Table: The best damage mitigation for your gold
I put together a table that shows how much damage mitigation I can get for my gold. I looked at items that increased armor and also items that gave a boost to dodge. They both do the same thing: reduce the amount of damage you take from auto-attacks (towers, creeps, demigod's standard attack).
I didn't include activated abilities like the Orb of Defiance's invulnerability or that Sludge item.
This table will show incremental mitigation which is how much more mitigation you're getting because of the armor. So if I move from 10% mitigation to 15% mitigation, my incremental mitigation is 5%. It also shows how much mitigation you receive per 100 gold you spend.
The formula for armor mitigation is 1-2500/(2500 + Armor). The amount of mitigation you get from armor will vary based on how much armor you already have. If I buy Scalemail and go from 200 armor to 600 armor, I'll move from 7% mitigation to 24% mitigation, a 17% increase. However, if I am at 2000 armor and buy scalemail, I only get a 7% increase in mitigation.
This table assumes you're at 200 armor to start with.
Most interesting item on this list is Assassin's Footguards which provides 10% dodge and 5% attackspeed. At 200 armor, it delivers good mitigation relative to the more expensive items but doesn't really compete with the only other item in it's price band (Nimoth). But as you stack more armor on, Nimoth gets less and less effective while the 10% dodge from Footguards continues to provide the same 10% damage mitigation. When you have 1400 armor, the damage you negate from Nimoth is equal to the damage you negate from Footguards. Mid to late game the two deliver equal mitigation and you just need to decide whether more attack or more health is appropriate.
I'd also like to point out that extra health is far more beneficial than extra armor in the early game. If you're Beast fighting Regulus, you've got 475 health and 1550 armor. Reggie is dealing 110 DPS from auto attack and maybe 56 DPS from spells. At that rate, it'll take 10 seconds of sustained pressure for Reggie to kill you. If you take Scalemail, you'll be mitigating 33 DPS, increasing your life expectancy by 1 second. But if you take Banded Armor instead, your life expectancy increases by 2.5 seconds.
| Item | Gold | Armor | Dodge | Incremental Mitigation | Mitigation per 100 Gold |
| Scalemail | 400 | 600 | 0% | 17% | 4.209% |
| Nimoth Chest Armor | 1500 | 750 | 0% | 20% | 1.342% |
| Armor of Vengance | 3250 | 1050 | 0% | 26% | 0.798% |
| Assassin's Footguards | 1750 | 0 | 10% | 10% | 0.571% |
| Platemail of the Crusader | 4500 | 1000 | 0% | 25% | 0.556% |
| Groffling Warplate | 5200 | 1200 | 0% | 28% | 0.548% |
| Orb of Defiance | 3750 | 500 | 0% | 14% | 0.386% |
| Bulwark of the Ages | 16000 | 1500 | 25% | 58% | 0.363% |
| Duelist's Cuirass | 3000 | 350 | 0% | 11% | 0.354% |
| Ring of the Ancients | 3500 | 400 | 0% | 12% | 0.341% |
| Cloak of Elfinkind | 12000 | 750 | 15% | 35% | 0.293% |
| Godplate | 10000 | 1200 | 0% | 28% | 0.285% |
| All Father's Ring | 25000 | 1500 | 10% | 43% | 0.172% |