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.

David OlorenshawI 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))

Phoenix11What 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

sann0638Post authorScoring 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!

DarksonI 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! 😉

sann0638Post authorSorted.

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

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

sann0638Post authorFixed. If only there were a maths teacher handy…

CattoI 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.

sann0638Post authorNo, 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?

CattoI 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!

sann0638Post authorAbsolutely right about the brackets – corrected. Will ponder the other…

sann0638Post authorAfter 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.

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

blizzardHello,

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

sann0638Post authorCan you give an example?

StimmeThe “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?

sann0638Post authorGood question – I don’t think it has changed, no.

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

Cheers

sann0638Post authorDon’t have this one to hand, sorry! Will hopefully find it out soon, some work is being done on the database.