And if you're noticing that the group is not making it out of pulls alive, slow down. Your healer may be too proud to admit that they're just clinging on to the edge, but losing DPS is actually going to make your run slower, not faster, as you wait to res and rebuff. Compare that to the time lost by pulling one pack less and you'll see how it works.
2. Keep an eye on mana levels
This is another tip that centers on making sure your healers can take care of themselves, but it can be the case that a healer is working their backside off trying to keep a DPS alive while they're standing in poop, and therefore doesn't quite have the time to type "Mana" before you charge headlong into the next group of adds. Yes, a healer should take control, and if your healers are on half mana, don't assume that that means they want a top-up.
But just take a glance at their blue bar before you keep pulling. If they're running on empty, you're not going to get very far, as the pulling big packs approach usually requires some healing input. Yet again, if we're looking at this as a time-saving exercise, you're going to go faster with a healer that can heal. And before a boss, particularly one that requires some healing, just take a moment before pulling if your healer is below, say, 80% mana. If they don't sit down to drink, then you're probably good to go. The 5-man ready-check can be a good option here, too, to be doubly sure.
With DPS mana regeneration as high as it is at the moment, your DPS are unlikely to have problems, but again, if you've got a player on 0% mana, that can slow you down.
3. Know your enemy
This is certainly among the most important factors in successful chain-pulling. If you don't know the fights, pushing ahead in a huge rush isn't likely to work out that well. Of course, you could well be in one of the more straightforward dungeons with the more straightforward packs, and you'd be fine, but largely it really helps to know what you're getting yourself into.
For example, from Shado-Pan Monastery, unless you're pretty well geared, you'd probably do well not to pull all the required Sha together on the run from the second boss room to the bridge. Those would be best left until at least a few are dead before chaining to the next two required groups. And the same applies in, as another example, Mogu'shan Palace, where, once the Flameseekers or Stormcallers are down, packs can easily be chained. Largely, taking out casters is a priority, but if your trash has special abilities, that might differ.
4. Use your cooldowns
Don't save them for special occasions. The vast majority of my tanking is done on a paladin, so forgive a lack of in-depth knowledge of other classes, but most of our cooldowns are not on such long timers that saving them for a rainy day makes much sense. Using cooldowns regularly and sometimes pre-emptively can make a run far smoother and faster. What's more, as a paladin, some of our cooldowns can be placed on other players to aid damage mitigation and help the healers with their task.
5. Watch the rest of the group
Yes, it's their responsibility too. But you know who's going to get the blame when the boss is pulled and the door closed with two of the three DPS trapped outside? That's the tank, and rightly so, they're the one who does the pulling. Of course, if a DPS pulls, or a healer, that's a different matter, but don't assume your group are with you at all times, just because you're moving at a frenetic pace. They might be grabbing quest items, which, by the way, can often be done via a retrospective trip back from whence you came.
Even worse, if you pull a boss and shut a healer out of the room, you'll really be in trouble. Do set your raid frames to grey out when healers aren't in range, and make sure they're at least en route before pulling. And if your DPS are tunnel-visioning and don't realize they're standing in purple, you can make your healer's life easier by kiting mobs out of it.
The moral of the story is that, unless you really outgear the content, you'll be the best chain-puller by being the best tank you can be, so aim high. And you'll get satisfaction from your success, too.
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