I'm seeing not only much smaller DPR numbers than you have listed (around 15, rather than around 25), but I am also seeing the DPR of the 2 higher strength higher than the DPR of the feat user (15.65 over two attacks with a greataxe vs. 13.55 over two attacks with a greataxe and using great weapon master's -5/+10).
Could you elaborate upon your math, and the assumptions behind it, so I can see why your math just doesn't even kind of line up with mine?
The spreadsheet has everything referenced so you can see it all in formula form.
Since the spreadsheet is rather big and can not be so user-friendly I'll write it out here. Numbers all provided on the 5th level of
DPR of Classes
Ignoring rage:
To Hit: A 5th barbarian has a 3(str)+3(prof) = +6 to attack. Compared to an enemy AC of 14.4 (rounded to 14 for flat 5% numbers for ease of use). If you want to see monster AC then look at "Monster Stats". It assumes fighting an distribution of enemies between CR 2 and CR 8 based on the numbers in the monster manual.
Back to the math: That's +6 vs AC 14. Barbarian needs to roll an 8 or above so his standard to hit is 65%, or 88% with Reckless Attack. Add in -5 and we're at 40% or 64% after advantage.
So we can take 64% and multiple it by the damage
Damage: I have the Barbarian using a battleaxe for thematics (Greatsword is slightly better). 6.5+3+10 = 19.5 damage if he hits. Add in crit of 5% and we get 20.1 (math can be seen in formula).
So if we take 20.1 and multiple it by .64 we get 13.1.
Multiple Attacks: We have 2 attacks so 13.1 becomes 26.2
Crit Chance: Advantage with 2 attacks gives us a 18.5% chance to crit.
Chance to Kill: Take the 26.2 damage from above and compare it to the average HP of an enemy. Average HP of an enemy for a 5th level character is 71 (see monster stats - same system as above). If we assume enemies are on average at about 80% of normal hp as our allies have hurt them (80% is probably very conservative) and we focus the hurt ones that gives us .8*71 = 56.8. 26.2/56.8 = 46% chance to kill an enemy
Overall GWM Chance: If we add the crit chance and kill chance (19%+46% = 65%) and remove the overlap we end up with 56%.
GWM Damage: So if we take our 13.1 from earlier and multiple it by .56 from GWM chance we get 7.4
Opportunity Attack: I assume opportunity attacks happen 1/10 rounds (or 10% of the time). This is very conservative I'd wager. Either way I multiple that by the greataxe (normal hit chance and without +10 as Reckless attack only works on your turn) we get .4 damage.
So a Barbarian without rage gets 34 DPR. Let's come back to this.
With rage
We have a similar process here.
14.4 damage on each attack. 28.8 total. 8.6 from GWM, .8 from OA. For a total of 38 DPR
Adventuring Day
If we now look at the number of rages the barbarian has we see he has 3 rages. Based on the DMG's XP system I use 4.44 combat encounters per day with 5.6 rounds per encounter to give us 24.9 rounds in a day. (I can expand on this if needed, but it would be really difficult to come up with more rounds per day using the game's expected system)
If the average combat is 5.6 rounds and we have 3 rages that's 16.8/24.9 = 67%. I assume a Barbarian can lose his rage 10% of the time and after rounding end up with raging 58% of the time.
Total DPR
So using the adventuring day above I multiple .58*38 DPR and .42*34 DPR and end up with
36.5 DPR.
Hopefully this has been helpful to understand what is going on.
When comparing the DPR of the -5/+10 boost vs. +2 strength, it is clear and unquestioned that the times when the -5/+10 option isn't used that the +2 strength has superior DPR, since it is both more accurate and more damaging.
This is not true. I showed the math on this above. GWM's cleave > +2 Str.