[Resource] Ever wondered how much ELO you will win/lose?

Discussion in 'Card Hunter General Chat' started by Sasoo8, Feb 7, 2018.

  1. Sasoo8

    Sasoo8 Guild Leader

    Hey all! Sasoo8 here. Shoutout to gurel and Liquid_Paper for helping me with this project.

    In this post, I'll discuss how ELO/ratings works in this game. We all know that when a higher rating player wins, they will win fewer points than if the lower rating player wins. But exactly how many points will you win from a certain match? That depends on the ELO difference between the two players.

    I've spent a couple of weeks collecting data from hundreds of multiplayer matches, and from that, I created a chart to help you predict ELO wins/losses from the game. To demonstrate how to use the chart, I'll give you an example:

    Screen Shot 2018-02-07 at 5.12.40 PM.png
    (more complete chart at end of post)

    Scenario: A 1500 player is matched against a 1400 player.

    Prediction: Their ELO difference is 100. From the chart, if the higher ranked player wins, he will gain 12 ELO (stealing that ELO from the lower ranked player). Therefore, the end result would be 1512/1388 ELO for the two players.

    How about if the lower ELO player wins? There's a formula for this: If the lower ranked player wins, they will win 32-X points, where X is the Winner's Change that you see in the charts.

    In this example, if the 1400 player wins, he will steal 32-12 = 20 points from the 1500 player, with the end result being 1420/1480.


    Now you try: Suppose a 1732 ELO player plays a 900 ELO player. What happens when the lower ELO player wins?

    Prediction: The ELO difference is greater than 700. From the chart, the 1732 ELO player would be expected to win zero points if he wins, and regarding the opposite outcome, the 950 ELO player is expected to win 32-0 = 32 points if he wins. The end result will either be 1732/900 or 1700/932.

    General Conclusions:

    -The minimum ELO you can gain is zero, if you beat a player 700 points or more below you
    -The maximum ELO you can lose is 32, if you lose to a player 700 points or more below you
    -If two players of the same rating (or within 10 rating) plays, then the ELO gain or lost is 16 points
    -If the higher rating player wins, and he gets X points, then the lower player, if he wins, will get 32-X points

    But Sasoo, why is your chart incomplete? What about if the players have a 300 ELO difference?

    These are my results so far, and I'm still working on this project. I've collected hundreds of data points so far, but I still need to collect a few specific data points for games that have above 200-300 ELO difference, since those games are more rare.

    If you would like to help, here is a link to the full spreadsheet with the missing info highlighted, and i'll paste a picture below for reference. If you have a game that fits one of the missing data points, for example, a game that has a 205 ELO difference, I'll need you to write down the players' names and ELOs before and after the game, and send me a private message (preferably with screenshot proof).

    Screen Shot 2018-02-07 at 5.30.11 PM.png
     

    Attached Files:

    Last edited: Feb 8, 2018
    gurel2, Happenstance, tolkien and 6 others like this.
  2. Scarponi

    Scarponi Moderator

    Note: If a new player has never reached 1000 Elo the above won't hold for them and their data will corrupt your findings.
     
  3. Sasoo8

    Sasoo8 Guild Leader

    That's a great point Scarponi, I forgot to mention that for new players under 1000, their ELO ratings work very differently.

    Namely, they gain a lot more and lose a lot less, mainly to prevent Negative ELOs and to make sure that new players reach ~800 ELO in 5-10 games instead of 30-40 (if they were to gain 32 max elo per game).

    For example, if a zero ELO player wins against Gary (usually around 600 ELO), they gain 168 rating instead of the expected 31, and Gary does not get the 168 ELO stolen from him.
     
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  4. Sasoo8

    Sasoo8 Guild Leader

    Screen Shot 2018-02-08 at 12.36.33 PM.png
    More data just came in, so here's an updated chart
     
    ParodyKnaveBob likes this.
  5. winner

    winner Mushroom Warrior

    nice job sasso
     
    ParodyKnaveBob likes this.
  6. Sasoo8

    Sasoo8 Guild Leader

    Another application of knowing how ELO changes works is that you get an idea of what winrate you need to have in order to maintain a given rating.

    Suppose you want to see how hard it is to maintain a 1800 ELO:

    We know that for an 1800 ELO player, in order to maintain his current ELO, he must:

    Win 50% versus another 1800 player (win=+16 points, lose=-16 points)
    Win 62.5% versus a 1700 player (win= +12 points, lose= -20 points)
    Win 75% versus a 1600 player (+8, -24)
    Win 84.4% versus a 1500 player (+5, -27)
    Win 90.6% versus a 1400 player, (+3, -29)
    and so on!

    We also know that the pool of players around 1700-1800 is low, and most of the opponents will come in the 1400-1600 range. Thus, we can assign relative weights to the above percentages:

    For example, from my experience:
    5% of the opponents will be around 1800
    15% of the opponents will be around 1700
    20% of the opponents 1600
    25% 1500
    20% 1400
    15% Below 1400 (including cardotron)

    Using these relative weights, you arrive at a win percentage of 80%, which correlates with my personal experience. On good seasons where I have a 75-80% winrate for the whole month, I usually can maintain a 1800 rating for at least a couple of weeks.

    Repeating the same calculations for other ELOs of interest, with some adjustment on the frequency of opponents at different ELOs, we arrive at:

    1500: 56% winrate
    1600: 60% winrate
    1650: 66% winrate
    1700: 71% winrate
    1750: 76% winrate
    1800: 80% winrate
    1850: 85% winrate
    1900: 88% winrate
    1950: 91% winrate
    2000: 94% winrate

    These numbers correlate with real life examples:
    (1) Pappas was able to maintain an ELO of ~1900 in February 2018, with a peak ELO of 1966. His season winrate was 89%, hitting a monster 36-streak to get the peak ELO.
    (2) Gameleader hovered between 1650-1750 in February 2018, with a peak ELO of ~1790. His season winrate was 71%
    (3) krystalis1 was stable at mid 1600's in December 2017. His season winrate was 68%

    One of the most common questions that new players often ask is: "what ELO and winrate should I aim for to join a decent guild"? Most people answer with good estimates, and I usually answer with 1500+ with the potential to hit 55% winrate consistently, but now I have numbers to back me up!

    I'm going to finish with a nice rule of thumb that summarizes the findings:

    If you want a 1600, aim for a 60% winrate. If you want a 1700 , aim for a 70% winrate. If you want a 1800, aim for a 80% winrate!
     
    Last edited: Mar 2, 2018

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