Ever since Armor 2.0 with random stats started dropping in Destiny 2: Shadowkeep, many have been chasing the perfect stat distribution. An important aspect of an armor set is the natural total tier: Players only gain beneficial effects from stats in intervals of 10 (30 Mobility has the same effect as 39 Mobility), so a large number of effective stat points with few stat points "wasted" indicates a high-quality armor set. Destiny Item Manager's Loadout Optimizer can help you find high-quality sets, as can D2ArmorPicker.
DIM's Loadout Optimizer found a natural T32 build
A natural T32 build is a set of fully masterworked armor which, without any stat-modifying mods or Stasis fragments, can hit a sum of 32 tiers in the six stats. A T32 set requires some high-quality armor, but most players who regularly complete activities with high-stat armor rewards (see TMMania's How Do I Get Better Armor guide) will be able to create these T32 sets with the help of optimization tools.
But can we go higher? Could an exceedingly lucky player with some amazing armor drops create a natural T33 set?
This is where you are going to have to do some background reading, particularly this reddit post by u/Jgugjuhi:
As far as I can tell, the information and data presented in this post is accurate. Understanding that post is necessary to understand the following. A very rough summary:
- Armor 2.0 pieces have a maximum base total stat of 68. Some exotics get +2 or +3 points in Mobility, Resilience, and/or Recovery for a natural base total of 71 for some exotics.
- Stats roll in two groups: The Mob-Res-Rec group (MRR) and the Dis-Int-Str group (DIS). There's a predetermined list of possible stats values each group can choose from (plugs).
First, let's strip the masterwork. Masterworking all pieces gives a +10 in every stat, so we can ignore the masterwork and instead say we're going for a base T27 build. This makes things easier, I promise.
Then, the argument as to why such a set could exist is easy: We have 4 statful pieces, each with a maximum of 68 base stats: 4*68 = 272, so we have a total of 272 stat points to distribute, which could give us a base T27 build with 2 stat points to spare. Factoring in the exotics with up to 3 extra points, we could have 5 stat points to spare.
In the comments of the post I linked above, u/theamarant said they "ran the numbers to look for the highest stat possible using the plugs, using 4x 68-stat armor and from the 272 total stat points, only a max of 260 affect stat tiers (in other words the max tier stat in a non-masterworked set is T26)". Some criticized that this search isn't exhaustive: We have 2, 4, or 5 stat points to spare depending on our exotic choice, so we could use one piece with a slightly lower stat total if it gives us more favorable distributions.
We could do an exhaustive search, but that's not fun. Instead, we're going to prove this in a much simpler way.
Please review the stat plugs list. There are a number of observations:
- MRR plugs and DIS plugs are symmetric. For any given armor piece, the set of possible values for MRR are exactly the set of possible values for DIS.
- MRR plugs and DIS plugs are independent: The game's choice of MRR plugs doesn't affect the choice of DIS plugs, any armor piece has a maximum of 34 points (2x17) in MRR and a maximum of 34 points in DIS, which are possible at the same time and the only way base 68 pieces exist.
Let's consider the maximum possible stat points in each group: We have 4 statful armor pieces with a maximum stats sum of 34 in each of the two groups. This means that the maximum number of points assigned in each group for a full set is 4*34=136. This means that even if these were perfectly distributed, each group individually can only hit T13 and the upper bound is 2xT13, so we just can't hit a natural T27. With fully maxed out armor, we waste 6 points in MRR and 6 points in DIS.
There's also an elegant and simple proof by contradiction: Assume a T27 build is possible. We'd need T14 in the MRR stats, and T13 in the DIS stats, or the other way around. 2xT13.5 doesn't really exist because 2xT0.5 in different stats doesn't add up to T1.
But we just observed that the possible stat plugs are symmetric: MRR stat values must be possible in the DIS stat values at the same time. So if a T14+T13 build were possible, then a T14+T14 must also be possible. Or in terms of masterworked armor: If a natural T33 build were possible, then a natural T34 build must be possible as well. But it clearly isn't -- we just don't have the stat points for that.
As per the intrinsic exotics stats list, some exotics gain 3 extra points in MRR. This still doesn't help us because we'd end up with at most 139 stat points in MRR and 136 stat points in DIS, which is still 2xT13 and still a base T26 build. The proof by contradiction is similar -- we'd need 137 points in MRR for the +3 to push us to T14, but then it must also be possible to have 137 points in DIS at the same time, which is a total of 274 base stat points, which is 2 more than the maximum achievable 4*68=272.
Some people want to minimize the "wasted" stat points, only want builds with stats that end in 0s or 5s. Don't do this for build quality. For one, we just showed that the best armor available won't have 0 wasted stat points, ever. Your best possible build will have wasted stat points. A 4x68 build necessarily wastes at least 12 stat points (2 if you allow +5s), and a 3x68 + 1x71 build wastes at least 15 stat points (5 if you allow +5s). On top of that you're scamming yourself out of better armor. You're choosing to use worse armor over better armor. Your tiers matter, your +5s matter, but the notion of "wasted" stat points isn't helpful.
