What is Shaper DPS, and how is that different from tooltip DPS?
What is the difference between Shaper DPS and tooltip DPS?
The Shaper has 40% elemental resistances, 25% chaos resistance, and 66% reduced curse effectiveness. These effects can significantly reduce the damage that many builds can deal against him, especially builds which rely on elemental damage and/or curses.
The same properties are present on many other endgame bosses, like The Elder, Shaper guardians, Elder guardians, and Legion generals, as well as in lesser forms on Atziri, Delve bosses, Abyssal liches, Incursion architects, etc. As such, "Shaper DPS" is a useful proxy for a build's effectiveness against endgame content.
Additionally, "tooltip DPS" generally refers to the number displayed on the in-game tooltip. This number is calculated in a relatively simplistic fashion, by summing all types of damage dealt by a skill and multiplying by attack/cast speed; it does not take into account other effects which may boost a player's effective damage, like elemental penetration, debuffs placed on enemies, conditional bonuses, or damage-over-time effects you can cause such as ignite, bleed, or poison. (It is also entirely ineffective at calculating DPS for skills which deal damage indirectly, like minions, traps, or mines, or for skills which are triggered by Cast on Critical Hit or other trigger supports.)
"Shaper DPS" is generally calculated using the third-party Path of Building tool, which can take most of these effects into account.
Tooltip DPS - number shown in your game, it simply represents damage (divided onto your attacks per second) you can deal with a single attack of your skill to a normal enemy. It could miss lots of things, like additional damage over time from the same skill or piercing into other targets. So, tooltip DPS is about your single skill versus some abstract enemy.
So community come up with proper tooling to calculate actual DPS. For example, one can use Path of Building (I am not affiliated, but I use and recommend it), where you can customize lots of things - for example, effect of curses you apply. Also, in PoB you can take into consideration enemy skills or resistances - there is drop down menu with different bosses.
So here comes Shaper DPS - DPS in PoB against Shaper. His resistances are 40 fire, 40 cold, 40 lightning, 25 chaos, and he has 66% less curse effectiveness. So Shaper DPS is about your character applying whatever skills they have onto this specific end game boss.
Why Shaper though? I don't know, he is one of the end game bosses, maybe the toughest.
Also, this Shaper DPS makes little sense - you cannot deal damage all the time, you will spent majority of the battle running from that huge flying thing or crazy laser beam or that growing spot on the ground.