I agree that overall the Xanathar Zealot subclass is superior to Berserker, but the initial calculations for this seem off....
Good thoughts! A nice reasoned analysis just like I like.
In terms of damage though, Berserker should ultimately come out ahead by a moderate amount -- not huge, but discernible.
Since it appears you are agreeing with me that this is only true at level 14+, I'm not sure where you are noting a disagreement. Berserker does a little more damage than Zealot at levels 14+ due to Retaliate. (I'd prefer it if they did more damage before 14th level too, but we also seem in agreement that they don't.)
While I'm going to try to exercise some self-restraint, rather than giving into forumitis and debating a point simply because a point was stated, I do think that one of your conclusions might not be entirely correct, so let's go into those.
If I am interpreting you correctly, you are proposing that Berserkers of levels 14+ should do even more damage than I am giving them credit for. I made an assumption that Retaliate would happen on about 75% of rounds, while you propose that we should consider it to occur on 100% of rounds. You're basing this on the ability of a player to reliably provoke opportunity attacks on their Berserker.
As you said, this is going to depend on how the DM runs opponents. I'll take my play experiences (as DM and player) as a baseline, supplemented by the experiences others have shared on the forum. Parties tend to face a variety of opponents, from creatures of bestial intelligence, to super-genius villains. With regards to creatures of bestial intelligence, I might allow a Berserker to do the opportunity attack dance you describe to get attacked most rounds until the creature decides it can't win and decides to run away. However, many DMs will likely argue that bestial intelligence is enough to stop doing something that hurts you unless you are clearly being more effective at preserving your life doing it than not. With more intelligent foes, I generally decide that you can tell if you are provoking an opportunity attack by an action, at least after you've provoked the first one. Some DMs always let you tell before provoking the first one. It has come up on the forum that most people seem to strongly dislike it when a DM makes it impossible to know if you are provoking an opportunity attack, so I'm going to count doing that as a non-preferred playstyle. It's also generally a non-preferred playstyle for NPCs to get benefits that PCs don't in situations like that. Most DMs are going to either run it equally (ie, smart NPCs make tactical decisions with the same sorts of information available as the players do with their tactical decision), or favor the PCs to some degree.
The assessment I'm going to make here is that DMs will tend to allow NPCs to determine if they are going to provoke opportunity attacks by attacking a Berserker, at least after the first observed such attack, and that intelligent play means that they will choose whether or not to take those attacks based on an analysis of whether it would be to their advantage, which means that some of the very times the Berserker is trying to make it happen are going to be times they are certainly not wanting it to happen. I'll assume they are slightly more accommodating with creatures of bestial intelligence.
Overall, I think it may be true that use of this technique (including the advantage on attack from Reckless attack due to being on your own turn) could increase the expected damage output on a Berserker of level 14+ to a somewhat higher level that I assumed. I do not, however, think it would approach 100% due to the somewhat situational nature of its effectiveness.
There is also, I'm going to propose, a downside to using this technique.
Note: Often when you provoke an opportunity attack you are going to be provoking it from more than one opponent--especially when attempting a back and forth dance like this each round. Subjecting yourself to additional attacks obviously means you are going to take more damage on average. Keep that in mind, because the possibility of multiple opponents getting opportunity attacks on you (while you're still just getting one Retaliation) just amplifies the points I'm going into next.
Let's examine the resiliency/damage output of a Barbarian in general.
Reckless Attack by itself (without raging) is trading hp for damage. This means that a non-raging Barbarian using Reckless Attack effectively has less hit points than d10 HD classes. They have less staying power than a Fighter, Paladin, or Ranger if they use that feature by itself.
When a Barbarian rages
without Reckless Attack they gain both an effective increase to their hp, and additional damage. It's a pure buff.
When a Barbarian uses Reckless Attack while raging. we can consider (and I think this was design intent) that the vulnerability they get from Reckless Attack is basically offset by the damage resistance they get from raging. This leaves the net result of raging with Reckless Attack being a really nice damage boost, with their effective hp staying pretty close to that d12 HD range. My gut tells me that it might actually, on average, weaken them a bit to be closer to a d10 HD class, but in any event it is a fairly minor difference overall. (Obviously it would be difficult to determine precise numbers here, but I think the pattern is intentional.)
How does the Berserker's Retaliate feature interact with that? Well, in and of itself, it doesn't. It just gives an overall, no downside, damage boost depending on how often it triggers. But if you are
intentionally provoking attacks to trigger it, beyond the attacks that a Barbarian would normally expect to be taking, you are trading hp for damage output. At this point you are weakening the overall staying power of your Barbarian similar to using Reckless Attack without raging. You now have less effective hp than Fighters, Paladins, and Rangers.
The choice to do that is great! You can do the opportunity Retaliation dance when it seems like a tactically good idea. But if you are doing that intentionally all the time your Barbarian effectively has less hp, which makes them a less effective meatshield than is assumed for a Barbarian.
So if you are always making use of that technique (opportunity attack Retaliation dance), you are either playing a less tanky Barbarian than expected, or if you want to keep your resiliency where expected for a Barbarian, you must have another way of moderating that effect, such as a healer in the party who is particularly dedicated to spending higher level spell slots (or other character resources) keeping your Berserker's hp where they are expected to be. Generally D&D doesn't assume the MMO style in-combat constant healing, since it's generally better to save all but emergency healing until after combat, so that really is a cost to the character who dedicates extra focus to healing the Berserker, and therefore it is a drain on party resources.
In other words, the dance may increase damage a bit, but it isn't free.
As far as Fanatical Focus versus Mindless Rage, I personally agree with you that Fanatical Focus is more desireable than Mindless Rage (and good catch that it can be used multiple times by restarting your rage!), but in previous discussions about Mindless Rage many people have seemed to value it quite highly, so I went with treating them as roughly equivalent. If you and I instead interpret it based on our shared opinion on that, Zealot gets even better.
Overall my suggestion remains the same: just straight-up remove the exhaustion from a Frenzy. The class by no means becomes unbalanced by doing so, and is possibly still weaker than its similarly damage focused cousin the Zealot (but at least you don't have to feel cheated by taking it, because it is then pretty close in power).
So, again, thanks for the additional thoughts to contribute to the conversation. I really enjoy detailed analysis of this sort of thing.
