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It works. Trust me. I'm a doctor.

Having full tank runes really helps with your tankiness throughout the game. A bonus 110 health at the start of the game is great for your jungle sustain.

Your core items are Spirit of the Elder Lizard, Randuin's Omen, and Banshee's Veil.
These items together give you a ton of armor, magic resist, and attack damage, all essential to a nice big hurting tank. The Banshee's Veil passive gives you a nice form of initiation without being stopped while the Randuin's Omen active gives you a nice way to cc the enemy team while you're in the middle of all of them.

BOTRK or Frozen Mallet?

Which one do you get?
I find the slow passive from the Blade of the Ruined King to be good as an all around tool for chasing and escaping. The slow has easily picked me up many kills and makes tower diving a whole lot easier. The 15% health active is also extremely good if the enemy has a hyper tank such as Dr. Mundo or Udyr.

The Frozen Mallet, however, can give you a permanent slow (if you can catch up to and hit your target) and gives you a huge boost in tankiness.

Generally, take Blade of the Ruined King. If you're the only tank on your team, take Frozen Mallet.

Always start with your bottom lane for the best leash. Generally, an invade start isn't the best with Evelynn due to her lack of cc and level 1 mobility. Don't try it unless you're sure you know where the enemy team is.

Blue Buff Start (Purple Side)

When on purple side, start with the blue buff. Ask your top lane to ward your Red Buff if the enemy has the ability to go without blue. From there, take the Wolves while you wait for smite cooldown. Then, use smite on the Wight and head over to the Wraiths. When you finish those, smite should be back up for the Red Buff. If you can, take the Golems after that then back. This is the most effective route as you hit even single camp before going back.

Red Buff Start (Blue Side)

If you load up on blue side, go for the Red Buff with your bot lane. Ask your top lane to ward your blue. When you finish Red, take the wraiths while your smite is on cooldown then go down to your Blue Buff. When you finish that, take the Wolves while your smite is on cooldown, then smite the Wight. If you're still healthy you can go back up to Wraiths again before heading back.

By far the most fun part about Evelynn is the ganks. It's the reason we all want to play her. When ganking any lane you have the option of coming through lane or going from behind. Being an invisible champ, it often doesn't matter too much.
When ganking, wait for the best moment. When it's time to go in, walk as close as you can to the enemy until you're spotted. Once you are, use Dark Frenzy to close the gap and be right on them. Spam your Hate Spikes on them and use Ravage for the damage and to get as many auto attacks off as possible. If you can, use Dark Frenzy again to catch up again and get more auto attacks. You should end up with a kill or at least a flash.

Ganking Top Lane

Before ganking top ask your top lane to poke them a little bit and let them push lane. This will make it easier since most top lane champions have a built-in escape tool like Renekton's Slice and Dice. You can head through lane or the river, though make sure there's no Pink Ward there if you go through the river. If you go through lane, wait until your opponent tries to jump on or hit your ally, then take that opportunity to jump on them and surprise them.
If you can gank top successfully, go for the counter-jungle and hit up the Big Wolf and a Small Wolf, leaving the other small one so the camp doesn't respawn. Likewise, do the same to Golems if you're on the blue side.

Ganking Mid Lane

Mid lane can be tough to gank especially against a high mobility champion like LeBlanc or Zed. Just follow the same steps as above and try to get as much damage off as possible. If you get a kill try to go for the tower, but be careful of the enemy jungler. If you manage to push the enemy mid away but not get the kill, take the enemy wraith camp, leaving only a small wraith.

Ganking Bot Lane

Bot lane is the most fun to gank and usually most successful. Wait for the enemy ADC and Support to get close together, then Agony's Embrace them and use Dark Frenzy to jump on them. The shield you get from Agony's Embrace should be fairly large so use it to your advantage and take a couple tower shots if you need to get the kill. Don't forget you can use Dark Frenzy again after getting the kill to quickly run out of tower range.

The best part about Evelynn is her team fight engage potential. If the enemy team is grouped up close, you can use Agony's Embrace on all of them to do a lot of damage and gain a huge shield. With this you can use Dark Frenzy to run into the middle of their team and activate your Randuin's Omen ability to cc the entire team, all while spamming your Hate Spike and dealing tons of damage to most of the team. In this perfect situation your team should be able to easily clean up while the enemies are all confused and trying to focus you with your 1500 hp shield. Also, if you have Blade of the Ruined King, use that active on their tank along with the rest of your initiation to prevent him from reaching the front line if he's not already there, and to take of another 15% of his health.
If you can pull this off correctly, you should be able to get an easy ace and push a couple towers or even get baron.

In conclusion, Evelynn is a great initiating damage dealer!
This is my first guide on Mobafire, so please leave feedback when you rate! Have fun and happy jungling :)