It might make you stronger or weaker, depending on your build
For finalized builds, it might make you stronger or weaker depending on how much Str you have. While leveling, your HP might go up slower than you'd normally expect at first, especially if you have a high HD, but it'll catch up once you increase your Str. (And you'll actually be able to prioritize maxing Str first as a melee fighter without losing out on HP gain.)
You'll also often be starting with even less HP than normal at first level, which might make surviving the first few levels extremely difficult.
Let's look at the two extremes:
A min/maxed Barbarian would normally have a +5 Con mod, a +5 Str mod and a d12.
Under the normal rules and using averages, the Barbarian would get 7+5 = 12 HP per level.
Under the new rules, the Barbarian would get 5+5+4 = 14 HP per level.
A min/maxed Wizard, assuming point buy, might have as low as a -1 Con mod and a -1 Str mod and a d6.
Under the normal rules and using averages, the Wizard would get 4-1 = 3 HP per level.
Using the new rules, the Wizard would get -1+-1+4 = 2 HP per level.
This might become more extreme in the case of rolled stats, where strength would often be your dump stat of choice, and a 4 in Str means you're essentially doomed to have 1 HP per level unless your Con can compensate.
It will benefit you if:
- Your build uses high strength, especially if you'd normally have a lower hit dice.
- For example, a fighter normally has a D10, if they use this new system and min-maxed for +5 Str and +5 Con, they'll effectively be getting 3 more HP per level now as before.
- If you use a D6 hit dice, you're at an advantage if you have 12 or more Str. (if you use averages.)
It will disadvantage you if:
- Your build doesn't use a lot of strength, obviously, especially if you had a high HD.
- A Halfling Barbarian may very well favour Dex over Str and go for +5 Con, +5 Dex and -1 Str. Under normal rules that's 12 HP per level, under new rules that's 9 HP per level, a huge difference.
Breaking even on levelup (assuming we use average HP):
- If your HD is 12, you'll need 16 Str to break even on a levelup.
- If your HD is 10, you'll need 14 Str to break even on a levelup.
- If your HD is 8, you'll need 12 Str to break even on a levelup.
- If your HD is 6, you'll need 10 Str to break even on a levelup.
If you are breaking even on a levelup, you still have less HP because your starting HP would normally be higher:
- If your HD is 12, your overall HP will be 5 lower.
- If your HD is 10, your overall HP will be 4 lower.
- If your HD is 8, your overall HP will be 3 lower.
- If your HD is 6, your overall HP will be 2 lower.
How quickly you will be able to compensate the lost starting HP depends on your Str. Determining when you truly break even if your Str is higher than required to break even per levelup, you'll need to divide your base HP difference by how much more Str bonus you have than required. For example, a Barbarian with 18 Str has 1 Str bonus more than required, so will break even in 5 levels and will be at an advantage after that.
A wizard with 14 Str has 2 Str bonus more than required, so will break even in 1 level and be at an advantage after that.
In short, if you do well or not depends on the chart above, if you have enough Str to break even, it makes no difference. If you have more Str, you're at a benefit. If you have less, you're at a disadvantage.
In addition, if you're able to get your hands on a Belt of Giant's Strength, you'll suddenly have a lot more HP.