Car bonuses in 2009

[zaqrack]

I like the bonus system. But I don't like bonus renormalization and ever-growing bonuses. I want to avoid this.
In order to avoid this, there is a simple mathematical rule to be followed:
In each round add only as much bonus as much we substract.
So I reversed this simple rule, and created the rule for 2009:

After each track the bonus for the unused cars (+2,+3,+4 and so on) will be summed.
The resulting value will be distributed between the cars on the podium the following way:
50% for the winner car
30% for the second
20% for the third.
(of course all rounded to integers)

This guarantees the continuous flow of the season, and also - if there is a dominant car on a track, surely less other cars will be used -> more bonus for unused cars -> more substracted from the dominant cars. Hopefully this will result in a self-balancing system.

From this point read on only if you're interested in details:

Remember, there will be more cars in the 2009 season, so probably there will be slightly bigger fluctuations, which I'd prefer, as I'd like to see more winner cars compared to 2008.
In 2008 the average positive bonus / track was 16. We had 11 cars. we'll have at most 15 in 2009, (16/11)*15=21.8
That means an average 22 negative points/round, which would result in
-11 for the winner (takes 4 rounds to regenerate when unused)
-7 for the second (takes 3 rounds to regenerate when unused)
-4 for the third (takes 2 rounds to regenerate, when unused)
A car occupying the whole podium would need around 5 rounds to regenerate to its previous bonus value, when completely unused. So maximally 2 wins/car a year, which I think is an optimal value.

What do you think? Should we further raise the positive/negative bonuses and kick out strong cars for a longer period, or does this system sound balanced this way?

[Mark L. Rivers]

A car occupying the whole podium would need around 5 rounds to regenerate to its previous bonus value, when completely unused. So maximally 2 wins/car a year, which I think is an optimal value.

I don't think to have understood all you explained, but I like very much the phrase I quoted, and I trust in it. 

[CTG]

We will see in use. Since I don't like the multi-car racing (participating only because of the addiction to the game and of course the permanent high level of ZSC), I don't really care about this bonus system. Do, whatever you want to do - I'll be there and race.

[zaqrack]

Do, whatever you want to do - I'll be there and race.

thats the spirit, thanks! I'll try my best making car switching painless to you

[BonzaiJoe]

Two questions come to mind:

1. Doesn't this undermine the whole point of the multi-car system? (that at each race, it should be possible to win with several different cars). This seems to get closer to having one car per track, only determined by the circumstances of the track rather than the competition manager.

2. Why the bonus for unused cars? I don't think it makes any difference if the car was unused or someone came in 11th with it, 30 seconds after the winning time.

[zaqrack]

1. Doesn't this undermine the whole point of the multi-car system? (that at each race, it should be possible to win with several different cars). This seems to get closer to having one car per track, only determined by the circumstances of the track rather than the competition manager.

Why would it? More or less it is the same system as now, just the winning cars get stronger negative bonuses. It is impossible to balance all the cars -  but if on every track there are 3-4 cars which are all capable of reaching the podium, the race gets interesting.

2. Why the bonus for unused cars? I don't think it makes any difference if the car was unused or someone came in 11th with it, 30 seconds after the winning time.

You have to draw the line somehwere. It surely makes no difference, but we can't just hand out only negative bonuses all the time.

[BonzaiJoe]

How about bonus for all cars out of top 5 then?

[Duplode]

After seeing Zak's new system, I felt the only way to really understand the implications would be to perform a full-fledged simulation... so I did it, picking from Z82 (when the current bonus rules more or less settled) up to Z93 (the furthest I could predict reasonably). Predicted podiums, used cars and bonuses for each race are below; a graph and the full calculation spreadsheet are attached.

