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How I work out the car allocation

Author Topic: How I work out the car allocation  (Read 42469 times)

Offline Wally

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How I work out the car allocation
« on: October 03, 2014, 09:01:41 PM »
Grab some popcorn and settle back...

Firstly, I averaged the world record times on RSR rank for each of the cars at a good variety of tracks. Then I scaled all the averages in relation to the Exige 240R S3, out of 100, so I could get a percentage of how much slower each car was than the Exige 240R S3. You have to use a percentage like this, to account for different length tracks, like Magione to Nords. This is something I used with the NKP ballast calculations. For example, on Nords a 24 second difference in lap times means you have to slow a car down by 5% of the lap time, while a 3 second gap at Magione is also a 5% slowdown. You'd end up with the same car with these gaps, because it's the same percentage.

So now I have a ranking of all the cars. This is how much slower each car is than the Exige 240R s3, in seconds, over 100 seconds.

 
Exige 240R s30
Evora S S20.5
Exige Scura0.6
Exige S Roadster1
M3 E92 Step 11.4
Evora S1.7
Exige 240R1.8
M3 E921.9
BMW 1M2.4
Elise SC S22.7
Elise SC S13.1
Elise SC3.4
Z4 E89 S15
Z4 E896.4
At the end of each round, I average each driver's fastest laps in each race. If a driver only completed a few laps before DNF'ing, say, that race is excluded. I then toss out anyone who's average is way off the others, so the results don't get skewed.

Then I scale those average fastest lap times so that the slowest is 100 seconds, to account for different length tracks as explained above, so I can work out what percentage each car is slower.

I might get numbers like this:

 
Flattop
100.000
Grubbet
98.293
Dave O
98.080
Schmittez
97.835
Phil
97.452
GWyar
97.427
RPM
97.412
Rob [Team MRT]
97.280
Bacchulum
97.243
Imperious
97.236
Peter Reid
97.013
Krahl
96.937
Vipergod [Team MRT]
96.928
Dick Forrest [CramDick Racing]
96.761
Enforcer-J
96.709
Guybrush Threepwood [Achilles Heels]
96.534
Freezer
96.520
EdWood
96.476
Wally [TKO Racing]
96.418
Ysu [TKO Racing]
96.008
Marty [Achilles Heels]
95.573
Mopz
95.444
Then I take the median of those times - the number where half the lap times are slower and half are faster. This is 96.98 in the example above. Anyone who was faster than 96.98 secs needs a slower car; anyone who was slower than 96.98 secs needs a faster car.

So in the example above, Phil needs a car which is 97.452 - 96.98 = 0.48 seconds slower than the car he currently has. He got that lap time in a BMW 1M, so he needs a car which is 0.48 seconds slower than a BMW 1M, which in that first table is the Exige 240R (the real calculation uses more decimal places than the rounded numbers I've shown here).

Another example: Mopz needs a car which is 95.444 - 96.98= 1.53 seconds slower than his Exige 240R. From the first table, this gives him the Elise SC S1.

Looking at the car rank above, you can see why lots of people end up in the Elise SC. Once you need a car that's between 3.4 (Elise SC) and 5 (Z4 E89 S1) seconds slower, which is quite a large gap compared to the other car differences, you end up in the Elise SC zone.
“You can please some of the people all of the time, you can please all of the people some of the time, but you can’t please all of the people all of the time”

Offline Bacchulum

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Re: How I work out the car allocation
« Reply #1 on: October 03, 2014, 09:20:04 PM »
If you use a Taylor Series and an Exponential mapping you can refine the result by an order of magnitudes. ;)

But that would make no difference as the car differences are set. :-\

2+2=√16

Offline Guybrush Threepwood

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Re: How I work out the car allocation
« Reply #2 on: October 03, 2014, 09:28:49 PM »
Seems fairly solid to me.

The only thing I can't figure out is how so many people of varying abilities end up in the standard Lotus when it is only 3 tenths on average quicker than the S1?

Offline Wally

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Re: How I work out the car allocation
« Reply #3 on: October 03, 2014, 09:43:59 PM »
If you use a Taylor Series and an Exponential mapping you can refine the result by an order of magnitudes. ;)

But that would make no difference as the car differences are set. :-\

Coming from Aleph Null, I have no idea what you're talking about :)

The only thing I can't figure out is how so many people of varying abilities end up in the standard Lotus when it is only 3 tenths on average quicker than the S1?

I suppose the slice between the SC and the S1 is small, only 0.3 seconds, yet we still have ended up with 3 guys in that car.
“You can please some of the people all of the time, you can please all of the people some of the time, but you can’t please all of the people all of the time”

Offline Guybrush Threepwood

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Re: How I work out the car allocation
« Reply #4 on: October 03, 2014, 10:16:47 PM »
If you use a Taylor Series and an Exponential mapping you can refine the result by an order of magnitudes. ;)

But that would make no difference as the car differences are set. :-\

Coming from Aleph Null, I have no idea what you're talking about :)

The only thing I can't figure out is how so many people of varying abilities end up in the standard Lotus when it is only 3 tenths on average quicker than the S1?

