With AA costing no stamina or dueling swords, people are using AA to conduct massive arena scoring research right now and I think they are now pretty close to the exact formula. Some of the findings aren't new, such as the confirmation of 1 arena point = 10 BST = 1 merge, and 1 rarity/star level = 5 points, but here is the new finding: 200SP cost = 1 point. Not just that, they have also found out that only the 4 skills with the highest SP cost a unit equips will be counted.
For example, say we have an Ike equipped with Ragnell (400SP), Reposition (150SP), Aether (500SP), Heavy Blade 3 (240SP), Sword Breaker 3 (200 SP), and Hone Def 3 (200 SP). The total arena points contributed from his skills will be (400 + 500 + 240 + 200) / 200 = 6.7. Experiment has confirmed that this fully equipped Ike and him with Reposition and Hone Def 3 unequipped yield the exact same point. However, if you further unequip Sword Breaker 3, you will start to see fewer points; 1 point fewer to be exact.
tl;dr:
1 merge = 10 BST. 1 rarity/star level = 50 BST. 20 SP = 1 BST.
Don't be afraid of equipping low-SP-cost skills like the movement skills (150SP) or stats + 3/5 skills (160SP). As long as your other skills are 200 SP or above, it won't affect your score at all.
Aether/Galeforce are gold mines; don't merge your Ikes/Lucinas/Lyns if you care about points. Even the 300SP trashes that are the AOE specials can give you +0.5 point compared to Moonbow/Luna/Bonefire.