Skip to content

Latest commit

 

History

History
168 lines (104 loc) · 5.79 KB

README.md

File metadata and controls

168 lines (104 loc) · 5.79 KB
Raw

Rankify

Open source ranking app for diverse activities like pool, fussball, table tennis, etc.

Contributing

Please read the CONTRIBUTING.md file for details on how to contribute to this project.

Development

Requirements

  • Node.js >=20.x
  • MongoDB >=7.x

Running the development server

First, update the .env.local file with your MongoDB URI.

To run the development server:

npm run dev

Before creating a pull request, make sure to run the tests:

npm run test

And to test your changes with the production server (important with NextJS):

npm run build && npm run start

Guidelines

Juste keep it clear and simple. KISS.

Stack

  • NextJS 14 with Page router
  • MongoDB
    • Drizzle (coming soon)
  • Zod (coming soon)
  • Vitest
  • Tailwind CSS
    • DaisyUI (for the design simplicity)

Deployment

Pushing to the main branch will trigger a deployment to Vercel.

Elo rating system

In order to keep a fair ranking, I implemented an Elo rating system. I built something new inspired by this article, which I adapted to an unlimited number of players in each team. If you want to understand why this ranking system is reliable, you can watch this video.

All of the elo implementation is in the elo module. Unit tests are also there to ensure the correctness of the implementation.

The elo module is following these rules:

  • Players start with a rating of 1000 (DEFAULT_RATING)

  • A difference of 400 (THRESHOLD) points between two players means that the weakest player as 1 out of 10 (POWER) chances to win the game.

  • The new rating of a player is calculated as follows. With

    • $R_{new}$ the new rating of the player
    • $R_{old}$ the formed rating of the player
    • $P$ the P-Factor
    • $K$ the K-Factor
    • $S_{p}$ the score of the player: 1 for win, 0 for loss
    • $E_p$ the winning expectation of the player against its opponent

    $R_{new} = R_{old} + K \cdot P \cdot (S_{p} - E_{p})$

Factors

  • The newer the player, the higher the KFactor. K starts at 40 and tends to 20 as the player plays more games. With:

    • $K$ the K-Factor
    • $x$ the number of games played

    $K = 20 \cdot(1 + \frac{1}{1+\frac{x}{10}})$

    K-Factor

  • A big difference in game scores will increase the PFactor. It starts at 1 and grows slowly. For example: a scrore of 8-0 will result in a PFactor of 2.83 while a score of 8-7 will result in a PFactor of 1. With:

    • $P$ the PFactor
    • $s1$ the score of player 1
    • $s2$ the score of player 2

    $P = \sqrt{|s1 - s2|}$

    PFactor

1 vs 1 situation

  • The expectation of a player is calculated based on its rating and the rating of its opponent. It represents the probability of winning against the opponent. With:

    • $E_{p1}$ the expectation of player 1
    • $E_{p2}$ the expectation of player 2
    • $R_1$ player 1 rating
    • $R_2$ player 2 rating

    $E_{p1} = \frac{1}{1 + 10^{\frac{R_2 - R_1}{400}}}$

    $E_{p2} = \frac{1}{1 + 10^{\frac{R_1 - R_2}{400}}}$

Team A vs Team B situation

  • The expectation of a team is calculated based on the average rating of the players in the team. Otherwise it follows the same rules as the 1 vs 1 situation. With:

    • $R_tA$ the average rating of team A
    • $R_tB$ the average rating of team B
    • $r_in$ the ratings of the players of team A and n the number of players in team A:
    • $r_jm$ the ratings of the players of team B and m the number of players in team B:

    $R_{tA} = \frac{r_1 ... r_i ... r_n}{n}$

    $R_{tB} = \frac{r_1 ... r_j ... r_m}{m}$

    The Expectation is calculated as follows, with:

    • $E_{tA}$ the expectation of team A
    • $E_{tB}$ the expectation of team B

    $E_{tA} = \frac{1}{1 + 10^{\frac{R_tB - R_tA}{400}}}$

    $E_{tB} = \frac{1}{1 + 10^{\frac{R_tA - R_tB}{400}}}$

Examples:

  • Team A has two players with ratings of: 1000 and 2000

  • Team B has two players with ratings of: 900 and 1300

  • Let's imagine that team A wins against team B.

  • For simplicity, let's take a value of 1 for P and 10 for K.

    $R_{tA} = \frac{1000 + 2000}{2} = 1500$

    $R_{tB} = \frac{900 + 1300}{2} = 1100$

    $E_{tA} = \frac{1}{1 + 10^{\frac{1100 - 1500}{400}}} = 0.9$

    $E_{tB} = \frac{1}{1 + 10^{\frac{1500 - 1100}{400}}} = 0.1$

  • Let's imagine that team B wins against team A.

    $R_{new-tA1} \newline = R_{old-tA1} + K \cdot P \cdot (1 - E_{tA}) \newline = 1000 + 10 \cdot 1 \cdot (0 - 0.9) \newline = 1000 - 9 = 991$

    $R_{new-tA2} \newline = R_{old-tA2} + K \cdot P \cdot (1 - E_{tA}) \newline = 2000 + 10 \cdot 1 \cdot (0 - 0.9) \newline = 2000 - 9 \newline = 1991$

    $R_{new-tB1} \newline = R_{old-tB1} + K \cdot P \cdot (1 - E_{tB}) \newline = 900 + 10 \cdot 1 \cdot (1 - 0.1) \newline = 900 + 9 \newline = 909$

    $R_{new-tB2} \newline = R_{old-tB2} + K \cdot P \cdot (1 - E_{tB}) \newline = 1300 + 10 \cdot 1 \cdot (1 - 0.1) \newline = 1300 + 9 \newline = 1309$

  • Let's imagine that team A wins against team B.

    $R_{new-tA1} \newline = R_{old-tA1} + K \cdot P \cdot (1 - E_{tA}) \newline = 1000 + 10 \cdot 1 \cdot (1 - 0.9) \newline = 1000 +1 \newline = 1001$

    $R_{new-tA2} \newline = R_{old-tA2} + K \cdot P \cdot (1 - E_{tA}) \newline = 2000 + 10 \cdot 1 \cdot (1 - 0.9) \newline = 2000 + 1 \newline = 2001$

    $R_{new-tB1} \newline = R_{old-tB1} + K \cdot P \cdot (1 - E_{tB}) \newline = 900 + 10 \cdot 1 \cdot (0 - 0.1) \newline = 900 - 1 \newline = 899$

    $R_{new-tB2} \newline = R_{old-tB2} + K \cdot P \cdot (1 - E_{tB}) \newline = 1300 + 10 \cdot 1 \cdot (0 - 0.1) \newline = 1300 - 1 \newline = 1299$

Conclusion: the rewards are higher if the weakest team wins.