Moving average leaderboard

Idea based on:

https://jonatanklosko.github.io/wca_statistics/moving_average

You may think of it as “how well the given person has been doing recently”. This computes exponentially moving average (EMA) of competitor averages. EMA is a weighted average, with weights decreasing exponentially, meaning that more recent values contribute more to the computed average. Here we use α = 0.8, meaning that the average emphasizes last ~5 results (weight of results older than 5 is around 1/3 in total and decreases quickly for particular results).

This could be used to create a leaderboard celebrating top players by showing their ability from all tracks they played while keeping the ability to easily climb the rankings when just joining.

Implementation ideas:
1. (easiest to explain to everyone)

Assign each player for each track a point score according to current F1 points system

1. 25 points, 2. 18 points, 3. 15 points etc.

Take an average according to the weighted moving average rules. Would personally recommend alpha value of 0.9. This means that yesterday (latest) track’s results would be worth 1x, 2 days ago 0.9x, three days ago 0.81x etc.

Expected results:
1. Facade 21.xx
2. Adelocossa 19.xx
(…)

2. (rewards more people)
Same as above but find a more inclusive scoring system. I would recommend FIS ski jumping points but if you want to stay in racing then I guess Indycar points system?

3. (accounts for times)
Set worst possible time = 1.1*winners time. People who didn’t finish or got worse get worst possible time. Score everyone with (winners time)/(their time). Easy to scale, for example ((score)-10/11)*1100 will give you everyone’s points in 0-100 scale.

For example today’s points (15.10) after rescale will look like:
Facade (6.812) 100
SMXT (6.815) 99,52
Adelocosa (6.816) 99,35
Rex (6.823) 98,23
Minerv1 (6.833) 96,62
(12) Me (6.854) 93,26
Someone behind (7.054) 62,26

Would recommend lower alpha to discard old results faster or setting lower worst possible time and rescaling the rescale (1.05, ((score)-20/21*2100) would double the differences). Of course the same moving average idea applies for every previous track