Why are Armor Items so Much More Effective than Magic Resist?

Because AD-scaling damage can come on two ways: abilities AND basic attacks. Also, physical damage from basic attacks can be further augmented with critical chance and attack speed. Lifesteal is a pretty efficient stat on AD champions, too.

With a few exceptions, such as 's passive, 's E, and 's E, most AP-scaling damage can only come from abilities. Even then, most of those abilities are burst, instead of sustained damage. Some champions, such as and , come very close to dealing sustained damage with only their abilities, but they are still limited by their cooldowns, whereas an auto-attack reliant champion would not have this limitation and would not bother that much if it were to be silenced.

Also, as I said above, Lifesteal is pretty good on most AD campions, but the reverse is not the truth; Spellvamp is bad on most AP champions. Only a few of them have the sustained damage needed to make Spellvamp a worthy stat. Examples are the aforementioned Cassiopeia and Vladimir. But for most of them, they will not benefit from spellvamp because their burst will not let them apply enough damage to be able to heal, and they are better off just itemizing to be able to kill their opponent in seconds, instead of directly trading with them. AD casters can build lifesteal despite having the same play pattern because their auto-attacks let them heal in an efficient way, they still have a few sustained damage despite building mostly for bursting.

Most AP-scaling damage is magic damage, and most AD-scaling damage is physical damage. Most magic damage skills are burst damage spells. While there are many physical burst damage spells, many AD champions have a lot of sustained damage due to their auto-attacks, which they can combine with their attack speed, their critical chance, and even their on-hit effects.

Sustained damage is much more efficient than burst damage, against tanks. Armor items need to be stronger and more effective than magic resistance items to be able to take physical damage on the same way as magic damage. If armor items were to be weaker, physical damage would be extremely effective against tanks (and even squishies) while if magic resistance items were to be stronger, magic damage would be unviable because it would be too easy to itemize against it. In either case, there would be no reason to play AP champions at all.

The literal opposite is true. The MR items are usually bundled with other relevant stats and a huge variety of useful passive/active abilities--their utility is what gives champions the game-to-game flexibility they need to adapt to different team comps. Aside from the raw stats that they give, armor items don't offer nearly as much flexibility.

"Because you get AD per level and AD also scales off of AS, which you also gain per level"

The logic is that AD has much higher DPS, so armor needs to be stronger.

DPS is so easy to escape from tho. Not sure I like this. Does anyone else think Randuins is OP?

HP is also a good defense against burst AP, so a randuin/sunfire cape function better as a dual resist item to help control the scaling of mid lane (and a few others), otherwise you would likely end up needing to nerf damage on burst APs to achieve the desired consistency of team fights the game is aiming for, since armor is a necessity in objective control, like dragon/baron and tanking tower shots.

If Riot wanted the games to go longer and be more defensive, hide under the towers style, they could reduce the HP on armor items.