So the basic point system is that higher points == less competitive combinations.
I try to base tiers off of the map and game mode. 2v2 Cataract. This means that interrupts are VERY important because of portal flags and just the map in general. Minions are stronger 2v2 then they are 3v3, and being a General is a "significant" boon because of monks. In general, we can assume all teams will have at least one general, but there should be minimal double-general teams possible because of 2x minion swarm combinations with 2x Ring of Divine Might (so, Erebus and Oak should not be able to be with another general since Occ, Queen and Sedna all have shitty summonable minions).
Furthermore, there should be more-obvious super-combination, and all combinations should have a fighting chance against all other ones, except for a few just "bad" matchups (like Erebus + TB would probably really push around a Queen + Rook team, but Queen + Rook would do fine against most other matchups).
1 point - Erebus, Oak
1.5 points - Rook, UB
2 points - Sedna, Torchbearer, Occulus
2.5 points - Queen
3 points - Demon Assassin, Regulus
You must have at least 4 points. There is no maximum amount of points that you may have (you can go DA + Reg) but if you do so you are probably going to be at a disadvantage.
Tier explanations as follows:
Erebus: He is fast, very hard to kill, holds lanes very well. Has a good AoE stun that covers up locks. Batswarm enables him to port-ninja with minimal risk. He's a general, with excellent free minions that work towers well. He doesn't have very many weaknesses and few demigods can easily push him out of a lane. This puts him at tier 1: he is able to hold a lane alone, push towers well, lock flags, ninja portals and is a general.
Oak: Though Oak has difficulty early-game, 2v2 tends to last longer than 3v3, so levels are less of an issue. He's somewhat expensive, but not to the point where he is a liability. He's virtually impossible to kill, and end game he is a time bomb. He has very few weaknesses, since he has great minions, good AoE, good team support. This puts him at tier 1: he is able to hold a lane alone, push towers well, lock flags, ninja portals, and is a general.
Rook: Rook is insanely strong 2v2 Cataract since he can beat most demigods 1v1 for most of the game while fighting for lanes. He can hold enemy portals and basically liquidate an enemies portal side. However, he is extremely vulnerable to minions and is also very slow. He's also a little expensive since he needs 2 helms to keep up a decent tower farm. This puts him at tier 1.5: He is able to hold a lane alone extremely well, and push towers extremely well. However, he is unable to ninja portals and has a few weaknesses that other demigods do not have. He is also an assassin and therefore dependent on priests and monks.
UB: UB is probably easily the most powerful demigod in the game. He is fast, does insane DPS, has awesome stuns and when combined with Sigils, Acclimation and his native speed, one of the most hardiest demigods. He isn't terribly expensive (though he isn't cheap) and has excellent AoE. However, he's an Assassin and therefore highly dependent on monks. This knocks him down half a tier. This puts him at tier 1.5: he is able to hold a lane, push towers well, lock flags and he can pretty much saunter up to your portal and kill you 
Occulus: Occulus with a stun would be Tier 1. However, he does not and this makes him a bit of a liability end game. He has the second-best AoE in the game, and is able to push creeps and towers very well. He can health stack like crazy and hold flags quite well. Blast Off! enables him to ninja portals, though not as well as Erebus. He is a general, though his summonable minions don't work well until his level 15 ability. He is able to hold lanes well, and push towers and ninja portals and push creeps. But he cannot prevent an enemy from locking.
He is arguably tier 1.5 and not tier 2, since I think that a Sedna + Occ combination would be "too" strong. If we move Occulus to 1.5, I think we should drop TB to 2.5, so that we can keep an Occulus + TB combination tournament legal. Plus, I think it is extremely unlikely that anyone is going to go Rook + TB or UB + TB anyway.
Sedna: Sedna is underestimated She is very strong through most of the game, and is able to fight most upper-tier characters for most of the game just fine. However, she is extremely vulnerable to minion builds, and her effectiveness also begins to taper off as giants come out since she lacks a proper AoE. She also has a very hard time against Rook. This puts her at tier 2: She is able to hold a lane alone for the majority of hte game, has 2 interrupts so she can lock. She can push towers decently because of her insane regen though it takes her longer to do it than most other demigods. She can ninja portals with Inner Grace. She is also a general.
Torchbearer: TB is strong level 1 against generals, but he is greatly, greatly weakened after the first or second shops. Until Catapults and Giants come out, he tends to struggle against most other demigods. Once they do, however, he starts to really shine. He can push creeps extremely well, and since he never ooms he can get a nice level advantage over everyone else. He has access to 2 interrupts, one of which covers a lock at level 15.
I currently have him at tier 2. You could probably move him to tier 2.5 because of his difficulty fighting Oak, Erebus and Beast for the majority of the game. I think that UB + TB and Rook + TB combinations aren't going to happen anyway. Regardless, because of his massive AoE, I'm putting him at tier 2 for now. I wouldn't be against dropping him down to 2.5
Queen: Queen is... also underestimated. With Ground Spikes she does absurd damage in conjunction with friendly minions and giants. However, she is really expensive, and has very low HP which makes her more vulnerable to chain-stunning than other demigods. She also lacks a way to interrupt or secure a lock which makes her a liability. This puts her at tier 2.5: she can hold a lane decently through most of the game, and she can push towers very well. However, she cannot ninja portals and is extremely expensive. She is a general, though, so that's a plus.
Demon Assassin: DA is insanely strong at level 15. Don't get me wrong. However, until he gets to that point, he is struggling. He has excellent burst damage, but horrible mana issues to compensate. He is also extremely expensive. He has poor AoE and struggles against Giants. He is also dependent on having an ally with him in order to secure a kill with Swap, which is sort of useless when alone in a lane as long as your enemy doesn't horribly overextend. This puts him at tier 3: he cannot hold lanes very well, he can't push towers, Swap is a poor interrupt and he is uesless for most of the game.
Regulus: Reg ... basically means you get the HP flag the whole game. Though Reg can do pretty well at countering a Rook and snipe-harass lets him push around a DA or TB or other squishies, his only utility comes in netting the team extra gold and map control via snipes and the occasional snipe-kill. However, because of Cataract's map design, he has to give up a flag to get a snipe off. This can put his team way behind in warscore. Additionally, he has no way to interrupt or secure a lock which causes problems. He isn't /too/ bad at pushing creeps and he can push towers without taking damage. This puts him at tier 3: he cannot hold lanes very well, and though he can push towers decently and provide snipe support... that's all he can really do.
Legal combinations are in the post above this. Moving Occ to 1.5 and TB to 2.5 removes Sedna + Occ and addes Rook + TB and UB + TB to the "less competitive" list.
