A fair scoring system in racing competitions

(Originally posted on Monday, 17 May 2021)

While playing various computer racing games I had been using my own scoring system (in a spreadsheet, just for fun) that awarded points for the top-10 places. Old scoring systems, both in computer games and in real life competitions, awarded points for only top-6 places. I thought that my scoring system was “fair”, but I have just realised that it wasn't quite like that.

Thanks to my in-depth analysis of the current FIA scoring system (points: 25, 18, 15, 12, 10, 8, 6, 4, 2, 1) I have finally realised what a fair scoring system should be like. By the way, the current FIA scoring system is NOT fair/consistent!

In the end I have created a new, near-perfect scoring system that is very easy to remember and use! Points: 30, 22, 16, 12, 9, 7, 5, 4, 3, 2, 1.

What is a “fair scoring system” in racing competitions? It’s a scoring system where the same “rules” apply to ALL the places that are awarded points. Which means …?

Let’s analyse two examples from a fictional season with 10 races, but with the current FIA scoring system (points: 25, 18, 15, 12, 10, 8, 6, 4, 2, 1).


Example I.

Ia. Driver A (8 wins and 2 non-finishes) vs. driver B (10 second places).

Obviously the driver A should win the title because the 2 non-finishes could have been caused by his opponents and/or by a mechanical failure of his car and the driver B was not able to win even a single race! This rule is true in the FIA scoring system:

Driver A: 8 * 25 points = 200 points
Driver B: 10 * 18 points = 180 points

Ib. Driver A (8 second places and 2 non-finishes) vs. driver B (10 third places) + all the races won by 1 driver (the winner of the title).

The rule is exactly the same: the driver A should finish second because the 2 non-finishes could have been caused by his opponents and/or by a mechanical failure of his car and the driver B was not able to finish second even in a single race! This rule is NOT true in the FIA scoring system:

Driver A: 8 * 18 points = 144 points
Driver B: 10 * 15 points = 150 points

So, the FIA scoring system is inconsistent on different “steps of the ladder” and this is why it’s not fair.


Example II.

IIa. Driver A (6 wins and 4 non-finishes) vs. driver B (10 third places) + all the remaining wins and all the second places evenly split between several different drivers (overall they are all behind the drivers A and B).

Obviously the driver A should win the title because the driver B was not able to finish SECOND even in a single race! This rule is true in the FIA scoring system, but only thanks to a tiebreaker:

Driver A: 6 * 25 points = 150 points
Driver B: 10 * 15 points = 150 points

The number of wins would be the tiebreaker.

IIb. Driver A (6 second places and 4 non-finishes) vs. driver B (10 fourth places) + all the remaining second places and all the third places evenly split between several different drivers (overall they are all behind the drivers A and B) + all the races won by 1 driver (the winner of the title).

The rule is exactly the same: the driver A should finish second because the driver B was not able to finish THIRD even in a single race! This rule is NOT true in the FIA scoring system:

Driver A: 6 * 18 points = 108 points
Driver B: 10 * 12 points = 120 points

So, the FIA scoring system is inconsistent on different “steps of the ladder” and this is why it’s not fair.

Please notice that even if you don't agree with the rules above and you apply a different rule then the rule (any rule) should be true for all the “steps of the ladder”. I gave the 2 rules above as EXAMPLES, just to show you that the FIA scoring system is inconsistent on different “steps of the ladder”, which proves that it’s not fair.


How to create a fair scoring system in racing?

Obviously the starting point should be the difference between the first and the second place (depending on various factors), but all the following places have to roughly maintain the ratio between the first and the second place. Obviously the difference between the first place and the third place should also be roughly maintained (by default) for all the following pairs of drivers being two places apart (2 and 4, 3 and 5, 4 and 6, …). It should give you a near-perfect scoring system – the points are total values, so there will always be some slight “fluctuations”, especially at the lower places. Please notice that such a fair scoring system should be consistent on every “step of the ladder”, no matter what rule (of comparing drivers) you invent/analyse.

My near-perfect scoring system that is very easy to remember:
points: 30, 22, 16, 12, 9, 7, 5, 4, 3, 2, 1

Differences between places: 8, 6, 4, 3, 2, 2, 1, 1, 1, 1
Number of places that are awarded points: 11
The sum of points for all the places: 111

Points in reference to the previous place: 1.364, 1.375, 1.333, 1.333, 1.286, 1.400, 1.250, 1.333, 1.500, 2.000.
Points in reference to the place two places behind: 1.875, 1.833, 1.778, 1.714, 1.800, 1.750, 1.667, 2.000, 3.000

Verification:

Ia. Driver A (8 wins and 2 non-finishes) vs. driver B (10 second places).

Driver A: 8 * 30 points = 240 points
Driver B: 10 * 22 points = 220 points

Ib. Driver A (8 second places and 2 non-finishes) vs. driver B (10 third places) + all the races won by 1 driver (the winner of the title).

Driver A: 8 * 22 points = 176 points
Driver B: 10 * 16 points = 160 points

IIa. Driver A (6 wins and 4 non-finishes) vs. driver B (10 third places) + all the remaining wins and all the second places evenly split between several different drivers (overall they are all behind the drivers A and B).

Driver A: 6 * 30 points = 180 points
Driver B: 10 * 16 points = 160 points

IIb. Driver A (6 second places and 4 non-finishes) vs. driver B (10 fourth places) + all the remaining second places and all the third places evenly split between several different drivers (overall they are all behind the drivers A and B) + all the races won by 1 driver (the winner of the title).

Driver A: 6 * 22 points = 132 points
Driver B: 10 * 12 points = 120 points

Practically flawless scoring system that is very easy to remember! Boy, I am proud of myself!

PS. You can create many different fair scoring systems in racing competitions, each with a particular ratio between places and a particular number of places that are awarded points. The problem is that the number of points for the first place rises very quickly, so with every additional place that is awarded points, the system is harder to remember and use. This is why I am so proud of myself – the scoring system that I have created is very easy to remember and use!