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Posted by: Christer on Sunday, March 04, 2007 - 23:58
As some of you probably noticed already, your coach rankings (CR) have just changed. This is due to a change in how CRs are calculated. In short, the change involves the addition of race as a parameter to the ranking system.

Together with this change, all CRs have been recalculated from the beginning of the site. This means that matches that predates the ranking reset(s) we've had in the past are now part of your coach ranking.

In addition to the formula change, I have also changed the recently added limit on when CR starts to be a factor. It is now updated if both involved teams have played 4 or more matches. This change was made due to the introduction of the [U]nranked division.

For those of you who are interested in the (mathematical) details, read on for more details.
Before this change, the ranking system treated all races as equals. Two coaches with the same ranking, playing eachother with teams of same Team Strength (TS), would be considered equally likely to win a match, having a win probability of 50%.

Now, this is all good if the teams being played are of the same race. However, consider the situation where these two coaches are playing a game between dwarves and goblins. The dwarf coach most definately has an advantage here, and therefore the ranking system benefits the dwarves.

In order to prevent this situation, I decided to introduce something I call the racial factor. This is another number which is meant to target this problem with the old ranking system.

This racial factor is a number which varies between 0 and 100%, giving the win probability of each side where both CR and TS of the playing coaches is equal. This figure is incorporated into the ranking system as follows:

r: racial factor
p: win probability according to the Ranking help page
P: Modified win probability.

P = p ^ [ 5 ^ ( 1 - 2*r ) ]

This modified win probability is used in place of the old win probability in the ranking formula.

Easy enough, right?

Ok, so what about the racial factor then? How is that calculated?

This is the part where it gets tricky...

The racial factor is based on a racial ranking. This system works much like the coach ranking, using the same formula.

For each match that is played, the system looks up the racial rankings for the two involved teams, and changes the ranking based on the outcome of the match. For this ranking change, the system ignores the TS values of the involved teams since the TS effect of a match is taken into account elsewhere in the CR. Remember that the racial factor is supposed to be the effect of the race on the win probability and nothing else.

So this results in a large number of rankings for each race (in fact, 441 different factors at this time) and updates two values (for example dwarf vs gobbo and gobbo vs dwarf) for each match that is reported.

So, now we have a large table of racial rankings. To get the racial factor we use in the ranking formula, we again use the functions we all know and love. We set up an imaginary match between these two races, "your side" using the racial ranking of your team and the opposing side using a static ranking of 150 (which is the starting point for racial rankings just like CR itself), and again assume equal TS. Using these numbers, we use the same win probability formula we've used before, and the result is the racial factor!

Oh my, I am very sure that I lost most of you long ago, but there you have it.

Note that the racial factors change over time, and I will be publishing the current matrix of factors on the site shortly. I hope that this change will make CR more accurate and believe that most of you understand why this was put in place.

Enjoy!


** Edit: You can now find the current racial factors on the statistics page.
Synn on Mar 05, 2007 - 00:46
After seeing where a few coaches ended up with their CR.....

I like it!

__Synn
    Smess on Mar 05, 2007 - 00:52
    yeah I like it too
    I'm back at nr 1, so I recon the new system must be accurate as hell :D
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    Walks_in_the_Sun on Mar 05, 2007 - 01:06
    Mine went up a couple points, I think, but I'm still under 140, so all is well!
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hunter on Mar 05, 2007 - 00:58
Out of curiosity, will the championship formula receive a similar change? I realize that it is incorporated to some extent because CR differential is factored, but it seems as though since TS is also a factor that the "racial factor" should also be included. Just a thought I had... nice change IMO.

Regards,
~hunter
StarBreeze on Mar 05, 2007 - 01:01
Thanks Chris and the crew for the work they are doing making this place better and funnier! :)
    Blainkhard on Mar 05, 2007 - 01:13
    I will play League untill all this changes get stablished and posted..
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Snappy_Dresser on Mar 05, 2007 - 02:10
I like this. I like this a lot.
Mully on Mar 05, 2007 - 02:11
Could you just clarify the part after "Together with this change" ?
def909 on Mar 05, 2007 - 02:23
Cool! So now we can all determine how much we have been cherrypicking before this change... if you lost CR (like me) you´ve obiously been picking cherries a lot :P
But seriously it´s a great idea, because now "weak" races like vampires and ogres will become interesting even for coaches who are concerned about their CR.
Thank you Christer!
Laviak on Mar 05, 2007 - 02:42
Very nice indeed.

I guess the only thing that maybe isn't taken into account now is the variation at different ratings (i.e. zons vs chaos greatly favours the amazon team at low TR, but at high TR, when the chaos have a few claw/tackle players, the teams are much closer). Maybe the TS formula does a pretty good job of dealing with the variation anyway.

