Okay, so there are some interlocking synergies here that are going to need some explaining, so bear with me (as usual, the WALL OF TEXT warning was not idle!).
Perhaps the biggest overall factor that will decide how enjoyable (or well) this build will play for you is going to be determined by … investing in Arms from Levels 10-20 in order to acquire Anger Management as quickly as possible. I
cannot stress enough
how important this investment is to your efforts (or should I say, NEED) to fend off Rage Starvation during your adventuring career. That’s because Anger Management IS … hands down, bar none … the single BEST source of Rage generation in ANY talent tree or item you can equip or invest in. It is simply that level of game changing. 
So what does the tooltip on the talent say Anger Management does? 
- Anger Management - Rank 1/1
Increases the time required for your rage to decay while out of combat by 30%.
Sounds pretty useless, right? 
Why should anyone care if it takes 30% longer for Rage to decay when you’re OUT of combat? You need Rage while IN combat, not while OUT of combat, right? So Anger Management doesn’t DO anything for you while you’re actually IN combat, right? 
WRONG! 
Here’s what Anger Management ACTUALLY DOES under the game mechanical hood. Ignore what the tooltip says and pay attention to what I’m telling you it does in the proper context (because a chart is worth hundreds of words!).
| Combat |
Rage |
Rage Decay |
Anger Management |
 |
0+ |
-0 every 2.5s |
+1 every 4s |
| NO |
1+ |
-2 every 2.5s |
+1 every 4s |
| No |
0 |
-2 every 2.5s |
+0 every 4s |
Note the lack of a proc chance in that itemized description of cases.
Anger Management is simply ON … at all times … that actually matter. 
But wait … there’s more … 
I’ve run a quick little test using my Warrior in Stormwind. I cast Taunt on a Rat within 5 yards … with Anger Management … while starting at zero Rage to test the notion.
- Taunt put my Warrior into combat, which turned off Rage Decay.
Combat mode lasted for about 13 seconds (PvE), while the Rat ran around and I just stood there, waiting for the Rat to “leash” and come back.
- Anger Management started ticking for +1 Rage every 4 seconds … even though I’d started at zero Rage(!) … because my Warrior was In Combat.
- When Out of Combat, Rage Decay and Anger Management will both continue to run concurrently, applying their -2 Rage every 2.5 seconds (Rage Decay) and +1 Rage every 4 seconds (Anger Management) effects … until Rage reaches zero.
This is then why I can walk out of Stormwind to the Deer and Fawns just to the southwest of the gate, park beside the two Fawns, and alternate casting Taunt on them and slowly gain Rage at a rate of +1 Rage every 4 seconds, staying in combat the entire time (meaning no Rage Decay), even when starting with zero Rage … because use of Taunt puts my Warrior into combat mode for what looks like 13 seconds (3 seconds of Taunt duration plus 10 seconds of no other damage or interaction) before the Critter, in this case 1 of 2 Fawns, would “leash” and drop combat so as to return to their spawn point, Evading the whole way.
But Taunt has a 10 second cooldown (untalented).
This means that with Anger Management and Taunt, it is perfectly possible to make use of Critters (without killing them!) to generate additional Rage for your Warrior by deliberately putting yourself into combat, turning off Rage Decay for a short time (13 seconds = 6 Rage Decay ticks = -12 Rage loss avoided), during which time Anger Management will gain +3 to +4 Rage (depending on the timing of the +Rage ticks during those 13 seconds) … before you drop out of combat (if you haven’t Taunted a different Critter, or the same Critter again as soon as Taunt cooled down) and Rage Decay starts taking effect and “overpowering” Anger Management (like it’s supposed to) in order to drag your Rage down to zero again.
For comparison purposes, you could spend go for 5/5 Unbridled Wrath in the Fury tree for a 40% chance to gain +1 Rage every time you deal damage with a weapon. 40% of 4 seconds is the (rough) equivalent to needing a 1.60 Weapon Speed in order to rival the Rage generation (averaged over time) you’d get from 1 talent point spent in Anger Management. You can get close to (or even exceed) that by use of fast(er) weapons and/or Dual Wield combos, although the latter means discarding your Shield options. 
Basically, Anger Management will be generating 15 Rage per minute for you ALL THE TIME … FOREVER … so long as you are either:
- In Combat
- Out of Combat but Rage is above zero.
