Well, I was going to just answer the question: CC. They offer tons of lockdown in teamfights, and they can disengage when teamfights are going poorly. (You can't ask for much better than a Janna knockback.) But you want "excruciatingly deep detail"?
Excruciatingly deep detail. Okay, here goes.
You pick Annie. You take AP runes and masteries, but use utilities instead of defense. Start with a spellthief's edge, but go immediately into Rod of Ages as soon as you can. Make sure you brought flash. When teamfighting, make sure your stun, flash, and Tibbers are up. When the enemy team is grouped, you drop a 5-man Tibbers stun on their heads and commence spamming spells. Make sure to use E, because Tibbers benefits from it as well.
Sure, this isn't going to give you a single-handed, no-assist, 1v5 wombo combo. But I'm going to go out on a limb here and say, your team was probably actually doing slightly more than no damage. Graves wasn't stacking Crucibles, was he? If you can land a good Tibbers stun in a teamfight, ping excessively for them to attack the stunned-up enemy team. Odds are, one or two or four of them will begin attacking, and probably get a kill or two. Win teamfight, proceed to objectives (dragon if up, Baron if feasible; at the very least push a lane and try to take a tower).
Got all that?