Bloodthirster's too efficient

I've tried arguing this from the side of needing to buff other items, but that wasn't well-received, so I thought I'd argue why BT should be nerfed. It's actually been too strong for awhile now, but the lowering of price to 3000 gold makes it even clearer that BT is overtuned.

The big mistake people make when evaluating BT's gold efficiency is that they underestimate the gold value of lifesteal. This is because the base item used to calculate lifesteal's gold efficiency is a completed item, and its recipe value raises the gold value of the item above its gold cost. In other words, vamp scepter isn't actually 800 gold for 800 gold of stats, but it's better, just like every other combined item in the game. To account for this, we need to figure out how much gold the recipe value adds for other items around the same price as vamp scepter. This is pretty hard because most of these items have passives that are hard to evaluate, but I've chosen to look at tear (no stacks), chalice (base of 7 mp5, used at half mana), seeker's (full stacks), philo (no passive), and hexdrinker (no passive), which have gold efficiencies (ratios) of: 1.31, 1.28, 1.43, 1.13, and 1.11, respectively. Averaging these to a gold efficiency of 1.25 and applying to vamp scepter, we actually get 1000 gold of stats on that item, 640 of which is 10% lifesteal. Long story short, life steal should actually be valued at 64 gold/1%. (note, i've ignored some passives, so I feel these are conservative estimates of recipe value)

Applying this to Bloodthirster, we get 3288 gold value at 0 stacks and 4752 gold value at full stacks, yielding gold efficiencies of 1.10 and 1.58, respectively. 1.58 gold efficiency is ridiculously high. To demonstrate how high, I'll compare it to some other high-tier items:

To get a 1.58 gold efficiency with DCap, DCap would need to provide 1.58x3300=5214 gold worth of AP. Using the gold value of AP from the wikia (21.75 gold per AP), this comes out to 5214/21.75 ~ 240 AP that the DCap itself needs to provide. DCap has 120 base AP and adds 0.3xtotal AP, so we can solve 120x1.3+delta_APx0.3=240, where delta_AP is all AP that doesn't come from DCap. Solving we find that delta_AP = 280 (NOT total AP), which is where DCap breaks even with BT.

IE would need to have a value of 1.58x3800=6004 gold. The AD and Crit Chance on IE are worth 3770 gold. Therefore, the passive on IE would need to be worth 2234 gold for IE to break even with BT. This is hard to judge, so let's compare it to an equal gold value of AD (~62 AD) to see what stats are needed for the IE passive to breakeven in average damage added to an AA (ignoring the fact that crit also doesn't work on spells). Average AA damage is: ADx(1+cc x cb), where cc is crit chance and cb is crit bonus (1 normally, 1.5 for IE). As such, damage added is delta_ADx(1+cc x cb) for the AD and it's AD x cc x delta_cb for the IE passive (delta_AD=62, delta_cb=0.5, cb=1, AD and cc are variables for total AD and crit chance). Therefore, the breakeven point is when AD=(delta_AD/delta_cb)x(cb +1/cc). If you have 25% crit chance from IE, AD=620. If you have 75% crit chance, AD=290 - so even if you stack crit in order to make the comparison as favorable as possible, IE passive doesn't break even until you have 290 AD.

Trinity? More complicated than I'd like to get into for now. Don't want to figure out how much gold spellblade and phage passive are worth (easy way out would be picking an equivalent amount of AD or movespeed, but I feel that'd be cheating)

Sunfire would need to have 4187 gold worth of stats to draw even, meaning the passive would need to be worth 2100 gold. I don't have a good comparison here, but you could buy 2 giant's belts with that.

Randuin's passive would need to be worth 2021 gold, so pretty much same story as Sunfire.

I can go on, but it's pretty clear that BT is just too gold efficient, both compared to other high-tier items and in general.

PS: To those who think I'm pulling a fast one with my lifesteal change, let me explain myself. The problem of defining a gold efficiency for lifesteal from vamp scepter can be simplified down into a problem of knowns and unknowns. We know the stats on vamp scepter, we know its price, and we can estimate how much of that price goes toward AD by looking at how much AD costs on pure-stat items. We don't know how much vamp scepter is worth, and hence how much the lifesteal on the item is worth (put another way, we don't know either the item efficiency OR lifesteal's efficiency). The wiki assumes a 100% efficiency for vamp scepter to derive their value for lifesteal's efficiency. Instead of pulling such a value from thin air, I wanted to look to other completed items at the same price point to get my estimate of vamp scepter's gold efficiency. If anything, it's less arbitrary than the way the wiki does it (blindly assuming vamp scepter's 100% efficient, despite other completed items operating differently.)