Sheet DPS

Sheet DPS (AKA "Paper DPS" or "Profile DPS") refers to the damage per second listed on the Character window display in game, or seen in the Battle.net character armory. This value is meant to give a one-number indication of a character's total damage output and while it was a fairly useful figure in Diablo 3 vanilla, its' become much less so in D3v2 and especially in Reaper of Souls.

The problem with Sheet DPS is that the number does not include damage from Paragon Points, or from various item affixes such as +damage to individual skills, +damage to elemental skills, and +damage to Elites. Well-geared characters in Reaper of Souls often have 2 different items adding 10-15% damage to their main attack skill(s) and 20-100% (or more) damage to 1 elemental damage type. Neither of these increases to damage are factored into the Sheet DPS, so it's easily possible for a character to deal 2-3x their listed DPS with every hit of their main skill.

Players who want to estimate their "Effective DPS" must use guess work, figure out the numbers in their own spreadsheets, or use character planners or damage trackers via third party websites such as Diablo3Ladders.com or DiabloProgress.com.

Stats Improvement?

The Profile Toughness display has similar issues, with bonuses from item sets, passive skills, and paragon points not included, which makes for an even larger disparity between the "sheet Toughness" and the in-game figure.

The incomplete nature of the sheet DPS and Toughness has prompted fans to make unkind references to Diablo 2's infamous "Lying Character Screen" (LCS), and strong majorities of fans[1] want to see accurate information or even a full-on "DPS meter". Despite this popular demand, Blizzard has resisted making any upgrades to the character window, asserting that it's good enough and meant to be a rough estimate of character power and survival, rather than an exact measurement. [2]

Nevalistis: The DPS, Toughness, and Healing stats are all meant to be general, quick evaluations of your character’s power. While you will have a better grasp of exactly what your character is capable of by more closely analyzing your individual stats, these overviews are there to provide this information at a short glance. Similar to the green or red Damage/Toughness/Healing estimations that show up when evaluating a new piece of gear, scrutinizing the details will give you the information needed to make those more precise gearing decisions.

...

Ulvareth: We know that a DPS meter is a fairly frequent request and you can be sure that we’ve talked about it. Ultimately though, we feel that a DPS meter would put too much focus on one single aspect of the game and we currently don’t have any plans to implement one.

Let me explain why we feel this way: DPS is certainly important, but Diablo is a combination of activities. Healing and Toughness are are important, too, and your movement and positioning, your ability to aim with certain abilities and using them at the right moment also play an important role in “determining” how “well” you’re doing. DPS alone shouldn’t be the only number that matters when you play.

Fansite Diablo.IncGamers.com ran a public vote on the issue when those two Blue quotes were fresh:[[3]]

Would you like an advanced DPS meter in Reaper of Souls?

• 1) I'd like a damage output meter that tracked all damage done. (50%, 1,023 Votes)
• 3) I like the current DPS, but it should estimate +skill and +elemental damage (say when I hit the Ctrl key). (36%, 737 Votes)
• 2) I think the current DPS display is fine. (6%, 115 Votes)
• 4) I'd like the DPS display removed entirely (at least for others to see). (5%, 112 Votes)
• 5) No opinion or something else. (3%, 57 Votes)
• * Total Voters: 2,044

Despite these clear fan opinions, Blizzard has resisted improving the DPS or other in-game number displays. The only thing they've allowed is that Toughness and Healing can be misleading (over-valuing HPs above defense and resistance damage mitigation stats) and they might make some changes there. [4]

Wyatt Cheng: We’ve been talking about changing Healing into a “Toughness healed per second” value. This unfortunately makes it even more of an abstract concept, but it would help take into account that your damage mitigation enhances the value of your Life recovery stats. The ultimate goal of the three summary stats is to provide a “quick gut check” of an item’s effect on your character, and making this change to Healing could probably help guide people better.

It's unclear if the developers' satisfaction with the inaccurate numbers is really their opinion, or if they just think making more accurate numbers would be too much trouble with the programming or explanation/display to make them understood by fans.