delericho
Legend
This seams unfair, the Barbarian loses ~41.7% of his HP per level compared to the maximum 12, the fighter and paladin loses 30% of maximum of 10, and the ranger loses 12.5% of maximum of 8.
The first, key thing I would note is that comparisons with the theoretical maximum are largely invalid - the barbarian may have the potential of 36 hit points at 3rd level, but they're highly unlikely to get that. On average, they can expect to get 25 hit points (12 + 6.5 + 6.5). My system gives 26 (5 + 7 + 7 + 7), so they come out ahead. And that's the case across the board - nobody loses as a result of this change when compared with the average roll, though not everyone gains as much.
You are correct to note that the Fighter and Paladin gain more than the Barbarian from this change. But the RAW Barbarian is actually quite a bit more powerful than the Fighter, so giving the Fighter a bigger boost really is no bad thing, IMO. (Obviously, relative power levels between the Paladin and the Barbarian are much more debateable.)
As for the Ranger...
The truth is that tying the number of hp to BAB was done following the Pathfinder approach, which is why Rangers move up to the Fighter level and Barbarians move down. (Pathfinder left the Barbarian at d12 as an exception to their general rule; I dislike exceptions, so got rid of it.)
For the medium BAB, d8 classes its a 47.5% loss.
For the medium BAB, d6 classes its a ~12% loss.
Those are huge gaps IMO.
Compared with the average, the Cleric gains 0.5 hp per level on average, while the Rogue gains 1.5. But given that the Cleric and Druid are basically the most powerful classes in the game, again, I don't see it as a problem that the Rogue (and even Bard) gain more.
(That said, the Monk doesn't do well out of this, given that she's already amongst the weakest classes and she's also the one that gains least from this change. But the problems with the Monk go much deeper than can be fixed with a tweak to hit points. So the Monk didn't feature in my consideration when making this change.)
The idea of a fixed HP gain per level is fair compared to rolls, IMO. But the best idea is to make the gain either 50% or 100%, then you get nice round numbers.
Giving 100% of hit points is a pretty significant boost to PC power levels, and really not something I wanted to do. And giving 50% has the downside of reducing everyone's hit points versus the average, which I also didn't want to do.
If I gave out the average on the die (2.5 for Wizards, 3.5 for Rogues, 4.5 for Clerics, 5.5 for Fighters, and 6.5 for Barbarians), then that would require dealing with fractions, and an endless nitpicking of PC for players who choose not to understand "round fractions down".
The final option, to give "50% plus one", was something I did in the past. But it had exactly the same problem as is seen here - Wizards were getting 75% of maximum while Barbarians were getting 58.3% (and Fighters 60%).
Having used the 7/5/3 split in a couple of campaigns now, I've found that it does work really quite well. Granted, I've avoided the Barbarian/Fighter/Ranger problem you noted because I've only ever had one "primary combatant" in the group ("primary spellcasters" are much more popular). And replacing "max hit points at 1st level" with "everyone gets +5 at first level" has the effect of getting rid of an awkward bit of multiclass math (where a Rogue 1/Wizard 1 by RAW will either have more or less hit points and skill points depending entirely on the order in which the classes were taken), and has the useful side-effect of giving all those 1st level characters that little bit more sticking power.