Car bonuses in 2009

[Krys TOFF]

Good job Zak, well done.

[Mark L. Rivers]

Yeah, really a good job! 

[Duplode]

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

[Chulk]

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

[zaqrack]

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

[zaqrack]

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.

[zaqrack]

We have solved the problem of the ever-growing 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 ever-bigger 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 full-ferrari race, the amount for ZCT100 will be -67
With the +4 peak, if ZCT99 will be a full-ferrari 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?

[Duplode]

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.

[zaqrack]

(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

[Mingva]

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.

[Duplode]

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 zero-sum scheme. Of course it could be made fixed bonuses with zero-sum, 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 top-3 position. In fact, that is already done, in a way, as such cars do not receive pluses.