I created an infographic that explains the basic of the Competitive Racing License. I'm looking for feedback in the following areas:

* Is there anything that is unclear?

* Is there anything that is misstated?

* Is there anything missing?

Rating System FAQ

What is the rating system?

ProjectCARS 2 rates drivers in two main aspects: safety and skill. See the competitive racing license infographic above for an overview.

How does the skill rating system work?

We don't have specific implementation details, but we know the system is based on the Elo rating system. This same system is used in chess, baseball, and basketball. For example, FiveThirtyEight (a notable statistics based blog) applied Elo rating to basketball, starting back in 2015.

How might an Elo rating system work in pCARS 2?

Elo rating systems assign a rating to players based on their performance against other players in matches. The key thing to remember is that the result is a player's ratingrelative to other players, not a game score, and definitely not a traditional championship points system.

Because this is an Elo rating system, we can state some basic things about the system:

1) For a given round, there is a setmaximumnumber of points that can be acquired.

2) Placing better than players that have ahigherrating will earn youmorepoints.

3) Placing better than players that have alowerrating will earn youfewerpoints.

4) Placing worse than players that have ahigherrating will cause you to losefewerpoints.

5) Placing worse than players that have alowerrating will cause you to losemorepoints.

6) In a given round, your finishing position will be compared toall players in a lobby, which will result in anet impact to your rating.

How is my rating affected, based on my finishing order

Keeping in mindall sixof the points above, this matrix reflects how your rating will be impacted by finishing better or worse than higher/lower rated competitors. Keep in mind that you are compared toall playersin a lobby, so just because you beat a single high ranked player doesn't mean you get ++points.

Does my finishing order impact my safety rating?

Safety rating is separate from skill rating. You can finish last place in ever race and still have a good safety rating. Your safety rating is impacted by things like contact with other racers and going off-circuit.

Can you show me what a typical Elo rating would look like for a race?

Sure! Elo rating systems are pretty well established, but there's quite a bit of math involved. If you get bogged down, just keep going and try to follow the main steps involved.

Example Rating Outcome

Because Elo rating systems work by comparing individual players, your finishing position will be compared toall players in a lobby. This means that for any given race, there will beN-1 comparisons made, whereNis the number of players in the lobby.

For example, let's look at a hypothetical race finish for the following players:

1st - John 900

2nd - Zed (you) 1,200

3rd - Jane 1,300

This finishing order presents an interesting conundrum. Zed has finished better than a higher rated player, but worse than a lower rated player. How should Zed's rating move, up or down? Let's do the comparison.

In this scenario, there are three players in the lobby, so there will be two comparisons (N-1 = 2).

Elo Overview

Before we do the math, let's briefly discuss how Elo rating systems work. In an Elo rating system, comparisons are performed between two players. The system "expects" the player with the higher rating to win. The difference in their ratings represents the probability that the higher rated player will win. Put another way, the higher the spread, the greater the expectation that the higher rated player will win.

The outcome of an Elo "game" comparison is a new Elo rating for each player. When making this comparison, we must decide the absolutely maximum number of points that any player will be awarded for winning. This number is called the K-factor.

On to the math!

Reference: How to Calculate Elo-Rating

K-Factor

Caveat: we don't know this number for certain, but we think it's 12.

K = 12 / 2 (divide by two because we want to spread out the points awarded over both comparisons).

Caveat: we don't know for certain if the K-factor is divided up like this.

Zed vs John

We start by assigning our player's ratings to aRating variable.

Ra (Zed) = 1,200

Rb (John) = 900

Step 1:Transform the ratings for comparison (this makes the comparison math simpler).

TRa = 10^(Ra/400) = 1,000

TRb = 10^(Rb/400) = 177.8279410039

Step 2:Calculated theExpected rating.

ERa = TRa / (TRa + TRb) = 0.8490204428

ERb = TRb / (TRa + TRb) = 0.1509795572

Step 3:Calculate net change in Elo rating.

John gets S=1 because he is the winner; Zed gets S=0

SRa = 0

SRb = 1

(Ra + K × (SRa - ERa)) - Ra = -5.0941226567

(Rb + K × (SRb - ERb)) - Rb = 5.0941226567

Step 4: Review impact to Zed's rating.

Zed loses -5.0941226567.

Zed vs Jane

Ra (Zed) = 1,200

Rb (Jane) = 1,300

Step 1:Transform the ratings for comparison (this makes the comparison math simpler).

TRa = 10^(Ra/400) = 1,000

TRb = 10^(Rb/400) = 1,778.2794100389

Step 2:Calculated theExpected rating.

ERa = TRa / (TRa + TRb) = 0.3599350002

ERb = TRb / (TRa + TRb) = 0.6400649998

Step 3:Calculate net change in Elo rating.

Zed gets S=1 because he is the winner; Jane gets S=0

SRa = 1

SRb = 0

(Ra + K × (SRa - ERa)) - Ra = 3.8403899988

(Rb + K × (SRb - ERb)) - Rb = -3.8403899988

Step 4: Review impact to Zed's rating.

Zed gains 3.8403899988.

Total rating impact

If we sum up the impact to Zed's rating, we see that the result is a net loss of points: -1.2537326579.

Caveats

There are a couple of things we don't know for certain:

1) What is the K-factor used? (K-factor is the theoretical maximum possible points to be a won/lost) We feel pretty confident this is 12.

2) When computing the result for a single race how are multiple players compared? Specifically, is the K-factor treated as fractional, or is the total K value used for each comparison? Most Elo systems treat the K-factor as the maximum points for a "match", so I would assume this is a fractional value, otherwise winning in a large lobby could net you HUGE points... or cause a HUGE loss of points if you finish poorly.

Elo Calculator

You can use an online calculator called Turo.io to perform the Elo Math yourself. Just remember:

- Perform the comparison once against all competitors.

- Remember to set the player count.

- Set the S variable accordingly based on finishing position (win/loss)

ELO Calculator

Updates

2017-10-31 Update: Changed color of +/- symbols to match color of rating type.

2017-11-13 Update: Added rating system details.

2017-11-29 Update: Added calculator