# Improving on the GT Sport FIA points system

Discussion in 'Gran Turismo Sport' started by Skinny McLean, Dec 4, 2019.

1. ### Skinny McLean

Messages:
19
Not all GT Sport FIA championship participants are satisfied with how the points system works, especially not among top split players. There has been suggestions from fellow forum members for how to make it more fair, and while they did minimise the inter-split point overlap, I feel the proposed models still suffer from the same problem as the official one, namely that the points awarded in higher splits falls-off too fast per finishing position as opposed to in lower splits where the fall-off is too slow. To help further the discussion I will start by introducing some terminology and give a short description of how the points system works.

The points p given to finishing position n in a lobby with an average Driver Rating of d can be determined by an equation of this form:

$image=https://latex.codecogs.com/gif.latex?p(n,d)=&space;P(d)&space;\cdot&space;f(n)&hash=94f21d60736ae107b58544070978770a$

where function P gives the maximum points of the lobby, and function f scales the points in the lobby according to position. In the old system both P and f were linear functions, whereas in the newly introduced system P is exponentially decaying.

The main focus of this post, however, is on the fall-off function f:

$image=https://latex.codecogs.com/gif.latex?f(n)&space;=&space;s&space;\cdot&space;(n-1)&space;+&space;1&hash=9e62f9bc0f5e9fff97796955e55d94f4$

where the parameter s (also called the slope or gradient) is a negative real number. In the current system s is ca. -79.16/19 * 1/100 = -0.04166

My suggestion is to make the fall-off function f also dependent on d:

$image=https://latex.codecogs.com/gif.latex?p(n,d)=&space;P(d)&space;\cdot&space;f(n,d)&hash=270b7ac34d12487433b75bcf493e7fe3$

by replacing s such that

$image=https://latex.codecogs.com/gif.latex?p(n,d)=&space;P(d)&space;\cdot&space;\left(&space;1&space;-&space;\frac{1-R\cdot&space;\frac{d}{75000}}{19}&space;\cdot&space;(n-1)\right)&hash=bbda0388336a726ae4cac7f267540331$

where parameter R is the ratio of last place to first place points in a 75000 DR lobby (e.g. if R = 1/2 position 20 would get half the points of the winner, while in a 50000 DR lobby 20'th would only get 2/3*1/2 = 1/3 of 1st points, and so forth). I feel that the sweet spot for R is in the 0.80 to 0.85 interval.

Here are some plots of a modified points system (I haven't changed the max. points function) with R at different values:
And for comparison @Jomas' and @khkenni's system (notice how slow the points falls-off in lower splits):

What do you guys think - and what value of R do you think works best?

Last edited: Dec 4, 2019