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Fri Dec 11, 2009 4:57 am
Even before I saw the new proposal from the F1 Commission, I have already started on working out a good points system.
There are many possibilities to explore, actually too many, hence I'll use the convenience of the proposed 25 points for the winner.
Here is an analysis of the old scheme (2009), the proposed scheme (2010), and my proposal (new):
[plc] <year> pts gain gain/loss gain/1st
[10] <2009> 00 0 000.0% 000.0% || <2010> 01 1 100.0% 004.0% || <new> 01 1 100.0% 004.0%
[09] <2009> 00 1 000.0% 010.0% || <2010> 02 1 050.0% 004.0% || <new> 02 1 050.0% 004.0%
[08] <2009> 01 1 100.0% 010.0% || <2010> 03 2 066.7% 008.0% || <new> 03 1 033.3% 004.0%
[07] <2009> 02 1 050.0% 010.0% || <2010> 05 1 020.0% 004.0% || <new> 04 1 025.0% 004.0%
[06] <2009> 03 1 033.3% 010.0% || <2010> 06 2 033.3% 008.0% || <new> 05 2 040.0% 008.0%
[05] <2009> 04 1 025.0% 010.0% || <2010> 08 2 025.0% 008.0% || <new> 07 3 042.9% 012.0%
[04] <2009> 05 1 020.0% 010.0% || <2010> 10 5 050.0% 020.0% || <new> 10 4 040.0% 016.0%
[03] <2009> 06 2 033.3% 020.0% || <2010> 15 5 033.3% 020.0% || <new> 14 5 035.7% 020.0%
[02] <2009> 08 2 025.0% 020.0% || <2010> 20 5 025.0% 020.0% || <new> 19 6 031.6% 024.0%
[01] <2009> 10 0 000.0% 000.0% || <2010> 25 0 000.0% 000.0% || <new> 25 0 000.0% 000.0%
(Apologies for the formatting but trust me I have tried my best to make it look good. On Excel it's much cooler)
I chose to analyze the schemes on two factors: gain vs loss and gain vs 1st
-- Gain vs loss represents the payoff for the risk you take to overtake ("loss" being your current points).
-- Gain vs first represents the effective gains on the maximum score, i.e. the winner.
I would try to find a solution that gives greater passing payoff overall, and also greater effective gains towards the higher positions. I believe this should help promote the fight for higher positions.
Note that the focus is on 6th position onwards, because, for obvious mathematical reasons, it is impossible to care about 7th and 8th given the points now extend to the 10th (unless we wanna explore like 40 points for the winner...).
There are a few problems with the proposed scheme (2010), IMO:
1. There's no reason the gap between 8th and 7th to be 2 while for 7th and 6th it is 1 (already pointed out earlier).
2. Except for the 4th position, the passing payoff is the same as the old scheme.
3. The effective gains for the 5th and 6th positions are lower than the old scheme.
My proposed scheme (new) should explain itself quite clearly, and while it is still not perfect, I believe it is the best you can get under the fixed variable of 25 points for the winner.
I also have an easier-to-remember version: 1,2,3,4,5,7,10,15,20,25. However the gain factors won't look as good, and the ratio among the top 3 will still be the same as the old scheme.
On the issue raised about points not being comparable to historical data, I am not too concerned about it. First thing is that it has happened before when the point system changed, although not so dramatically. Secondly, we can always normalize it to 10-for-the-winner when accumulating points across seasons.