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To your right, you will see the top 5 ranked players for a particular race in NAF tournaments.  What does this mean?

Each coach starts with a Coach Rating of 150 for every official Blood Bowl roster. If you attend a NAF sanctioned event using a particular race, your NAF ranking for that race is then activated. When you win a game, you gain Coach Rating. When you lose a game your Coach Rating is reduced. The neat part is that your Coach Rating is adjusted based on the how tough the opponent was. For example, if you lost to a very good coach then you lose less Coach Rating than if you lost to a worse coach. If you play at NAF sanctioned tournaments, then the larger the tournament, the larger the potential change in your CR.

Coach rating is calculated by a complex formula and isn’t for the faint of heart. It’s based on the ELO ranking system. Here is the formula as it stands:

Win Probability = 1/(10^((Opponent’s Rating-Your Rating)/150) + 1)

This probability is then used to recalculate each player’s rating after the match. In the equation below, players receive 1 point if they win the match, 0 if they lose, and 0.5 for a draw. Players’ new ratings are determined as follows

Player’s New Rating = Player’s Old Rating + (K-Value * (Scoring Points – Player’s Win Probability)).

The number of NAF coaches in the tournament determines K-Value in this equation. The formula is:

K-Value = (Square Root (Min(Number of NAF coaches,MAX)) ) * 2

The MAX value is the maximum number of coaches that can contribute to the K-value.  The Majors have a MAX of 60 coaches, and are treated as always having 60 if they have fewer, while non-majors have a MAX of 32.

You can find the current rankings on the Members Area, and analysis of the games and tournament information on the Tableau page.

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19 thoughts on “Rankings

  1. David Olorenshaw

    I believe the line
    Player’s New Rating = Player’s Old Rating + (K-Value * (Scoring Points x Player’s Win Probability))
    should read
    Player’s New Rating = Player’s Old Rating + (K-Value * (Scoring Points – Player’s Win Probability))

    Reply
  2. Phoenix11

    What does the “x” mean in the formula?
    Is it a times? Because there’s already a “*”, and it’s strange…

    How do you calculate the “Scoring points”?

    Thx

    Reply
  3. sann0638 Post author

    Scoring points is 1, 0.5, or 0, and I think you are right about it being a minus rather than a multiply. I’ve changed it for the moment and will double check. Thanks for reading!

    Reply
  4. Darkson

    I think the K value is meant to read “K-Value = Square ROOT (Number of NAF coaches) * 2”, otherwise that would give the ARBBL 2014 a K-value of 2888! 😉

    Reply
  5. KFoged

    “Win Probability = 1/(10^((Opponent’s Rating-Your Rating)/150))) + 1)”

    So we have 3 “(” one way and 5 “)” the other way 😉

    Reply
      1. Catto

        I think that the rankings for two players of equal ranking that make a draw are expected not to change. Applying this equations they both increase.

        Reply
  6. sann0638 Post author

    No, this equation keeps them the same – the first gives a win probability of 0.5, and as the points for a win is 0.5, there is no change to the ranking. Do you have an example where they increase?

    Reply
    1. Catto

      I have compared the equation with the ELO system. There is an issue with parentheses. I think the equation is intended to be
      Win Probability = 1/(10^((Opponent’s Rating-Your Rating)/150) + 1)

      I am interested also about another aspect. In chess the constants used are much different. The formulation in chess is
      Win Probability = 1/(10^((Opponent’s Rating-Your Rating)/400) + 1)
      While the starting rank for a beginner is 1500.
      So to have a similar proportion in Blood Bowl the equation would be
      Win Probability = 1/(10^((Opponent’s Rating-Your Rating)/40) + 1)

      I think it is legitimate to use different parameters, but do you know if there is a specific rationale for this?

      Many thanks!

      Reply
  7. sann0638 Post author

    After a bit of digging and thinking, the 400 is basically arbitrary. A possible rationale is that BB is more based on luck than chess, so a rookie has more of a chance of pulling off an upset than in chess. Also, because of the different races, you can be a rookie with a particular race but a very experienced player, which again gives the rookie more of a chance of winning. Will try to find the originator’s thoughts, however.

    Reply
    1. Catto

      I agree this is a good rationale for the difference in parameters, otherwise all players would be between 100 and 200. Thanks!

      Reply
  8. blizzard

    Hello,

    thank you, i think there is a problem in the formula “Players new rating”, because :
    – with this formula when you lose a game you lose rating
    – but a coach with 0-0-2 is rating better than a coach with 0-0-1

    Reply
  9. Stimme

    The “number of coaches” in calculating the K value used to be capped at 30 for regular tournaments and 60 for majors (not set to 60, but capped at).
    Did this change?

    Reply
  10. D_Arquebus

    Do we have the copy of the formula that takes into account difference in TV please? For example, in a progressio tourney?

    Cheers

    Reply

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