Why I think the Backburner is an excellent Pyro weapon? Extra damage and rewarding crits for successful ambushes. What makes a good Pyro ambush now? That's what I'll try to explain in this topic since Backburners are all about ambushes.
Sucessful ambushes are somewhat complicated. To do successful ambushes you must:
STEP 1: Anticipation
Collect as many informations as possible as you play. You have to:
1) Anticipate the enemy team's movements at all times.
2) Know the general behavior of as many enemy players as possible.
3) Know the general behavior of as many ally players as possible.
4) Find a corridor/room enemies rarely use in a zone technically under their control.
STEP 2: Preparation
1) Head to the corridor/room enemies rarely use.
2) DON'T look at the nearby zones you know enemies pass by once you are in place (it's too dangerous for one of them to spot you). Use the sounds or in-game alerts (the carts multipliers or points being captures) to try and guess the enemy team's movements. What are their priorities? Where are they heading and where is the immediate problem they have to deal with?
3) Wait until enemies are in place for ambush (this step can take anywhere between 0 to 20 seconds). After 20 seconds, consider you found a bad spot for ambushes and look for another zone.
STEP 3: Strike
1) As soon as you judge a big group of enemies are nearby and don't watch in the direction you can take them from behind, attack.
2) Take out Heavies first. They are more dangerous than any other class when at close range for this step (explained below). Flame everything by behind and don't focus on any precise enemies but Heavies. You MUST take Heavies down.
3) Make sure you don't deadly wound at least one Soldier (or one Demoman if there is no Soldier).
4) Flee while looking at the enemies possibly still alive and reflect Soldier rockets at the enemy team to cover your retreat. At this point, you lost much fuel and have only enough for 1 or 2 airblasts. Have a good timing if you want to survive.
Short explanation: Why take Heavies down first and not other classes that can be pretty deadly at close range (say, other Pyros?). Simple. Heavies, once ambushed, shoot everywhere out of confusion and are the only enemies that can keep shooting you non-stop both at close range and when you get away and, at the opposite of Soldiers and Demomen, you can't counter Heavies. Pyros that flame out of confusion are not as deadly as Heavies as soon as you start walking away and can be airblasted further away if you believe they represent a danger.
Here are short exemples or my basic tactic in practice:
In this video,
STEP 1 is from 0:00 to 0:05
STEP 2 is from 0:05 to 0:30 (When you see me looking at the rock, I'm in fact looking at the blue outlines of the moving cart above the rock.)
STEP 3 is from 0:30 to 0:46
It's a 5 kills ambush.
Team Fortress 2 - Good Backburner Ambuch
In this video,
STEP 1 is from 0:00 to 0:06
STEP 2 is from 0:06 to 0:12
STEP 3 is from 0:12 to 0:27 (I don't actually flee from this ambush since that point was important for my team...)
It's a another 5 kills ambush.
Team Fortress 2 - Backburner Ambush