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How to play Swain?
Early game - Early game, your going to focus on last hitting. Your Dorans Ring will give you mana regeneration, as well as your runes and passive. You should have more than enough. Next your going to want to get a ToG as soon as possible so you can start stacking mana. You can also switch with the boots and get them after if you feel as if you want to get a head start. Spirit Visage is a must have. It increases your healing effects (including your ultimate). After that your going to want a hextech for the spell vamp to also increase the effects of your ultimate, as well has give you spell vamp on your other abilities.
Mid game - After that your going to want a hextech for the spell vamp to also increase the effects of your ultimate, as well has give you spell vamp on your other abilities.
You should be close to upgrading your ToG to your AA Staff.
Late game - After doing that you can either go for spell pen or rush the deathcap. I like to go spell pen so I put it first, however it is interchangable. After the deathcap if the game still lasts upgrade your hextech for a 5% increase in spell vamp and a minor increase in AP.
Ignite is amplified by your Torment always take it. Flash is good for mobility, mainly used for getting away. Some use clarity, but you have mana regeneration as well as your passive, so I find it as a waste.
Obvious spell pen and cdr for more constant spell use. The mana regeneration is good for most mana users. Very standard runes.
You may think I am insane for putting points into defense. Swain is very very squishy and putting points into defense will help you in the long run. I feel as if it is more beneficial to go defense on Swain rather than utility. If you disagree go find another guide.
Everything is explained in the How to Play. Generally speaking, I never build glass cannon, the extra boost in magic resistance and healing effects will help.
Never try to tank. You can take some damage because of all the spell vamp you have, but you are not a tank. In a team fight you want to stay back and and constantly use your spells. If you have a chance you can sometimes get into the middle and hit them all with your ultimate.
Thanks for reading. This is how I play Swain. No I do not have screenshots. Talk to me in game instead.