World-of-warcraft – How do the new PvP stats work in Mist of Pandaria

PvP Power is the aggressive form of resilience. It improves the amount you hit for against player opponents, acting as a rolled up AP/spell power stat. One interesting case is healing, where Blizzard was unsure on how to handle differentiating between PvP and PvE. They haven't confirmed what their plan for that was yet. Update: They have now, see edit at bottom.

Resilience works the same way it works now, but may have had its effectiveness tweaked given the addition of the PvP Power stat. They have added a base Resilience as well (see later).

Looking at Wowhead's Mists of Pandaria site, old PvP gear has not been changed.

Most of the information we have on PvP Power and PvP stats in general from from a Dev Watercooler blog post:

Resilience

• We are renaming this stat to “Defense (PvP)” or possibly “PvP Defense.” All players will have 30% base Defense, the same way all characters have some base Stamina. PvP gear will have Defense on it, as well as a new stat, “Power (PvP).” Power increases the damage you do to other players as well as the healing you do to other players in PvP situations.

• If you have a lot of Power, you’ll do more damage to other players, but they likely have Defense as well. If you fight players in lots of PvE gear, they’ll take more damage. Likewise, a player in PvE gear won’t have enough Power to effectively penetrate your Defense.

• The names PvP Power and PvP Defense may not be final, but we’re leaning towards going with stat names that are obviously PvP-related, rather than “fluffier” names that might not be as easy to grasp. We want it to be clear to players that neither Power nor Defense have any relevance when fighting creatures, such as in dungeons or raids.

• PvP gear will be lower in item level than PvE gear of an equivalent tier, however the Power and Defense stats will make sure that PvP gear is more powerful in PvP (both offensively and defensively) than PvE gear. In our budgeting system, the PvP stats will be free rather than causing other stats, such as Strength or haste, to be smaller as a result of including Power or Defense.

• The goal of this change is to make it easier for a PvP player to participate in PvE, or for a PvE player to get started in PvP. Currently, we feel it is too large a barrier to go from one to the other, and the result has been that we see more and more players choosing to focus exclusively on only PvP or PvE. In earlier expansions, it was more feasible to use PvE gear in Arenas or Battlegrounds until you acquired the more useful PvP gear. The same was true of being able to use your PvP gear in a dungeon or raid until you acquired something better. In Cataclysm, stepping into PvP with no PvP gear would result in a player being so ineffective that it was difficult to even make progress towards acquiring PvP gear.

• For the higher-end of PvP or PvE (say Gladiators or heroic raiders), we believe those players will still gravitate towards the dedicated PvP or PvE gear. It is the players who are working towards those two end games that will benefit more from some cross over.

Edit: Extra information on using PvP Power for healing:

PvP Power should do nothing for your healing in a dungeon or raid. When healing someone in a BG, Arena or in the outdoor world, PvP Power should increase your healing. The only exceptions are percent based heals.