But you can go as this:
Round 1)Fighter (AC 16, Str 16; 12 hp) vs. wizard (AC 12, 16 Intelligence, 7 hp), 20 feet distance: Initiative doesn't matter, but a Mage can easily win it as probably it's his second score).
Mage: casts MM. 9 dm (average -1). Walks back 10 feet.
Warrior: If dashes, doesn't attack; if don't he goes 10 feet, and doesn't hit. If I were the warrior, I will run in the moment that the MM hits. Presupose that the warrior actually dash forward. New distance 10 m.
Round 2) Wizard: walks back, then MM. 6 dm (minimum). The warrior dies.
You see? Two Level 1, wizard wins. Of course, if the Initiative goes wrong, I, as a wizard, can cast Frost Ray or Grease to delay the warrior. Not a sleep spell. If the warrior is an archer, you are probably screwed, but archers always screw the wizards, and you can screw his vision with Fog, or drop prone and go MM (I'll probably do that). If things go awful, I can shield myself. If I was prepared to the battle, I will probably cast a Mage Armor, and then take a short rest, so my armor goes to 15 for the battle.
This is so funny it's sad. Nobody here is comparing a wizard vs. a fighter in a one on one fight. Doing so is always unconvincing.
Given that you are doing that, and you set up the combat so that they are a decent enough distance away to give an edge to the wizard and you also are not using the Fighter's Second Wind, I'd say that you are not being objective. Why doesn't the fighter go into total cover until the wizard comes in close enough to melee attack?
Plus, the fighter does not need to be an archer per se, he can just have a longbow and Dex 14. +4 to hit versus AC 12 typically and a single arrow has about a 27% chance of killing the wizard round one (this includes chance to hit and criticals). This is with a subpar attack because you set the distance of the scenario.
With a starting Con of 14 for the fighter, a magic missile spells has about a 30% chance of killing the fighter. If the magic missile spell does not kill the fighter, the fighter uses Second Wind and shoots his subpar arrow again.
The odds of the fighter killing the wizard (again assuming a Con of 14 for the wizard as well) with two arrows is about 65% (about 85% with Dex 16 and archer).
The odds of the wizard killing the fighter with two magic missile spells is about 80%.
So, whoever wins initiative tends to win the fight. The wizard has an edge. If the fighter could melee, the fighter would fare better.
If the Wizard wastes spells and time on Fog Cloud or Frost Ray or Grease or even Shield, he's toast because he'll have no first level spells remaining and a Fighter would tend to have a better chance to hit and has a real decent chance of wiping out the wizard in 2 to 3 rounds.
PS. Dropping prone and casting Magic Missile works if the fighter is not in range. If he is in range, it's a terrible choice because in that case, he'd probably be fighting two handed weapon or two weapon and has a really high chance with advantage of killing the wizard in a single round.
PSS. According to the rules, attacking someone in or out of a Fog Cloud does nothing. Both sides have to pick the correct square in order to attack properly. If they manage it, then the attacker cannot see the defender, so the attacker has disadvantage. The defender cannot see the attacker, so all attacks against the defender have advantage. Advantage cancels disadvantage, so if the attacker can figure out where the defender is located, it's just like a normal attack. I know that doesn't sound right, but it's the quirky rule.
Now, let's give both the fighter and the wizard a cleric helper. Suddenly with just one additional party member, the fighter/cleric team wins the fight more often than the wizard/cleric team unless the wizard has the Sleep spell. But, I have repeatedly said that the Sleep spell is the one spell that allows a low level wizard to somewhat hold his own in a few fights.