OT: WCC Championship formula - The Technical Forum Archive (2024)

wawawa

• 

Member

• 4,315 posts
• Joined: May 02

Hi,

I'm aware of the thread in the RC discussing ways of eliminating/mitigating team orders. I thought there might be a way to do it by fiddling with the formula for calculating the WCC points. It got a little bit mathematical and it is still half-baked, so I thought I'd put it here. If we can come up with something clean, we could add it to the RC thread.

Here is my idea. Its a bit long - sorry!

Suppose the drivers X and Y score x and y points respectively.

Currently, the WCC points are calculated as WCC(x,y) = x + y.

This means that teams can order two drivers to swap positions - affecting the WDC points - without affecting the WCC points.

Let us keep the current points system fixed - the Readers Comments are full of suggested points changes.

Can the formula for WCC(x,y) be changed so that team orders could harm the WCC points?

Consider WCC(x,y) = maximum{x + y, x * y}

For most teams, x * y should be much bigger than x + y. The maximum is there in case one driver has very few points, e.g. Sato this year.

For simplicity, assume that x, y are "large enough" so that x * y > x + y.

Given that the drivers score a total of x + y points, the WCC score would be maximized when x and y were equal, i.e. both (x+y)/2 to the nearest integer.

Now, team orders used to bump up the WDC would affect the WCC and vice versa.

Are these two effects "equal"? I haven't a clue. I don't even know how to pose this question formally. But let's try this formula out on the 2000 Championship:

1. Ferrari = 6696
2. McLaren = 6497// I haven't factored in the penalty for Austria
3. Williams = 288

So far so good - this is the same order as the original Championship. Now comes the screwy part:

4. Jordan = 66 = 11 * 6 (was 6th originally)
5. BAR = 51 = 17 * 3 (was 5th originally)
6. Benetton = 36 = 18 * 2 (was 4th originally)

That's the trouble with a non-linear expression like x * y... The other positions are the same...

7. Arrows = 10 = 5 * 2
8. Sauber = 6 = 6 + 0 (6 * 0 would be bad here)
9. Jaguar = 4 = 4 + 0

Well, this Championship looks very skewed in terms of raw points, but what the hell - only the relative positions count.

Observations so far: the non-linear formula means that nasty surprises can occur.

E.g. suppose Sauber has NH = 5, FM = 3 for a total of 5 * 3 = 15 points, and suppose Jordan has GF = 10, TS = 1 for a total of 10 + 1 = 11 points.

Now, if Sato comes sixth and the others don't score, Jordan suddenly jump to 10 * 2 = 20 points. Somehow, I can't see this being acceptable.

One more issue, this time with the 2001 Championship as an example. Jordan had three drivers who scored points for them: HHF (6), JT (12), JA (1).

The above formula, if extrapolated in a natural way to 3 drivers, gives 6 * 12 * 1 = 72 points, putting Jordan in 5th (as they were in the original Championship). If JA had scored 2 points, however, Jordan would have 144 points, beating Sauber's 108 = 12 * 9 points.

Perhaps the formula should be:

WCC(x,y) = max{x+y, square-root(x*y)} for 2 drivers

WCC(x,y,z) = max{x+y+z, cube-root(x*y*z)} for 3 drivers

etc.

You see what I meant about things getting ugly

Looking forward to your ideas and suggestions/criticisms ;)

desmo

• 

Tech Forum Host

• 28,266 posts
• Joined: January 00

wawawa

• 

Member

• 4,315 posts
• Joined: May 02

Originally posted by desmo
I am amazed the lengths people will go trying to keep MS and Ferrari from repeating. Maybe it would make better sense just to have the other teams develop better cars instead. If you can't beat 'em, fiddle with the rules!

Yeah, its a long weekend... Cheers!