His analysis is correct, its been done on many threads by many other people before, but like I said the damage per round difference between a fighter and ranger should be 10+ round at level 5 and then go up from there to balance out the other things the ranger gets compared to the fighter. Same thing goes for other martial classes, the Fighter will out damage them all in static competition, but not by enough to really matter compared to the other things the other martial classes get.
For example, build an optimized fighter compared to an optimized Paladin at a level, say levels 5-11 where most games are. Both get weapons and armor and a fighting style. The base Paladin chassis gets self healing with Lay on the Hands (takes an action by still good,) Smites (fun and useful and adds a lot of spike damage), immunity to disease (always useful,) bonuses to saving throws for you always and the party sometimes, immunity to fear for you always and your party sometimes, and then improved divine smite, adding more damage to your base attacks (but not as much as an additional attack.) The base fighter chassis gets an extra feat and an extra attack at 11th level, Second Wind (less effective but more action efficient then Lay on the Hands) Action Surge, and a reroll on a failed save. I would argue Divine Smite is better than Action Surge since its impossible to miss using it and it also gets doubled on a crit, but Action Surge is still good. Rerolling a failed save is not all equivalent to getting bonuses to all save for you and party plus immunity to disease and fear. Both get a subclass, BM is good but so are Paladin Oaths.
The real difference is the Paladin gets so many good and useful base abilities to its class that a fighter can't compete unless they are significantly buffed. The same goes for the other martial classes too.
The idea here is make the fighter base chassis better. The more I think about it the more I think the Champion subclass should just be melded into the fighter base chassis and then go from there.
That's the big-picture point that I made several times but somehow got lost in argument over numbers.