# TMM Rating Allowance Needs to Use Ladder 1v1 Matching (or close to it)

Could you randomly generate some imaginary players with rating values/number of games, put them into random teams, and then calculate the quality? Without concrete examples its rally hard to judge such an algorithm.

Edit: And throw away examples where fairness is too far off.

I don't have a lot of examples because I have just started making some, but here are a few for you:
(Keep in mind that a game quality of 0.5 is the cutoff here for a game to be considered)

A "Search" is a party of players that is searching for a game. the "pX" are the player names, so you can see how many players there are in the search. The number at the end is the average rating of that search party. The game quality uses the formula that I explained in my previous post.

``````team a: [Search(['p12'], 842), Search(['p15'], 738), Search(['p1', 'p2'], 781)] cumulated rating: 3142   average rating: 785.5
team b: [Search(['p11'], 745), Search(['p5', 'p6'], 788), Search(['p16'], 816)] cumulated rating: 3137   average rating: 784.25
bonuses: 0.0 rating disparity: 5 -> fairness: 0.9916666666666667 deviation: 44.917806881013234 -> uniformity: 0.8502739770632892 -> game quality: 0.8431883605877618

team a: [Search(['p5', 'p6'], 788), Search(['p16'], 816), Search(['p13'], 971)] cumulated rating: 3363   average rating: 840.75
team b: [Search(['p1', 'p2'], 781), Search(['p12'], 842), Search(['p17'], 951)] cumulated rating: 3355   average rating: 838.75
bonuses: 0.0 rating disparity: 8 -> fairness: 0.9866666666666667 deviation: 79.45399612354309 -> uniformity: 0.7351533462548563 -> game quality: 0.7253513016381249

team a: [Search(['p3', 'p4'], 1004.5), Search(['p17'], 951), Search(['p16'], 816)] cumulated rating: 3776   average rating: 944
team b: [Search(['p13'], 971), Search(['p12'], 842), Search(['p5', 'p6'], 788)] cumulated rating: 3389   average rating: 847.25
bonuses: 0.0 rating disparity: 387 -> fairness: 0.355 deviation: 92.79134859996378 -> uniformity: 0.6906955046667874 -> game quality: 0.24519690415670953

team a: [Search(['p7', 'p8', 'p9'], 1011.3333333333334), Search(['p12'], 842)] cumulated rating: 3876   average rating: 969
team b: [Search(['p13'], 971), Search(['p3', 'p4'], 1004.5), Search(['p17'], 951)] cumulated rating: 3931   average rating: 982.75
bonuses: 0.0 rating disparity: 55 -> fairness: 0.9083333333333333 deviation: 67.96035149261664 -> uniformity: 0.7734654950246113 -> game quality: 0.7025644913140219

team a: [Search(['p7', 'p8', 'p9'], 1011.3333333333334), Search(['p11'], 745)] cumulated rating: 3779   average rating: 944.75
team b: [Search(['p10'], 1047), Search(['p15'], 738), Search(['p14'], 1032), Search(['p13'], 971)] cumulated rating: 3788   average rating: 947
bonuses: 0.0 rating disparity: 9 -> fairness: 0.985 deviation: 125.21026066181636 -> uniformity: 0.5826324644606121 -> game quality: 0.5738929774937029

team a: [Search(['p7', 'p8', 'p9'], 925.3333333333334), Search(['p15'], 1328)] cumulated rating: 4104   average rating: 1026
team b: [Search(['p13'], 1115), Search(['p16'], 1231), Search(['p3', 'p4'], 998)] cumulated rating: 4342   average rating: 1085.5
bonuses: 0.0 rating disparity: 238 -> fairness: 0.6033333333333334 deviation: 152.77004778424336 -> uniformity: 0.4907665073858555 -> game quality: 0.2960957927894662

team a: [Search(['p7', 'p8', 'p9'], 925.3333333333334), Search(['p13'], 1115)] cumulated rating: 3891   average rating: 972.75
team b: [Search(['p3', 'p4'], 998), Search(['p5', 'p6'], 918.5)] cumulated rating: 3833   average rating: 958.25
bonuses: 0.0 rating disparity: 58 -> fairness: 0.9033333333333333 deviation: 84.13976467758869 -> uniformity: 0.719534117741371 -> game quality: 0.6499791530263718

team a: [Search(['p7', 'p8', 'p9'], 925.3333333333334), Search(['p12'], 846)] cumulated rating: 3622   average rating: 905.5
team b: [Search(['p5', 'p6'], 918.5), Search(['p1', 'p2'], 810.5)] cumulated rating: 3458   average rating: 864.5
bonuses: 0.0 rating disparity: 164 -> fairness: 0.7266666666666667 deviation: 79.85612061701971 -> uniformity: 0.733812931276601 -> game quality: 0.5332373967276633
``````

I assume all players in that list have a newbie bonus of 0?
Search(['p7', 'p8', 'p9'], 925.3333333333334) means those 3 players are in the queue together, and 925 is their average rating?

What is inside the match array?
rating_imbalance = abs(match[0].cumulated_rating - match[1].cumulated_rating)
What is match[0] / match[1] reffering to?
Why is has_top_player() important and what does it do?

top_player is used in the matchmaking process already. It's defined as anybody with over 1600 mu. It's used to eliminate certain players/teams from consideration when the system is just trying to throw a new player into a game after a few failed queue intervals.

I assume all players in that list have a newbie bonus of 0?
Search(['p7', 'p8', 'p9'], 925.3333333333334) means those 3 players are in the queue together, and 925 is their average rating?

Yes to both.

The match array just holds the two teams, so the rating imbalance is just the difference between the sum of the ratings of the two teams.

As ftx explained a top player has >1600 mu.
This way the newbie bonus gets only awarded if the team has no pro players. But now that I think about it, I am not sure anymore if this is a good idea.

Okay, what does `deviation = stats.pstdev(ratings)` do?

So guys, this is great and all (good work - seriously) but most people playing FAF do not understand nor have the time to translate the code to layman terms explanations. It would be really appreciated if some "as precise as possible" explanation was given when distributing information that shows rating brackets as a requisite for what they will experience while playing the game.

I don't think I understand what you want to say. Are you talking about the map pools? The matchmaker won't use rating brackets at all. There will also be no further explanation of the matchmaker inner workings in the client. The end user just queues up and will automagically get some nice balanced games (hopefully).

Ok i think the formula makes sense, except checking top_player. If there are a top player and a noob in the same team it will probably already create bad uniformity right?

However, for finding good parameters, i would have to code that formula up and try it with varying numbers, cannot really tell anything from your example calculations. So yeah i don't think you will get much use out of the forum for that^^