An opponent is on a higher platform.

What do you do?
What if There's no wall behind him for splash damage.

Do you try to get a direct hit with rocket?
Take out the shotgun?
Run away?
Rocket jump to him?

Its just something i've never figured out. I tend to try to get direct hits, if i hit him i take out shotty. If not I rocket jump up there.

The best thing that I have found is that If you have near full health, rocketjump to him. If you are talking about the middle point on granary or something, rocket jump onto one of the healthpacks that are ontop of the crates.

Otherwise, let a demo sticky crit him.

Same as you Fanlaen...as I have no rocket jumping skills ><...I would fire one or 2 rockets to see if direct hit works...if not then just run away...

There are several factors to consider, such as class, current objective, health/ammo levels, and priority.  If we assume that it is beneficial to your team to reach this platform and you and your enemy both have full health and ammo, then it really comes down to class.

If its any heavy-hitting class, i would try to find an alternate means of taking them out.  A soldier is an even match, but if you rj, you'll have to deal with having less health.  Heavies are the same story.  Demos could lay stickies as you're in the air.  Assuming there isn't a friendly medic around, a pyro could just set you ablaze and run away.  Any other class, though, i would rj up to it and put a rocket in the guy's mouth.

Use some teamwork, have a demo lob explosives up there, or employ a sniper.  You could pretend to ignore them and run towards a main objective, then wait for them to drop down behind you and 'splode his ass.

If I'm full health and he's not a scout or heavy I'll rocket jump. Otherwise I'll fire 2 rockets to keep him busy so I can get away.

it depends on the situation...

1. if i'm healthy and I think I can beat him in i'll rocket jump up while attacking.
2. If he's not aware of me I'll try to rocket jump up then start attacking.
3. If he's aware of me and/or I don't really have a decent chance in close range combat (heavy, demo with stickies out, or pyro) I'll try to disappear
4. the exception to 3 being "anyone with a medic"
I don't stand a chance against anyone with a medic (excluding crits),
but the surprise rocket jump might give me enough time to kill or knock down the medic then retreat.

of course all of these situations become moot depending on your objective...
5 guys about to cap your spire? get up there even if it kills you!
a lone scout on top of an essentially useless platform? leave it alone.

Two Stickes, and watch the body parts fly.

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If this thread was in the Demo forum that would make alot more sense.

rocket jmup up, shoot one rocket at him while in the air, hopefully making him "bounce", whip out the shotty and finish him off

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I like this strat. Cept, if you can manage to get the soldier to bounce than wouldn't it be better to time a rocket with the guys landing instead of using the shotty?