An Attempt to Model a New FIA Points System

Discussion in 'Gran Turismo Sport' started by Jeeves_ACBC, Jun 15, 2019.

  1. Jeeves_ACBC

    Jeeves_ACBC

    Messages:
    48
    There has been much conversation on, mainly the "FIA Race Discussion" thread, about the FIA points system. The main issue pointed out is that there is incentive for top split drivers to drop into lower DR splits in order to score good points more reliably. Furthermore, a mid-A lobby winner will get the same points as 10th place in the top split. So the top drivers in each region can fight contested races mid-pack, and still get non-satisfactory points for their skill and overall race pace. These are only 2 of many issues others have raised, but these are the 2 I intended to tackle.

    I will show 2 different models for a potential change to the points system. It is by no means perfect, but I think it more fairly assigns points to each lobby based than the current system. These models are somewhat flexible equations and can be tuned based upon any suggestions you may have. Please see the graphs and charts below for a visual representation. I write an extensive explanation of each model and their equations are further below if you care to read it all.

    upload_2019-6-16_0-27-32.png upload_2019-6-16_0-36-4.png
    (sorry for the blurry images, for some reason when copying from Excel, they lose their sharpness)

    For comparison's sake, I used several different tiers of lobby to make sure that each lobby will be treated fairly by the models. I assumed 73k for top split, 65k for 2nd split, then 50k, 40k, 30k, and 20k for representative A+/A, A, A/B, and B lobbies. On each of the graphs I show where the winner of each lobby would position in the top split as well as successive higher tier lobby. A general goal of mine was to put the winner of 2nd split at around 5th top tier points. Additionally, I tried to make the winner of a lobby get the same points for about 10th in a 10k higher lobby; but this was not strictly held. I made no attempt to fix the actual driver rating system since that would be much harder to model and test its affects without a lot of player data.

    First, the current points system is a quite simple calculation. The maximum points for 1st place = avg DR/24, rounded to the nearest point. Last place gets 0 points and it is linear gaps between each successive place. For example, a top split room with 73k avg DR will have 3042 pts available, and 160 points between each car.

    My first model is one that has been suggested several times; have base points for all races. No longer will the last finisher get 0 points. This model will assign base points to all lobbies by simply dividing the maximum points by a factor. I present here a 50% base points system. I also played with 33% base points but decided gaps between lobbies weren't quite big enough. For example, the 73k avg DR lobby will still have 3042 pts for 1st place as in the current system, but now last place is guaranteed 1521 pts. Now the gaps between each successive position will be smaller as a result, with only 80 pt gaps.

    For the second model, I wanted to create non-linear gaps between each position as well as a non-linear progression for maximum points in higher lobbies. So now, rather than the gap between 1st to 2nd and 10th to 11th being the same, you get a larger reward for gaining higher positions. For example, in the 73k DR lobby, the gap from 1st to 2nd is 109 pts, whereas 10th to 11th is 78 points. Additionally, the maximum points get smaller more quickly as DR is reduced. This helps keep each tier of lobby slotted in terms of points. So now is will be more difficult for B-rated drivers to have similar points to A-rated drivers, and similarly for A drivers with A+ drivers. Some may see this as an advantage, so your overall season score better reflects your skill level. However, this will also adversely affect manufacturers with no top-tier representation. This is still somewhat a work-in-progress, but I am mostly satisfied with the model shown. Additionally, I feel like lower lobbies are overly closely bunched in terms of points since the maximum is now quite small.

    An explanation of the actual equation is as follows:
    Positions 1-20 are assigned a "position factor" (PF). The equation is a power function; PF=(1.037)^(1-Pos). So 1st place gets a 1.00, 2nd place 0.96, 5th place 0.86, and so on to 20th place at 0.50. This factor is the same for all lobby tiers. The 1.037 was chosen because this results in 20th place receiving 50% of total points.

    upload_2019-6-16_1-32-23.png

    To calculate the actual points for each position, I used a logarithm and power function to get the desired points "curve".
    Total Points = PF*(DR/29)*log(30*DR/75000)^0.5. DR = avg driver rating for the lobby.

    I multiply by the position factor (PF) and a scaling factor (29) in order to get the max top tier points near 3042 for 73k lobby. Inside the logarithm, I normalized the DR by dividing by max DR of 75k, then multiplied by a "log factor" (30) to tune the curves. The rate of change is for each tier is affected by the "rate factor" (0.5). Each of these factors were tuned until I got as good of a model as I could. I still feel like this equation is overly complicated and could use some re-tooling to get a similar result. But so far this is the best I found.

    For fun, I also made a model based on "real" FIA points of 25, 18, 15, 12, 10, 8, 6, 4, 2, 1. I scaled this up for 20 positions and 3042 max points. I don't think anyone would be happy and would make everyone's complaints with the current system worse...lol.

    Let me know what you think and how this can be improved. This was mainly a fun exercise for me while procrastinating at work and while sitting in my hotel on my current business trip.
     
  2. breeminator

    breeminator

    Messages:
    314
    I haven't spent much time thinking about what you've already done, but one important element that isn't in your current analysis is scores only being used from 1 in 4 races, if someone takes part in every race. One way to incorporate that would be with a Monte Carlo simulation where you have a probability distribution for each driver's finishing position. The reason why this is an important element is it makes it more beneficial to race in a higher split, because you only need to get lucky in 1 in 4 races to do better than you would in a lower split where you might consistently finish high up, but with a capped score.

    So a driver might get e.g. 2200 points almost all the time in a lower split, but in a higher split, if they race 4 times, they might get 0, 1000, 1800 and 2600 points, say. Only the 2600 points race would count, so they're better off in the higher split. So you can't equalise the scoring across splits without taking that into account.
     
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  3. Jeeves_ACBC

    Jeeves_ACBC

    Messages:
    48
    @breeminator I did think about the 1 in 4 races counting, but I didn't use it as major factor; perhaps I should have given it more attention. I didn't mention it above, but I targeted 5th place as the crossover point because in general if you are going to be competitive in your tier level, only top 5 finishes (or even podiums) will be the races that count for you. It is true though, that being in the top splits is the only way to give you the opportunity to get major points.

    However, it is an interesting idea to use some sort of statistical analysis tools (e.g. Monte Carlo, DOE, ANOVA) to better simulate different models. I would love to get the list of players from top 5 splits with DR before and after for a whole season and try to simulate results with different models. See what types of factors are most important.
     
  4. Majorwolf72

    Majorwolf72

    Messages:
    255
    Location:
    Germany
    Well, great work, but now we can be sure that this is never going to happen. Japanese will not adapt anything they haven’t come up with themselves.
     
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  5. vvise

    vvise

    Messages:
    639
    i think something like this is a pretty great idea. base starting points for higher lobbies makes sense.
     
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  6. SpecMiata-JSW

    SpecMiata-JSW Premium

    Messages:
    694
    Location:
    United States
    Wow, well done sir! Kudos!
     
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