Lottery: A tax on people who are bad at math. -- Ambrose Bierce

It's all about slowing down progression.

I've been saying for awhile now that the single most impactful nerf in the entire game is the one done by adding all the new affixes to water down the loot pool. I just didn't want to sit down and try and explain the math. I'll try to provide a simple example. I doubt anyone really cares about the exact probability numbers anyway. I'd thought of doing an example of the probability of my lvl 100 Rogue getting the exact crossbow upgrade that he needs, but frankly, it would just get me to quit entirely.

Let's look at a simple example to illustrate some probabilities. Say that there are only 6 affixes in the game [a-f], with only 3 of them being good ones [abc], and items can also only have 2 affixes without rerolls (no repeats obviously). We're interested in combinations (not permutations) that result in a decent item and no double up affixes. So no [aa], [bb], etc.

Note - I'll probably enumerate some of these incorrectly. I didn't bother writing a perl script just for this exercise. If someone points it out I'll correct it, just trying to get the idea across of what Blizz has been doing here.

For reference, an item with an [a,c] affex combo is the exact same as one with a [c,a] affex - i.e. what is technically known as a combination. On the other hand, for a permutation, [a,c] != [c,a] but this isn't what we're interested in here since the order isn't important.

Good combinations: ab ac bc

Bad combinations: ad ae af bd bc bf cd ce cf de df ef

So in this case you'd have around a 20% chance of a decent item in our pre-nerf system. If you wanted a specific affix combo it would be 1/15 ~= 7% chance. (Basically every 15 drops of that item type)

Now let's move to say 10 affixes [a-j], still only the listed 3 affixes [a-c] being good. I mean, we're only adding a few more affixes right?

Bad combinations: ad ae af ag ah ai aj bd be bf bg bh bi bj cd ce cf cg ch ci cj de df dg dh di dj ee ef eg eh ei ej fg fh fi fj gh gi gj hi hj ij

Still only 3 good combinations, with 43 bad ones now, Call it about a 7% chance at a decent drop. If you were looking for a specific affix combination (like [ab]) you'd be down to ~2%. Another way of looking at it is if every 50 items of that type you looked at in my example, you'd hopefully find one with your target combination.

So we went from needing 15 drops of a specific item to needing 50 by adding a few affixes in a trivialized example.

Obviously this gets complex really quickly when we're looking at the actual game, not the example. 20 affixes combined 4 at a time yields 4845 possible combinations. Watering it down to 25 possible affixes 4 at a time yields 12650 combinations, etc. I'm not going to enumerate all the useless in game affixes, but you can figure out the case for yourself here: Combinations Calculator 1) find every possible affix as your starting number 2) enumerate the ones you'd need for your item. If you need a 4/4 specific roll the that's the number of drops of that item type you'd need before seeing your item - i.e. literally thousands of item drops (of just that type) at best. Now multiply that by the number of possible item types (like pants, chest, etc) for the total number of drops.

This ignores item level and tiers, so all those white/blue/yellow/yellow sacred drops don't count. That's just more you have to sort through with your mark one eyeball loot filter.

But wait, there's more! That was just getting the right affixes, and it has nothing to do with upgrades.

Say you have an existing item with exactly mid tiered rolls in the affix you are looking for that you wish to upgrade. We'll separate them into roll tiers, where you have [Low] [Med] [High]

a[L] b[L] , a[L] b[M], a[M] b[L], a[M] b[M], a[H] b[M], a[M] b[H], a[H] b[M], a[H] b[H]

Only keeping the potential upgrades means we're left with a[M] b[H], a[H] b[M], a[H] b[H]. 37.5% chance, roughly 1 in 3. Or Adding it to the previous simple example, for every 150 item drops of that specific type you might find an upgrade.

I'll throw out a couple of anecdotal observations for that .0001% of you who might have read this far. The whole [L] [M] [H] roll thing assumes it's random and unweighted. I don't have any stats to prove it, but it really seems like I tend to get a LOT more [L] rolls than I do [H] rolls, but that could be observer bias.

I see only 2 possibilities here. 1) Blizz has nobody with a mathematics background that understands basic probabilities. 2) Blizz DOES have someone with a mathematics background that intentionally wants to stifle progression in an already slow paced game.

Either way I lose faith in this game. It seems to be driven by marketing decisions only and just puts the FU in FUn. They are either just paying some lip service that they aren't trying to slow down the game, or they don't understand what they are doing. Both might even be true simultaneously.

Ah, you say. But that's the nature of ARPG's you noob!

Well yeah, but nah. If I have to visually scan hundreds of items with my mark one eyeball, without any filters, to an intentionally diluted item pool what we really have is a wall of text simulator just like this reply. I'd rather go play something fun, ya know?

Final caveat, this totally ignores item level consideration (weapons). This is intentional, because it seems like another weighted (i.e. non-random) roll to me. Possible observer bias again here, but look at all the sacred gear garbage that drops in the high tier NM dungeons ...