Stunts Forum
ZakStunts  the Competition => Competition Archive => Competition 2009 => Topic started by: zaqrack on December 14, 2008, 02:47:20 PM

I like the bonus system. But I don't like bonus renormalization and evergrowing 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 selfbalancing 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?

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. :)

We will see in use. Since I don't like the multicar 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.

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 :)

Two questions come to mind:
1. Doesn't this undermine the whole point of the multicar 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.

1. Doesn't this undermine the whole point of the multicar 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 34 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.

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

After seeing Zak's new system, I felt the only way to really understand the implications would be to perform a fullfledged 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.
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 IndyPG 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 multicar 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 longabsent IMSA cars. Indy was the only repetition, but only after an 8race 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 multicar 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 longunused car by track design decisions has largescale 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, justforfun 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 nonpodium participations. That issue should, IMO, be addressed by only counting as "used" cars on the top half, or the top twothirds, of the scoreboard (only top 5 as BJ suggested seems a bit too restrictive).
4. Finally, the maxmin 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 multicar 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).

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.

Duplode is still a time millionaire. :D 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...

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.

I miss IMSA cars in ZakStunts.
IMSA + Melange cars have VIP tickets in USC. :D

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.

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

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... :)

Good job Zak, well done.

Yeah, really a good job! :)

It looks well balanced overall... good job indeed! :) Just one thing: expect the first race to be Speedgate's showcase... ;)

It seems quiete accurate, nice job Zak! And I agree with Duplode about Gate.

it all depends on the track :) but I don't mind an introduction in the first race...

I have done a simple graph showing how the car coefficients have changed so far in 2009.
Also added two extra data series:
AVR = average, which always equals to 14 with the new system, solving the ever growing bonuses problem from last year
STDEV = the standard deviation of the values. This month was the first time this value was lowered (but only slightly). I wonder whether this value will be always growing (which is sort of a problem), or will it stay in a healthy range. My bet is that it will alter between 20 and 22.

We have solved the problem of the evergrowing bonuses with this years rule modifications.
However, a new problem appeared. Take a look at the amount of negative bonuses (which is always the same as the sum of the positive) allocated this year:
ZCT92: 24
ZCT93: 26
ZCT94: 35
ZCT95: 37
ZCT96: 40
ZCT97: 45
ZCT98: 55
ZCT99: 60
The value is growing quite fast, which results in the polarization of the bonuses  some go skyhigh, while others are way under 0. Imagine if the podiumers would have all used the jaguar on ZCT98, now its "bonus" would be 39.
The reason for this is the system which raises the positive bonus by one each month, when the car was not used (for example the carrera currently got +8).
I do not want to interfere with this in this season, but this problem needs to be sorted out for 2010, else this will result in an automatic rotation of the car of the month, without the possibility for battle between cars. As some bonsues go way under zero, these cars are not used for long times. The bonuses keep growing and growing, thus further speeding this process, resulting in everbigger bonuses.
I see two possible ways to solve this problem:
1. Defining a peak value for the positive bonus. I would suggest +4 or +5. This would perhaps also solve another weak point in the system: kicking out popular cars for longer periods from being competitive, as some pipsqueaks not heading for the podium use it regularly, dropping its bonus. (the same reason why the only top 12 counts for the bonus changes rule was introduced)
With the current rules, if ZCT99 will be a fullferrari race, the amount for ZCT100 will be 67
With the +4 peak, if ZCT99 will be a fullferrari race, this amount would be: 47. The theoretical maximum with this recommendation (every car gets +4 except the one used by all the pipsqueaks) : 13x4=52. We are quite close to it :)
2. Furthermore, it might would be wise to start the bonuses for unused cars from +1 instead of +2. This would slow down the rotation a bit.
Your opinion and suggestions are welcome.
What do you think? Is this a good solution? Or is the problem even bigger than we think and we should react now, and not wait for the next season?

Yes, the bonuses are growing faster than expected. I think that's because when we debated the new system last year we were considering only eleven cars, and the three extra cars are making quite a difference.
The range reduction measures sound like a good way to tackle the problem. I'm not sure about the ideal set of numbers, though. +2...+5 would be quite similar to the current system up to about two races ago, so probably +2...+4 or +1...+4 are better choices. Between these two, it's hard to predict the different effects without a simulation. Maybe starting from +1 would not slow recovery times, but just keep all bonuses closer.
(PS.: a long while ago I thought about a different sort of renormalization, to be done every six months or so, that would keep the average of all bonuses unchanged, in order to not break the system, but would modify all bonuses so that the standard deviation is reduced, thus fitting the values into a desired range. I don't have the calculations with me right now, but after you do them the final formulas are a lot simpler than it sounds. But just changing the ranges is far less messy of a solution.)
Edit / PS2.: And I do not think there is real need of changing the scheme for this season. There are only three bonus updates left, and the percentages are not that imbalanced right now  other than for PG Ferrari, Z99 bonuses are fairly well matched. Besides that, if you plan to use average values from 2009 as starting values for 2010 it is probably better keep things as they are until the end of the season.

(PS.: a long while ago I thought about a different sort of renormalization, to be done every six months or so, that would keep the average of all bonuses unchanged, in order to not break the system, but would modify all bonuses so that the standard deviation is reduced, thus fitting the values into a desired range. I don't have the calculations with me right now, but after you do them the final formulas are a lot simpler than it sounds. But just changing the ranges is far less messy of a solution.)
Quite strangely, the standard deviation isn't rising so much as the summa of the bonuses do:
These are the values for this season so far:
15,23659562 15,38730746 18,58452624 20,54263858 20,34698995 21,71139368 20,76239204 21,59772068 21,28560366

I don't get it, but are the negative car bonuses equal to positive bonuses for not used cars? Is it means, if this/last month plus is 60, then LM002 and Jaguar get 60? If yes, then system isn't so smart.
I'd think it would be better to have constant negative bonus for podium cars. Let's say, 1st place gets 10%, 2nd 7%, 3rd 5%. Another solution  negative bonuses proportional to car selection value (taking in consideration top12; more people uses the same car  the bigger loss). Or even a mix of those two ideas.

Quite strangely, the standard deviation isn't rising so much as the summa of the bonuses do:
LOL... that makes my point moot anyway.
I don't get it, but are the negative car bonuses equal to positive bonuses for not used cars? Is it means, if this/last month plus is 60, then LM002 and Jaguar get 60? If yes, then system isn't so smart.
I'd think it would be better to have constant negative bonus for podium cars. Let's say, 1st place gets 10%, 2nd 7%, 3rd 5%. Another solution  negative bonuses proportional to car selection value (taking in consideration top12; more people uses the same car  the bigger loss). Or even a mix of those two ideas.
About constant negative bonuses: it used to be like that in 2008. Back then we used to have problems because the sum of positive bonuses used to be much larger than the sum of negative bonuses, and so the values grew boundlessly over time. Thus it was switched to the current zerosum scheme. Of course it could be made fixed bonuses with zerosum, but I guess that would make the arithmetics too messy (making it difficult to spread the bonuses equally and such).
The second idea might be used as a secondary factor, but IMO there is not much need of taking points off cars which failed to get a top3 position. In fact, that is already done, in a way, as such cars do not receive pluses.