This works even better than you think
The fog cloud makes the area heavily obscured, which means (p 183 PHB):
A creature effectively suffers from the blinded condition when trying to see something in that area.
And the blinded condition (p 290 PHB) has this effect:
- A blinded creature can’t see and automatically fails
any ability check that requires sight.
- Attack rolls against the creature have advantage, and
the creature’s attack rolls have disadvantage.
So other creatures will have disadvantage to hit you if you are in the fog cloud unless they also have blindsight.
Blind Fighting gives you Blindsight (p. 183 PHB):
A creature with blindsight can perceive its surroundings without relying on sight, within a specific radius.
You can still perceive other creatures in the cloud, as you are not relying on sight. Not only will they have disadvantage to hit you, you also get advantage on attacks on them.
One member of our group employs a similar tactic with darkness. It is very effective.
Fog cloud in many respects is even better than darkness, because it only costs a first level spell, not a second level spell, and because it is more reliable: there are a number of monsters that can see in magical darkness (for example, devils with devils' sight), but they will still be blinded by fog cloud. Even truesight is blocked. Only monsters that also have blindsight do not suffer the effect.
There is however one big disadvantage for fog cloud vs darkness: its location is static -- you will not be able to have it move around with you as you move in combat, and often combat is dynamic and requires you to move. If you want to be able to do that without losing the benefits of blind fighting, you could pick darkness instead, which you can cast on an object you carry such as your weapon so it can move with you. Blind fighting will work with that, too.