this analysis is based on 200% crit dmg. as you get more crit chance almost every physical attacker will buy an infinity edge and thereby increasing crit chance but also increasing crit dmg by 50%. so the bonus is even less. and also there are champs that do physical damage with skills (warwick, pantheon, ashe, garen, etc). for all those champs the crit dmg doesnt apply to abilities but armor pen does.

also, if your team is going for first blood (which almost every team does) its nice to have a 30 armor pen bonus (plus 6 mastery bonus in offensive, tier 3). so thats 36 arp, you will even have a 100% arp on most tanks at lvl 1. that hugely increases your damage output on first blood because the armor of the target is fully penetrated. also, at first blood most champs will have 2% crit chance from mastery, and max 8% from equips. thats 10% chance to do 233% crit dmg (thereby increasing damage output from 100% to 116% IF critted).

compared to the 25% extra phys dmg from arp there is no doubt that armor pen give much much more average dmg (and is also so much more relyable) than crit dmg.

so if you want to go for first blood, go for armor pen. it will give you a great money bonus if you get the first blood bonus.

also in mid game, you will have near 100% armor penetration against low armor targets, which you will mostly go for as a physical damager. so even in mid game arp is much better than crit dmg.

so in my opinion, get arp marks and quintessess, buy infinity edge (great in combination with phantom dancer) and pawn like hell against low armor targets like casters.

P.S. the mathmatical stuff shows that it makes nearly no difference if you have arp or crit dmg against medium geared tanks. so go for armor penetration, always!