Code Select Expand


C82 C83 C84 C85 C86 C87 C88 C89 C90 C91 C92 C93
ANSX 24 26 29 33 38 24 26 29 33 29 31 34
AUDI 29 31 23 25 28 32 32 32 34 34 36 39
VETT 33 31 22 24 27 31 36 36 38 31 33 36
FGTO 31 26 28 31 35 40 11 13 16 20 25 31
JAGU 13 10 10 12 15 19 24 0 2 5 9 14
COUN 32 34 34 36 39 39 39 41 44 33 33 35
LM02 35 35 37 37 39 42 46 46 48 48 15 17
LANC 29 31 34 38 7 9 12 16 21 27 34 42
P962 10 10 12 12 14 17 21 26 -7 -5 -2 2
PC04 33 33 35 38 42 28 30 33 37 37 37 39
PMIN -11 -9 -6 -28 -26 -23 -19 -14 -8 -1 7 -31

1st FGTO VETT PMIN LANC ANSX FGTO JAGU P962 COUN LM02 PMIN
2nd JAGU AUDI PMIN LANC PC04 FGTO JAGU P962 VETT LM02 PMIN
3rd VETT AUDI PMIN LANC PC04 FGTO JAGU P962 ANSX LM02 PMIN
Others LM02 JAGU LM02 COUN AUDI AUDI LM002 PC04
P962 COUN P962 COUN VETT AUDI COUN
PC04 LM02 PC04


In the simulation, the races would go pretty much the same up to Z86. According to Z86, the NSX would take a rather heavy hit (14%) and thus would not be competitive for Z87; the same goes for Carrera, which would be unlikely a podiumer in Z88. Instead, the GTO (which didn't lose much after Z82 for starters) would hit a really high bonus in Z87 and fully dominate the proceedings. With Z88 not being much of a powergear track and the highest PG car at 36%, it would be mostly a Jaguar (24%) race, but probably with a fairly good diversity of cars at midtable. In Z89, it would be P962 turn instead, but with a fairly stronger dominance (mostly due to the relatively large number of used cars in the previous two races). With the IMSA cars out of the queue, Z90 would be very balanced, with most cars being able to reach a decent result (crucially, the excellent bonus of Countach would be balanced by the PG possibilities). After that, for Z91 the LM002 would be 11% ahead of the closest car, so there would be little option unless Zak prepared a full Indy-PG track. By now, the Indy is astronomically high on bonus (7%, while Jaguar has 9%...), so Z92 would be a pure Indy race - which would then mean a 38% hit for Indy before Z93... Z93 could well be a Lancia race (at last recovered from Z85), but the PG cars appear to be competitive, while Audi, Carrera and Countach are not exactly far either. And so on...

What are the conclusions to be drawn?

1. The system would not be radically different from what it is now.
2. Most races would still be dominated by a specific car, although the probability of true multi-car races (like, on the simulation, Z82, Z90 and, with a little luck, Z88 and Z93) appears to have improved.
3. Rotation is definitely better: on 11 races (Z82...Z92) there would be 10 winning cars, including the long-absent IMSA cars. Indy was the only repetition, but only after an 8-race gap and, with -31% entering Z93 and several cars on the mid/high +30s range, it wouldn't reappear for a long time anyway.
4. The average positive bonus awarded will be in all likelihood larger than Zak predicted, even with 11 cars only (for the final 8 races, after the system got stable, the average was 29.75). Recovery times for a car reaching a full podium are similarly larger, typically of 7/8 races (Indy: Z84 --> Z92; Lancia: Z85 --> Z93)
5. The difference between the larger and smaller bonus values won't grow fast enough to destroy the balance (my main fear after reading Zak's post).

Overall, the system is a definite improvement over what we currently have, minimizing exaggerate growth of bonus percentages and improving the car rotation while making eventual true multi-car races more likely than now. There are a few important remarks to be made, though: 

1. Percentages will often reach the 40% / 50% range, even if they probably won't get past that. That raises again the issue of having to improve 0.10s to advance 0.05s on the scoreboard... Renormalization would be a poor solution, since it raises the absolute gaps between larger and smaller bonuses, and thus would destroy the elegance of this system. Most likely rounding corrected times to 0.01s instead of 0.05s is the way to go.

2. The usage of cars approaching the end of a long recovery period can have a huge influence on the evolution of bonus for all cars. If a car gets +8% on a single race (Indy on Z91, Lancia on Z92), it is necessarily subtracting that large gap from the podiumers (for instance, the long hibernation of Lancia is the main reason the Indy lost so much % after winning Z92). That also means Zak would have a powerful tool for modifying the pace of bonus evolution, as delaying or anticipating the resurfacing of a long-unused car by track design decisions has large-scale effects on the whole system.

3.

