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I seldom play engineer in normal games, but I played him a lot in MVM mode. Engineer is the busiest class in TF2. You need to construct, protect and maintain all your buildings. But hard work pay off, you are usually the one with highest damage output provided that you keep your buildings at the right place at the right time.
Tips:
-Move your buildings with plans. There are strategies to transport your whole nest to another location. Move teleporter exit first if many teammates are lagging behind, so that your team can group together and advance faster. Move sentries first in case the enemies start to counter attack and push the frontline towards your team, sentries do their job better at defending a point, so move it to assist your team fending off enemies. Dispenser should be the last to move as it is vulnerable without the protection of your teammates (teleporter) or sentries.
-Have your buildings as far from each other as possible in your melee range. For example, place the sentry first, then walk away from it to the point you can barely hits it. After that, build your dispenser opposite to the sentry at maximum range. There you go, your buildings have a big gap between each other, so only one of them will get damaged in an explosion. Placing buildings next to each other makes them very convenient....... to get blown up at once.
-You can help your team by yourself. Equip short circuit and block out projectiles for your team, this tactic is good if the enemy team has got many soldier/demoman. You can also bring down escaping enemies which is low on health, as you are a lower priority target in a fight.
-Use wrangler in wide open maps. Soldiers, demoman and snipers can blow up your sentry at long range even you keep on repairing it. Wrangler add a shield for your sentry and allow you to sweep down enemies far away. So you can watch and 'interfere' at team fight at high ground.
-What to do when a spy circle around you and keep on sapping your buildings?
Many engineers will be confused in this situation, should one kill the spy while sacrificing some buildings? Or repair them with the risk of getting backstabbed? What I usually do is hit the spy with my wrench first, then repair my buildings while calling out 'spy' in the chat option. If you are far from the battlefield, then I recommend you killing the spy and try to save your buildings afterwards, because the spy can kill you easily but teammates can help, and your buildings are in his pocket once you died.
My Builds:
Rescue Ranger + Short Circuit + Jag
This is my main build for engineer. The rescue ranger allows quick repair of buildings even you are on battlefield using short circuit to support your team. Although you will get marked for death when transporting building, you would probably be dead anyway if you get ambush when carrying buildings. And jag in my opinion is a must for engineers, because your damage output come from sentries, so setting them up as fast as possible benefits the whole team. Also engineer is no melee fighter due to his health and mobility, so one shouldn't focus on melee damage as an engineer.
Widowmaker + Wrangler + Jag
This build is for defending objectives. Wrangler maximize the damage output of sentries and its health, which makes it almost invulnerable with the support of your teammates. A wrangler controlled sentry plus a heavy can defend a point with no difficulties at all. Use widowmaker if you are low on metal for reparing buildings.
Frontier Justice + Short Circuit + Gunslinger
This is a special build for frontline engineers. Your main job is to push the line and be the leading player. Place mini-sentries to get sentry kills/assists, as soon as they are destroyed, switch to frontier justice and score a few kills with the crits. And short circuit is used to protect your team during fights. So you should play aggressively with this build.