Think about that. Other investments you can make on your Warrior can come close to that level of yield/return, but they’ll be hard pressed to match or exceed it, and the only thing that really comes even close would be Unbridled Wrath and Shield Specialization, both of which are highly situational (must be attacking stuff). In contrast, Anger Management is JUST ON … and STAYS ON … no damage dealing/taking required.
You can get Rage generation out of Shield Specialization in the Protection tree too, but it isn’t going to be able to match a +1 Rage per 4 seconds rate of return at all times that matter (both IN and OUT of combat). At best, you’ll be (reliably) generating about +2 Rage out of 5/5 Shield Specialization (plus 1/3 Improved Shield Block) per use of your Shield Block spell, which has a 5 second cooldown … meaning +2 Rage every 5 seconds, when using Shield Block on cooldown … yielding a 0.4 Rage per second rate of return, compared to Anger Management’s 0.25 Rage per second rate of return. This means that Shield Specialization CAN, in the right circumstances (meaning while tanking, in combat, when you have aggro), outperform the Rage generation of Anger Management … but only when you’re able to Block with your Shield, meaning melee attacks only. Ranged attacks and cast spells can’t be blocked by your Shield, so Shield Specialization isn’t helping you with Rage generation in those cases. 
Now, to be fair, you’ll also gain Rage simply by doing damage with your weapon, and also gain Rage by taking damage when hit. The preference is that you’ll gain a LOT more than +1 Rage every time you hit with your weapon, and you’ll often gain +1 (or a few more) Rage when you’re hit for damage by an enemy attacking you, and both of these means of Rage generation will often exceed what Anger Management can yield, but both of these methods require a trading of blows in order to happen. Anger Management will continue generating Rage for you even in the absence of damage being dealt or taken.

The key thing here is that Anger Management is “working for you” AT ALL TIMES (that matter).
This is true while in combat … and out of combat.
And better still, it’s perfectly possible to keep your Rage above zero full time!
Now, while you’re in combat, you aren’t losing any Rage to the mechanic of Rage Decay. Rage Decay ONLY occurs while out of combat (see: chart above
).
This is where the tooltip on Anger Management “gets it right” (kinda, sorta, maybe?
) while leaving out all of the other stuff I’ve been talking about above regarding the (actual) effects of Anger Management while in combat.
As you can see, losing -48 Rage per 60 seconds while Out of Combat from Rage Decay and gaining +15 Rage per 60 seconds from Anger Management in that same time span reduces the overall effect from -48 to -33 net Rage lost due to out of combat decay, which is actually closer to a 31.25% reduction in Rage Decay (30% would have been +14.4 Rage over 60 seconds, rather than +15 Rage, but I’m not complaining with the round up to integer). I consider this to be an acceptable margin of error with regards to the tooltip on the talent, given the complexities of what’s ACTUALLY happening under the game mechanical hood, and that the “error” in this case is (slightly) in the Player’s favor, no matter how you look at it. 
But that’s not the end of the story of how good Anger Management is for a Protection Warrior as a source of RELIABLE Rage generation, helping you to fight off Rage Starvation.
Over in the Protection tree, there is Improved Bloodrage, and with 2 talent points invested, you’ll get an additional +5 Rage instantly upon casting Bloodrage.
Okay … so what (I hear you ask)? Whoop-de-fricken-doo-doo. 
+5 Rage on a 1 minute cooldown? YAWN! 
Well, you can be forgiven for thinking that … until you realize Bloodrage will put your Warrior into combat. That means you can put yourself into combat ON DEMAND … and when you do so, Anger Management will be generating Rage for you … BECAUSE you used Bloodrage.
So here’s what the Rage math looks like for that. 
+10 Rage instantly (untalented), enter combat instantly
+5 Rage for 2/2 Improved Bloodrage
+1 Rage per second for 10 seconds, remain in combat for those 10 seconds (meaning no Rage Decay for those 10 seconds)
+2 to +3 Rage over those 10 seconds due to Anger Management adding +1 Rage per 4 seconds (variance purely due to the timing of the +Rage ticks during that time frame)
= +27 to +28 Rage … after 10 seconds, due to use of Bloodrage
Bloodrage will go into its 60 second cooldown upon being cast, but by the time the buff effect ends, it will have 50 seconds of cooldown time remaining. During those 50 seconds, assuming you don’t enter Combat again (thereby stopping Rage Decay), you will lose -40 Rage, at a rate of -2 Rage every 2.5 seconds. However, you gained +27 to +28 Rage from use of Bloodrage in the first place … and Anger Management will continue generating Rage for you after Bloodrage’s 10 seconds of combat effect ends! 