2. Why the bonus for unused cars? I don't think it makes any difference if the car was unused or someone came in 11th with it, 30 seconds after the winning time.

That is actually a pretty important point, for two main reasons. First of all, if a car is on a long hibernation and thus getting additional bonus really fast (as discussed on the previous topic), there will be a huge difference if it gets used in a listfiller instead of remaining unused by one more round (thus gaining several additional points), with several cars being affected indirectly. Perhaps more importantly, popular cars that tend to be used for listfillers, just-for-fun laps or by absolute newbies can get locked with unfavourable bonus percentages easily. That's the main reason we didn't have an IMSA victory this year. Even in my simulation, the Audi was the only car not to have a victory mostly due to a number of non-podium participations. That issue should, IMO, be addressed by only counting as "used" cars on the top half, or the top two-thirds, of the scoreboard (only top 5 as BJ suggested seems a bit too restrictive). 

4. Finally, the max-min gaps and the recovery times on the simulation appear to be pretty well balanced, even if relatively large. With more cars, however, more points will be distributed, and the gaps will be inevitably larger. More importantly, recovery times will become fairly longer - possibly a whole season in many cases. A simple option to counter that would be to make the bonuses for unused cars start to add up from 1 instead of 2 (+1, +2, +3... instead of +2, +3, +4 for successive races). That might also make multi-car races more likely and also help with the problem of casual usage harming popular cars discussed on the previous topic (by lowering the difference in bonus points gained between used and unused cars).

[BonzaiJoe]

Wow, that is an impressive piece of work you've done! I think most further discussion is unnecessary

By the way, I may have sounded a little harsh in my previous posts, I still want to give Zak credit for coming up with the clear improvement, and rather ingenious idea of normalizing positive and negative bonus changes.

[CTG]

Duplode is still a time millionaire. Nice work but you missed the human factor - with slightly different bonuses Ayrton would choose another car for insane tricks and from that point everything is totally different...

[Krys TOFF]

Good idea Zak. I hope it will bring more balanced season, I miss IMSA cars in ZakStunts.

Most likely rounding corrected times to 0.01s instead of 0.05s is the way to go.

I aggree.

[CTG]

I miss IMSA cars in ZakStunts.

IMSA + Melange cars have VIP tickets in USC.

[zaqrack]

I also did a small simulation before posting this idea but this was really thorough. Thanks a lot!

So I guess we'll go this way and also wont round times to 5 milliseconds.

One thing remains: the definition of the beginning values on the first track of the season.
My idea: take the average values of the monthly bonuses in 2008 and normalize it to 0 as we did before zct87.

[alanrotoi]

I understood Seems good, I fear about the cars I've never tryed. I hope not to find another "skoda".

[zaqrack]

After a 3 hours long testing session the base percentages for the 2009 season were born:

29% Lamborghjni LM002
26% Porsche Carrera
24% Lamborghini Countach
23% Nissan Skyline
21% Audi Quattro
21% Lancia Delta Integrale
20% Chevrolet Corvette
20% Ferrari GTO
20% Ford Ranger
18% Acura NSX
2%  Jaguar XJR
0%  Porsche 962
-1%  Speedgate XSD
-27% Porsche March Indy

Resulting in an average of 14%/car exactly.
The testing method in brief:
The base for the calculation was the average of last year's values normalized to the P962 as 0%.
Powergear cars except the Indy got -1% or -2% penalty on this value (Acura,GTO,Corvette)

The new cars were tested on 3 ZakStunts track from the 2008 and on Default.
First I drove a quick lap with the car I raced with on the track. I divided the achieved time with my time achieved in the competition, so a "race vs. practice" coefficient was born.
Then I drove a similar lap with all the new cars. Multiplied the achieved time with the racing coefficient, and then calculated what percentage would be needed to achieve the same result I did on the scoreboard.
Got the following results (rounded to integer, in the calculations I also used the fractions):
Speedgate: -4%,-0%,1%,4%. Averaged to 0%
Skyline: 21%,22%,23%,26%. Averaged to 23%
Ranger: 18%,19%,20%,22%. Averaged to 20%

I was happy to see such close results. I felt the variation too high at the skyline, so substracted 1% from the averaged results.

So, the coefficients were born Time to document stuff for newbies now...