D&D 5E On Die Averages and Hit Points in 5e

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Sure. But are you adding con bonus?

If you are, then the roll system you have has HP about as high as the baseline one at medium high levels.

Ignoring "keep the lower level version", at level X you have one less than (HD/2) + (Level/2) fewer HP on average. Relative to baseline, this has the largest impact at low levels, and is smaller at higher levels.

The ability to use lower rolls +1 gives you a larger boost at higher levels I think? Basically, the chance that 7d8 > 8d8 is higher than the chance that 3d8 > 2d8. It also is significant in T1, where the +1 over a max die is a reasonable possibility to help.

This is probably worth simulating, as the math gets annoying. It is small enough that a probability based simulation isn't needed; just do every die combination maybe with a bit of dynamic programming, and you can solve it completely.

Yes, adding Con bonus to each die. I cheated on the maths by making a monte carlo and that indicated to me on surface that most characters will fall several points behind taking averages. Possibly because of discarding (rerolling) that one first maximum die after 1st-level.

My comparative is 8+(7*5) vs the better out of 7d8 and 8d8. Looking at anydice, the chance of not doing better than 42 across those two rolls is above 80%. A similar case is 6+(7*4) vs the better of 7d6 and 8d6. The chance of not doing better than 34 across the two rolls is in the range of 90%. That's not considering the full progression of course, so the real odds must be a few % more favourable.

Based on our historical campaign tracking, to reach that level we're going to see eight or so characters. So crudely, I might expect one or two characters to do better than max-at-L1+(average-roundup*level). Most likely martials (as the bigger the die, the greater the chance of doing better).

I'm aiming for characters to feel a bit more precarious, so I do want them rolling. An alternative is to revert to reroll-1s, if I made that mandatory. I wouldn't use straight rolls due to the locking in bad rolls factor.