Let’s take the more conservative estimate of only getting +27 Rage from (Improved) Bloodrage. This is actually enough Rage to prevent Rage Decay from letting your Rage fall to zero during the remaining 50 seconds before Bloodrage finishes cooling down, because Anger Management will generate ANOTHER +12 to +13 Rage (again, variance depending on the timing of the +Rage ticks) for you before you can use Bloodrage again over the course of the entire 1 minute cooldown for Bloodrage. The important thing to know here is that Anger Management will grant +15 Rage per 60 seconds.
+25 Rage (Improved Bloodrage over 10 seconds in combat)
-40 Rage (Rage Decay over 50 seconds out of combat)
+15 Rage (Anger Management over 60 seconds)
= +0 net Rage gain/loss per minute
This means that with 2/2 Improved Bloodrage AND Anger Management combined, it is possible to perfectly break even on Rage gain/loss every minute without having anything around to target, attack or otherwise put yourself into combat against … so long as you cast (Improved) Blood Rage on cooldown. 
Which doesn’t sound all that impressive … until … you add in use of Taunt against Critters nearby to you during a 1 minute cycle of Bloodrage cooldown and you’re looking at a NET gain of roughly +13 Rage per Taunted Critter due to disabling Rage Decay while in combat for 13 seconds AND gaining +3 Rage from Anger Management during those 13 seconds for a single Critter you let run away and come back on its own … or an outright cancellation of the -40 Rage lost to Rage Decay if you can “juggle Taunt” a pair of Critters that will run back to you after they drop combat while simultaneously gaining Rage from Anger Management!
And if you “need a Critter on Demand” to Taunt (without killing) for “free Anger Management bonus Rage” while cycling Bloodrage on cooldown, so you can enter the Big Battle™ with close to 100 Rage … what you need is an Unconscious Dig Rat. 
Why? 
Two words … FREE RAGE.
You’re welcome!
What this means then is that you can, with Improved Bloodrage and Anger Management (and the occasional use of an Unconscious Dig Rat if needed), “carry” your Rage from fight to fight … even while standing around waiting for the rest of your dungeon party/raid group to get organized … without ever letting it drop down to zero. All you have to do is use Improved Bloodrage on cooldown and you’re at net ZERO loss of Rage per minute thanks to Anger Management. If you can put yourself into combat through Taunting a convenient Critter, you will have net POSITIVE gain of Rage per minute … enough to top up and stay conveniently high, either while on the move or just standing around waiting to engage, without needing to resort to use of Charge for the privilege.
And yes, Bloodrage will cost you a small amount of health to cast … but once the buff effect ends and you drop out of combat, it will typically take only a few ticks of Spirit recovery to heal that loss of health back up to full. In other words, your best use of Bloodrage will either be when out of combat (and planning to stay out of combat) for a while, so as to “carry” your Rage forward to whatever your next fight is going to be, or when you either have a healer willing to top you up real quick on the cheap, or you don’t mind using Bandages on yourself to speed up your own recovery because you don’t want to wait for Spirit to do the job for you.
Note also that this means that using (Improved) Bloodrage, Anger Management and Taunt only twice in a 1 minute Bloodrage cooldown cycle, carefully spaced to optimize your in combat/out of combat cycling, your Warrior will GAIN +33 Rage per minute … meaning that in as little as 3 minutes of not that much work, you can push your Rage to near 100 and then keep it there until everyone is ready to go tackle something.
If you’ve got 2 Critters that have spawned nearby to each other, you can “juggle Taunt” the two of them to keep yourself in combat all the time and never drop out of combat. With a friendly healer who can toss a cheap Heal over Time spell onto you, you can generate +20 to +25 Rage from Bloodrage (untalented versus improved) alone per minute, and another +15 Rage per minute from Anger Management, for a total of +35 to +40 Rage per minute gained without needing to do damage to ANYTHING, or take damage from anything (aside from Bloodrage itself). Needless to say, a mere 2.5-3 minutes of that activity will give your Warrior up to 100 Rage to take into pretty much ANY battle (just “carry it on over”).
So please, Warriors … educate your groups about the value of letting the Critters in dungeons and raids LIVE so that you can Taunt them for Rage because YOU have got Anger Management (and you know how to use it)! 
So, are we all clear now on the advantages to be had from Anger Management, despite what the tooltip for the talent says/implies?
Yes?
Alright, moving on …