This made me curious enough to sit down and do the maths on it all. At a point in this there will be a ton of charts. If you aren't interested in the charts don't click the link to the spreadsheet and just move on to the analysis.
The following list is the assumptions I will be using for this exercise. Much of this comes from the Constitution section of the current playtest.
- Level 1 HP is Constitution Score plus Hit Die Roll.
- Mundane healing is Hit Die plus Con bonus.
- Hit Die roll or Con bonus whichever is higher for leveling gains, adjusting the average accordingly.
- For the average number I will be adding all the possible numbers from a roll and dividing by the number of sides (example, a 2 con bonus on a d4 is 2,2,3,4 or 2.75).
- Any healing done is lossless. Basically I'm assuming every point healed actually heals hp and doesn't go over over max HP.
- No changes of the Con score throughout a career.
- Hit Dice are d4, d6, d8, d10, d12.
- Constitution scores between 8 and 20 used at the bonus threshold values.
The numbers that will be used will all be averages. While possible a fighter could end up with only 40 hp over his career, the odds of that are really really small, not even taking in account survivability, just probability.
To make my life easy I plugged everything in an excel spreadsheet. Because really, who wants to do all that by hand? I can't just paste the spreadsheet here as it takes up far too much room. However, I uploaded it as a google doc here, so you can play with it yourself. The only thing you need to change is the Constitution Value in cell 21B. Everything else adjusts accordingly.
This proves what was already known with Con affecting the HP totals of low hit die characters more than high hit die. The d4 hit die doubles from 8 to 20 con, while d12 hit dice gain about 30 hp on average.
But playing with it more I found that a +1 is pretty good overall for all classes. This is the level that you can actually double your hp through your mundane healing. And oddly enough, it happens at 12th level for all classes. At level 13 the level where all classes are over 100% healing is 13th, oddly enough. At Con 14 the level you reach over 100% healing is 8. Between 14 and 19 it moves very slowly over level 7 to finish with everyone over 100% at level 6 with 20 con.
I also noticed that the total amount of healing stays mostly equal among all levels of con. Which I didn't expect at all.
So if rolls are truely random and the average is achieved it's really not a bad system to roll. Things stay pretty even over time.
But what if we want to have static HP? This works fine if nobody has a con over 13. Once you get a 14 or over on Con the average amount of HP changes by various amounts, again affecting wizards more than other classes. It's hard to say that you just take their HD/2 to get static HP. If you do this you are actually going to underpower yourself if you have high Con.
So basically rolling should work, and the con floor for HP does help overall hp, again more for the lower hit die characters, but overall between hit die healing and hp gained, they stay generally level throughout the leveling process except at the low (8) and high (20) levels of Con. Most characters however, will get the most by having an average con. My guess is about 12-14 is the sweet spot for most characters, so between a +1 or +2 bonus. But this doesn't mean that extreme levels of con aren't useful.