Very situational scenarios, but I could give some things you can look for:
The heroes involved
I believe it is a scenario where solo laners are skirmishing in lane most of the time, which means some decent self sustain abilities as much as decent waveclear.
Solo laners can either survive their lane or be extremely good harassers.
So if it's two solo laners fighting each other, I would say it's some kind of mana war, except if one of them is overextending or overstaying in lane in order to maintain the other's push.
If your hero is more of a harasser (Zagara/Kerrigan/Sonya/Thrall) and the enemy hero is also a harasser, balance between poking the enemy and avoiding their skillshots.
If your hero is more of a survivor (Dehaka/Leoric/Artanis/Murky), make the enemy confident enough to spend all their mana and you can engage without severe retaliation. Try to deny their regen globes as well.
Leoric and Dehaka on the solo lane - Both use mana and both are about survivability - Dehaka having waveclear
Leo's survivability is about landing his creepy hand on the enemy hero, and the higher max hp the enemy has, the better, so Dehaka is a good target if he wants to stay in lane and probably kill him if he's stubborn enough to stay there at low HP
Dehaka's survivability depends on essence, he won't be able to outheal Leo's damage, he has to rely on avoiding his hand and waveclearing, and occasionaly drag Leo to his towers
The one who uses up all his mana to keep on this dance will be forced back to the fountain or to the hall or else will die, this is mostly a draw
Sonya is a case that we will consider next as a solo hero
Her survivability depends on enemy numbers available to spin on. It won't be very effective if the enemy has anything to interrupt her spin.
However, if the enemy has stuns, Sonya can force them to use it, depleting their mana overtime, as Sonya doesn't really have ressource issues.
The only problem may be the lack of enemy minions to replenish her HP. If you are Sonya, you want to be aggressive when there are enemy minions to back you up (I know, kinda contraversial) and if you're against Sonya, you want to be aggressive when you have no allied minion around, if you have enough damage to make her run away
Here, I am assuming the game carried on and you're all post level 10, and you would have checked all your enemies' talent choices. And here, it is more a skirmish outside of the lanes, like contesting a merc camp for example.
- At what level are you? At what level is the opponent?
- Do you have a talent advantage/disadvantage?
- What is the most important tier of your hero/the opposing hero (power spike)?
So, you want to have more single target damage than your opponent, could it be burst or sustain, or some way to survive through anything.
Let's see another example here based on a game I played two days ago
I play Pally build Kerrigan, and my damage output goes online at level 13
I tend to solo a lot, looking for stray squishies going for merc camps
I was able to combo a grav-o-bomb Gazlowe (less tanky than if he took Robo) - Combo + crit + Ultralisk + crit + Q + crit and he fell like a fly, and I had his turrets to Q on to regain my HP over the few shots I took in the process
However, if I was against a Robo Gazlowe, I'm sure I wouldn't have dealt all that damage, making me wait for reinforcements instead of engaging, and if no reinforcements at all, I just prepare my defenses against the mercs
And this kill wouldn't have happened pre level 13 because I wouldn't have the critical damage yet
Now let's assess the same situation with another perspective
If I were a tank, I would have walked in to delay his capture. I know I wouldn't be able to kill him, but I am sure I can survive this as I have a self sustain or an escape, I'm just delaying him at the best of my capacities and see if reinforcements are coming or if I have to back off.
But if the enemy was a Tychus or any sustain damage with any form of percentage damage (Giant Killer at level 13, Valla's Manticore at level 16), I wouldn't even go in, I would walk away as I'm sure I'll be dead meat in there.
You want to know if your opponent's heroic has been used lately (unless it's a passive heroic) and how long would be the cooldown.
If their heroic is available, you have to assess the consequences of getting hit by it: Can you survive through it? Will it affect how you deal and get damage? Can it be a follow up for the enemies if you survive your trade?
For most of the heroes, the heroic is what can change the output of a fight. A defensive heroic won't kill you, but will allow the enemy to leave. An offensive heroic may lead you to your death, but if it misses, it will be a big retaliation opportunity.
Your goal when taking on a 1v1 fight
I know getting kills is a lot of fun in the game, when you want to show off your dodging skills or show off that displacement comp wombo combo that you trained for four days with your teammates, but why would you like to pick 1v1 fights?
Those would be the only available reasons you want to pick a fight:
You are in early game solo lane and you want to shoo away your counterpart before your minions arrive at their gate which may allow you to take down a tower or to deny experience
You have a teammate taking a knight camp by himself (he's able to but will take a lot of damage in the process), you want to intercept those who may roam to that camp and would be able to finish him in one hit or one spell
You want to divert attention from your enemies on keeping them busy on one important place while your team is doing something more important somewhere else (like you contest the bottom sappers on Towers of Doom while your team caps Boss)
You want to defend a pushed lane, shooing away the pusher first so you can clear that wave properly
You do not want to take on a 1v1 fight:
When you and your opponent are catching each other in rotations, it won't end up well, just back off or run to your teammates
When you are the only one alive in your team and the enemy team has more than one man alive, they're coming for you, run to safety
When you have talent tier disadvantage, especially a 9 - 10 or 19 - 20
So, consider those options, and if the enemy is willing to engage 1v1 on you, make your team know that maybe something else is happening somewhere else