.