Kills are worth 1 point, Relics are worth 3. Let me repeat that: Kills are worth 1 point, Relics 3. So while helping in teamfights is nice and all, if you don't have a chance at a multiple kill and a relic sometimes it's best to go for a free relic and even out a losing fight. Not to never help your team, but if you see the enemy has 3 members at 50% hp maybe it's best to leave them be and get a relic.
Also sometimes it's best to sacrifice yourself to save a relic. Because remember, a kill is worth one point where a relic is worth 3. If you can slow down someone doing a relic long enough for your team to arrive and get either a revenge kill or the relic then you will have gotten a net gain.
Losing an Ascension is not always a bad thing, if you hurl 3 members onto a desperate Ascension and lose all three with no kills the enemy will have gotten a huge gain, more than the 5 normally. Remember that if the enemy gets an Ascension and you kill them before they can get any kills it's as if no one got it in the first place. If you didn't lose members to a smite battle then nothing gained or loss. Of course try to steal it, but tunneling on it with all your member may not always be the best option, try using one Champion and some AoE poke from afar to steal, even a single DoT spell can get you the buff.
Succeeding in Ascension is both learning advanced concepts and strong judgement. Every point above is pointless if you don't think about how they're being used in a specific situation. Knowing how points are distributed and how to delay and score points is crucial, as much as getting the best Champions.