5e has made a huge mistake with HP math. I am fearful of the designers having any modicum of sense when it comes to HP or if they are simply pandering to tradition. HP is a very important factor in the game, but must be dealt with carefully or you create disparities too wide in monster design. Anyway, let us look at some basics here.
For me, an ideal situation is one where a low HP class like the wizard goes down in 2-3 hits from equal "challenge level" foe. A high HP class like the fighter should survive 3-4 hits from such an enemy. This will keep combats relatively quick and deadly.
Let us say the wizard gains d6 (or 4) HP per level. The fighter then gains d10 (or 6) HP per level. The fighter has roughly 50% more HP than the wizard, and the ratio of hits to KO remains constant. This also means that monsters must gain +1 to 2 damage per "challenge level" to remain relevent. If monter damage increases at a rate slower than this, HP inflation will occur and high level battles will devolve into slugfests.
Well, that math works all fine and dandy except for one problem...the Constitution modifier. In the current packet, a level 16 fighter can have a 20 Strength and Con and a few feats increasing his toughness giving him almost 14 HP per level on average (15 if a dwarf). At the same time the wizard or rogue might be looking at 3.5 - 4.5 HP per level (those classes having many more abilities key off Dex, Wis, and Cha making Con a tertiary stat at best). Yes this is an extreme example, but the game should be able to support 20 Con PCs in the party with 10-12 Con PCs without having 300% HP disparity. Any attack which is challenging to Mr High HP is auto kill on the wizard an rogue. Any attack that is challenging for the wizard and rogue is little more than a scratch to the Mr High HP. The game needs to narrow the range for HP overall.
So, how do we do this? Remove the Con bonus from rolled HP. A fighter gains a flat d10, a rogue or cleric d8, a wizard d6. For those who do not like to roll they can take the average rounded up (fighter 6, cleric/rogue 5, wizard 4).
At level 1, PCs add their entire Con score to HP (+ their class HD - either rolled or average rounded up). For example: a level 1 fighter with a 16 Con will have 22 HP while a level 1 wizard with an 11 Con will have 15 HP.
Monsters should also add their Con score to HP. Level 0 monsters such as rats, goblins, kobolds, etc do not get a HD. Yes kobolds and goblins with 10 con will have more HP and are not garuanteed auto kills on hit. Yes it will be harder to kill level 1 PCs from a lucky roll by joe-schmoe with a 1d8 - 1d12 damage weapon. Yes, this is good for the game overall. HP is still low enough that taking more than a few hits could still prove lethal, but lethality no longer hinges on a single die.
Now Constitution might need a slight boost if if is no longer adding HP per level. Here are some thoughts on how to boost Con. We could have HP play a significant role in daily healing. Right now they play this roll by being added to each HD rolled from HD healing. I loathe HD healing. HD healing took everything bad about 4e surges, made it 5x as complex, and regurgitated it into an awful mess.
What if instead of HD healing, PCs had Stamina. Stamina would be similar to 4e healing surges, but with a few differences. The amount of stamina you have is 3 + your Con mod. After an extended rest you regain all of your stamina. During a short rest you can spend any amount of stamina to recover HP. Each point of stamina spent heals 25% of your max HP. This is where the similarities between healing surges and stamina end.
Stamina could also be spent for other benefits. Once per encounter (ie you need a short rest to recover this ability) you can spend a point of stamina to gain one of these benefits:
Action Surge: Spend a point of stamina as a free action during your turn to gain an extra action
Heroic Exertion: Spend a point of stamina as a free action to reroll any d20 roll you have just made
Second Wind: As an action you can spend a point of stamina to heal by an amount equal to 25% of your max HP
Stamina being based on Con combined with these abilities would help Constitution remain useful for all classes without contributing to the HP disparity it currently causes.
Last note: For more cinematic/heroic games there should be a 3 "rests"
Short - 10 minutes, can spend stamina to recover lost HP
Medium - 1 hour, gain benefits of short rest and recover 1 point of stamina
Long - 8 hours, recover all stamina
My 5e Homebrew Material