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 not all equipped skills are counted towards the arena score: (6 skills being weapon, assist, special, and ABC)
If you have 5 or 6 skills equipped, only the 4 skills with the highest SP cost are counted.
If you have 4 skills equipped, only the 3 skills with the highest SP cost are 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 Hone Def 3 unequipped yield the exact same point (because only the 4 most expensive skills are counted in both cases). However, if you further unequip Reposition, you will start to see fewer points (because now only 3 are counted).
Also, sacred seals do seem to affect scoring. Experiments show that when all 4 team members are equipped with sacred seals, you get roughly one more points. Sacred seals can be considered as level 1 skills (hence 40 ~ 60 SP per seal, around 200 SP for 4 seals) so maybe it makes sense that way. Anyway, no conclusion on the exact calculation on sacred seals yet.
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 arena points. Even the 300SP trashes that are the AOE specials can give you +0.5 point compared to Moonbow/Luna/Bonefire.
Put on sacred seals for all your arena team members.
Edit: My original interpretation was wrong. Updated now.