I suppose the slice between the SC and the S1 is small, only 0.3 seconds, yet we still have ended up with 3 guys in that car.

Aren't there 6 guys in that car for Silverstone?

Offline Wally

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Re: How I work out the car allocation
« Reply #5 on: October 03, 2014, 11:17:09 PM »
I meant the S1.
“You can please some of the people all of the time, you can please all of the people some of the time, but you can’t please all of the people all of the time”

Offline Bruce

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Re: How I work out the car allocation
« Reply #6 on: October 04, 2014, 10:13:19 AM »
Impressive on many levels Wally.  Thanks.
"I refuse to be what you call normal." Lemmy Caution

Offline Wally

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Re: How I work out the car allocation
« Reply #7 on: October 04, 2014, 10:58:04 AM »
Impressive on many levels Wally.  Thanks.
Thanks. I've been thinking about these things for many years now  8)
“You can please some of the people all of the time, you can please all of the people some of the time, but you can’t please all of the people all of the time”

Offline Bird

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Re: How I work out the car allocation
« Reply #8 on: October 04, 2014, 12:52:54 PM »
Thanks, Wally, I've actually enjoyed reading this!  I thought it might be something like this - but I've certainly not systemised it.  Great job!

And I've got no idea what Bacchulum is talking about, either ;)

Offline Bacchulum

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Re: How I work out the car allocation
« Reply #9 on: October 04, 2014, 02:02:25 PM »
You convert your function into an infinite sum, then take the derivative of those terms.
That's your Taylor Series. 8)
The exponential mapping was a joke. :P :P


 8)

2+2=√16

Offline Wally

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Re: How I work out the car allocation
« Reply #10 on: October 04, 2014, 03:08:47 PM »
You convert your function into an infinite sum, then take the derivative of those terms.
That's your Taylor Series. 8)
The exponential mapping was a joke. :P :P


 8)

Right. Gotcha now.
Not.
It's ringing vague bells from my uni days.
“You can please some of the people all of the time, you can please all of the people some of the time, but you can’t please all of the people all of the time”

Offline Bacchulum

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Re: How I work out the car allocation
« Reply #11 on: October 04, 2014, 04:10:41 PM »
I never did uni.
I just read maths for fun. 8)

2+2=√16

Offline Freezer

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Re: How I work out the car allocation
« Reply #12 on: October 04, 2014, 04:17:42 PM »
I just read maths for fun. 8)
Well its just getting a little weird now....!

Offline marty

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Re: How I work out the car allocation
« Reply #13 on: October 04, 2014, 05:55:07 PM »
Looks like you have done all the research Wally great effort thanks for that. I still think more could be done to balance the front end of the field especially all those in the elise sc in both last round and this round. I wonder if balancing vs the fastest and also others in the same car to some extent may be better then the medium or the slowest person.


Krahl   Elise SC   Elise SC 96.937
Guybrush Threepwood [Achilles Heels]   Z4 E89 S1   Z4 E89 S1 96.534
Freezer   Elise SC   Elise SC 96.520
EdWood   Elise SC   Elise SC 96.476
Wally [TKO Racing]   Elise SC    Elise SC 96.418
Ysu [TKO Racing]   Elise SC    Elise SC 96.008
Marty [Achilles Heels] Elise SC    Elise SC 95.573

Between me and Krahl there was 1.34 seconds and so even if you gave him a boost to a 1M that is 1 second and a e92 would be 1.5 seconds so it would bring our lap times much closer. Even Guybrush in the z4 is 1 second off my pace and he was on it pretty much all the way so he doesnt really have a chance if we have these 2 cars against each other for outright race pace.

Exige 240R s3   0
Evora S S2    0.5
Exige Scura    0.6
Exige S Roadster    1
M3 E92 Step  1   1.4
Evora S1 .7
Exige 240R    1.8
M3 E92           1.9
BMW 1M    2.4
Elise SC S2   2.7
Elise SC S1   3.1
Elise SC   3.4
Z4 E89 S1    5
Z4 E89   6.4

I still think the z4 has too large a gap to the next car so its not a great option as If Guy and me were both in this wed still be about .6 off Bird but as Im slower then Guy id be more like 1 second slower then Bird and .5 off Guy.

So the way Id see it is it would be better if say both me and Guy were in the SC or even just have him in the SC and me in the s1, then have all others in cars that would closest match Guys pace which is probably the one quickest if you compare his car and lap pace. He was in a car 1.6 slower then me but was only 1 sec slower so I should really have around .6 or .5 on him and then base everyone in a car that would closest match guys pace.

What do you think of that way of dealing with it Wally?

Offline Gratulin

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Re: How I work out the car allocation
« Reply #14 on: October 04, 2014, 06:11:24 PM »
Ballast!

 

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