Unresolved

Qualifying massive error

A possible explanation would be that tracks have a certain optimal balance value for the (performance type) car attributes (for example, the tracks had an importance factor for Downforce listed on their characteristics page in the old version of the game, that might be still in effect in the new, for Japan it was medium I think). 

Following that thought the amount of points on Braking in the most developed car might not only have a lower effect than those points spend on Acceleration and Handling, as in line with the general understood order of the 4, but might even have a more reduced impact as it's 37% of the big 4 compared to 33% and 32% if the track stats have an assumed optimal value of 29%. So for Braking the lowest developed car could have the most gain per point spent, followed by the, in the end, fastest. Downforce is extremely low and the same amount for all of them, but it's about 7.7% for the first 2 but quite less shabby 10.2% for the last due to its much lower total point count. So if anything below, say, 20% rakes up a little debuff on performance at this very track it would be much less affected and closer to the optimal performance, for the number of points spent, there. Still slower due to the much lower point count, but closing the better part of the gap towards the less optimised of the other two, perhaps additionally helped by a little bit less fuel.

Thanks, that's really useful information as your stats shoots any suspicion that fuel weight might be a major factor here right out of the water, as your car had the best FE and still is just 0.038 seconds faster than the one with the worst of this setup of cars. Also your cars are very similar, just more Acc and, half the difference in Acc, less in Braking. 

Now there's the question how fuel is applied, you need roughly 0.1 less per lap than the Amuchina car, so it's either 1 litre steps (then either no difference or the Amuchina car would've been actually faster without extra fuel) or fine grained fuel differences at race effect, for which I'd wish I had more data, but between my guesstimate (which I think is a bit too low) effect and Qualifying fueled for one lap (or 2 laps with the fuel for the out-lap already being burned) and the Qualifying difference of 2 similar cars with a difference of 3kg ballast (which I think is a bit high) at 2 laps fuel (Qualifying lap and in-lap) would be between 0.003 and 0.022 seconds. So it could gnaw away even more of your little bit of time difference towards Amuchina but almost meaningless in comparing the Amuchina, Paolo and Silva cars (and the effect between them would be half of it).

So about the balance thing and it having to be linear. Let's continue the thought experiment and try if I can fix a set of 'perfect balance' percentages based on your and Amuchinas time to resemble Paolo and see where it puts Silva (and this time on actual big4 and not just lazily taking the sums above without noticing they are actually Top3 :-) ).
So I assume 32% Acceleration, 25% Handling, 30% Braking and 13% Downforce is the ideal.
You've got 33.11%, 30.44%, 29.33% and 7.11%. Sum of difference 13.11
Amuchina 31.01%, 30.79%, 31.01% and 7.19%. Sum of difference 13.60
Paolo 29.31%, 29.08%, 34.45% and 7.16%. Sum of difference 17.07
Silva 34.87%, 26.8%, 29.11% and 9.22%. Sum of difference 9.34
So you and Amuchina are 0.49 in difference apart and your Qualifying times are 0.038 seconds, so it's 0.07845s per point difference, so let's say 0.08. Since you're 13.11 points off that would make a perfect lap time with your DP perfectly spent a 1:30.540, as it's based on you yours remains at 1:31.589, Amuchina unsurprisingly is close as well as it's just the rounding 1:31.628 (1:31.627), Paolos time would be 1:31.906 (1:31.953), so I got it fairly close. Silvas time with your amount of DPs would've been 1:31.288, so in this thought experiment he lost 0.838 seconds due to having more than 100 points less DP in his car.
I'd say close enough, but of course no proof it's really, even remotely, like this and completely disregards fuel and (albeit small as they are all pretty close) driver differences.

Edit: I do wonder now by how much a car with 144 Acc, 112.5 Handl, 135 Braking and 58.5 Downforce, which would've been the car matching those assumed values, would really fail to hit the 1:30.540, as linear and equal between the stats effect of being off sounds too easy (as the stat values per point differ and the effect per point during the range of 1-200 is far from being linear, plus that resulting 'perfect' lap time just looks too good).

While it's just a tenths of a second difference that Qualifying is much more telling as the other one, as, to me, it is just weird. Still it doesn't help to cry bug if we have no clue were to point the finger at. The devs have no time to do thousands of races to compare results and I'm sure they checked the theory of their calculations already at least once and found them sound.

Also, the doubling of the range made the game much more unbalanced by weakening the effect of DPs, and in the second half of the range a few points were not that powerful in the old range to start with. Also if effects of (missed) balance are calculated per DP, instead percent, then that effect has been effectively doubled.

Of course we can just enable driver randomness again and pretend anything off is just having bad luck. Or do manual Qualifying and if someones complaining that one of his cars is suddenly 1 tenth of a second slower than the other, or how it should, pretend it's just down to manager PL mistakes.

But if we want to get to the issue and want to have it fixed we have to be sure which results are pointing out that issue and which can be explained away by other factors, or even better know exactly what those factors are and how they are supposed to work and where occasionally is something amiss (or perhaps not and feeling like bumping the head against the desk to have missed something obvious explaining everything).