Great stuff Christer.
    Christer on Mar 05, 2007 - 03:14
    I'm considering this issue. Might ammend the formula a bit to take this into account. Stay tuned.
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      Wotfudboy on Mar 05, 2007 - 10:51
      I think it would be very interesting to see at least five charts of this nature, with bands of TR of 0-99, 100-149, 150-199, 200-249, 250+

      I certainly think all of a Chaos team's games will be red in 100-149, but many more will be green at 200-249... I've no idea how you will match this up against an opponents TR...

      My TR hardly changed, going down by roughly 0.8 I think... No idea what that indicates! :-)
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oeuftete on Mar 05, 2007 - 02:56
Any chance you could put the race names in the title attributes on the top row of table headers, so that its easier to see what the numbers refer without having to scan to the left?
    oeuftete on Mar 05, 2007 - 16:12
    Another thing that would be a nice bonus in the racial factor table would be title text on each individual cell that shows how many matchups contributed to the %. It's clear there are a lot of "N=0" at the high end... it would be nice to know which non-50.00 numbers have very small sample sizes.
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runreallyfast on Mar 05, 2007 - 06:37
Awesome change!

I asked for exactly this a few months ago - I think it will be a big improvement.

I would have thought my CR would have gone up more - I guess I have been cherrypicking even more than I had thought, and that I need to play more games with my vampires and rotters.
SideshowBob on Mar 05, 2007 - 09:12
Hmm I don't understand much, but as long as I'm at nr 5, it has to be good!
Khaan on Mar 05, 2007 - 09:38
Very interesting numbers there.

Especially that amazon vs halfling is the most lopsided matchup. I would have thought it to be dwarf vs halfling.

Also rather amusing to see the effect of the halfling wizard (chef) on a team like vampires (compare it to goblin vs vampire matchup for example).

Playing my gobos just got a hell lot more fun.
Forteza on Mar 05, 2007 - 09:44


Nice although it still doesnt help vs elfbowlers
sk8bcn on Mar 05, 2007 - 09:44
Great job! This is a very good improve!
BlackNWhiteDog on Mar 05, 2007 - 09:45
Sounds good to me...
I don't understand a word of it... but it sounds good :P
Purplegoo on Mar 05, 2007 - 09:56
Looks good to me - seems fairer.
smashyahelmut on Mar 05, 2007 - 10:07
i have played a few games now and my ranking neather rose nor droped

is there a place for me to understand this simpley so i can learn how to improve my cr ranking when i play people

easy answer is to win but it would be cool to be able to see what cr points were on the line when i play someone

thanks
its all very complicated but good
yep good
Mithrilpoint on Mar 05, 2007 - 10:13
Ho-hum.

A new factor to think about while pick... err selecting opponents.

It all makes sense though and i think the change is good. It is an intererresting read, the racial statistics but wouldn't it be an idea to subdivide them into TR groups - just to refine a bit more?

M
Qaz on Mar 05, 2007 - 10:41
I like this change. Althou it does not take into account the TR level the team is at. For instance Norse we all know that they are a strong starter but that they just dont cut it at hig TR. Maby devide every race into 3 TR brakets. That way playing Norse on low TR (Easy) = lower CR gain and playing norse above 200 TR (hard) = higer CR gain.
spubbbba on Mar 05, 2007 - 11:14
"It is now updated if both involved teams have played 4 or more matches."

With this rule, is that for ALL games where either team has played 1-3 matches?

I'm just wondering if it games before this change have now been discounted if either team had not played 4+ times.
Azurus on Mar 05, 2007 - 11:20
Bah, I just gained 5 points. Take them back, please! I don't want them!

Seriously though, good change. I appreciate the effort Christer puts into things like this.

As mentioned by others, it could use a tweak to split it up by CR, but this is a big step forward in my opinion.

Now all I have to do is find some people to lose against to get rid of those CR points.
lindwurmschlaefer on Mar 05, 2007 - 11:52
In general i would say that this way is a good idea - better a good start to talk about.
It was a very good idea to create an dynamic racial factor - i am curious about the development.

Still there are some open issues to talk/calculate about - like the thing with TR (Amazons & Chaos as said before).

But i have to confess that all this is an attempt to compensate the "mistakes" games workshop has made in creating equal strong teams.

(My tip to all coaches - stick to the teams you can play well - if you are an elfbowler from the heart, don't try to coach nurgle or ogre if you can't change your style of gaming.)
MickeX on Mar 05, 2007 - 12:23
Great work Christer! That change adressed a lot of issues at the same time. And those statistics are really interesting as well.

I dropped from 174 to 171 :D Those zon games must have been balanced by the vampire teams. I was a bit surprised to see that vampires had such a low win percentage for their TS. I always thought the TS formula underestimated them a bit. Perhaps they have a particularly strong "you've got to know your team"-factor? They're really fun to play, so I hope this change will get more coaches to have a try at them.
Arktoris on Mar 05, 2007 - 12:25
Wow, I think I gained 3 or 4 points! A nice change in the formula.
MSpanke on Mar 06, 2007 - 03:02
I have a CR? Is it serious?