Since I feel like the current rating system is rather uninformative and also confusing for some new players (first hand feedback from friends I'm trying to get to play FA ), here are my suggestions on how to change it.
TL;DR:
1v1 rating & custom game rating. Leaderboards visible for BOTH.
Custom games show custom & 1v1 rating in brackets.
-Example:1500(1300)
1v1 games show 1v1 & custom game rating in brackets.
-Example: 1300(1500)
Longer explanation:
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1) We have a "1v1 ladder rating". This will be used by the 1v1 matchmaker/automatch. It will be unaffected by custom game rating.
2) We have a "Custom game rating". This will be used by custom games. It will be unaffected by 1v1 ladder rating.
3) When hosting a custom game, when someone joins, their rating will be displayed as such R: *Custom game rating* (*1v1 rating*). This will make it easier for players hosting custom games to see if that person is good at 1v1's, even if his custom game rating is low. (With remnants of 1v1 rating from back when it counted into global.)
Likewise, in 1v1 automatches, the rating would be displayed *1v1 rating* (*Custom game rating*). This will remove confusion new(er) players have when a player rated 400 lower beats them, then they look in the lobby and see he has a 800 higher custom game rating, since he is good at teamgames.
This also means that in team games, one can see if a player is a team-player, or a 1v1 player by looking at the 1v1 AND the team ratings more easily (It's not clear-cut, but a great 1v1 player will still be at least somewhat good in team games too).
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Now why do I think the rating system needs a reformat? Because of a few things.
For one, new(er) players can be confused. They don't know the real meaning of "global" rating. What does "global" mean, exactly? It's not intuitive. Also, it is difficult to explain to them how to check their rating. Right now you check your global rating in the chat lobby, and your 1v1 rating on a far away dusty tab on the opposite end of the lobby. Quite unintuitive.
Secondly, it gives players more information to more fairly balance games. If someone who has exclusively played ladder starts playing teamgames, this will be shown, and he will still be allowed to play instead of getting kicked without question because his rating is 100 too low for the rating limit set by the host.
Thirdly, the original reason for the change of ratings to what we have now is that players used their ladder rating to lower their global rating in order to get easier team games. It was a huge problem and had to be dealt with. This is not possible with this system as 1v1 rating is not directly connected to custom game rating and vice versa. The other rating being shown next to it in brackets will simply help newer players or players who have recently switched from ladder/teamgame to teamgame/ladder.
(Example of abuse with the current system that the new system would solve:
A player has 1500 global and 1600 ladder rating. He makes a smurf account. For a while, he only plays teamgames on it and gets to his old rating eventually, because of trueskill. Then, he starts playing ladder again. He could get many easy games over and over again, because only 1v1 rating is shown. Which is, in his case, 0. He could also purposefully not play as well, or lose on purpose in a not so obvious way to keep his rating down in the first few games where the system is still learning your real rating. The new system would solve this by simply showing his custom game rating next to 1v1, and players would see that he is actually not that bad at all, since teamgame players are arguably still better at 1v1 than someone who just started.)
Lastly, it is more intuitive. We would have separate leaderboards for 1v1 and for custom game rating. This would make it more appealing for new players, because it would be easier to understand, and to veteran players aswell, since you would now have more (and easier to access) information to balance custom games. It would also be more resilient to abuse, as stated before.
To keep from confusion, when you would mouse over each of the ratings in a custom game it would pop up either Custom rating or 1v1 rating, so it's self-explanitory.