Left to their devices, minions will eventually be able to push even to the base turrets. Which side accomplishes this, however, is random, and it's basically based on how attacks are being distributed.
Minion targetting works on the following priority scheme, brought to you by the League of Legends Wiki:
- An enemy champion who is attacking an allied champion.
- An enemy minion who is attacking an allied champion.
- An enemy minion who is attacking an allied minion.
- An enemy turret who is attacking an allied minion.
- An enemy champion who is attacking an allied minion. (Tangential, but this lower priority is why they don't pay attention to you when they're bashing your towers)
- The closest enemy minion.
- The closest enemy champion.
Now, when waves engage each other, there are a lot of minions attacking a lot of minions. So each minion picks some sort of target, but it is mostly random within that scope. So blue's caster minions could all be focusing down one purple melee minion, while purple's caster minions are split with two on one blue caster and one on a blue melee. The focus fire will reduce the enemy numbers, in turn resulting in one side having an advantage. But because how the focus fire is attributed is random (both mechanically and because the actual positioning of the minions can differ greatly as a result), the side that gets an advantage is completely random.
This compounds due to two major factors as the game progresses.
- Once siege minions enter the fray, they both deal more damage and take substantially more damage. They can prolong battles long enough for secondary and tertiary minion waves to support them, which can greatly turn the tide of battle even more depending again on how focus fire is attributed.
- If a small minion wave pushes far enough, then when the next minion wave comes in the enemy will have a shorter travel time before its support shows up. With the aforementioned siege minion stalling, the end result is that one side builds up a massive force that just has to deal with the opposing side one wave at a time.
As such, eventually, they amass enough force to push down full towers, much harder than the defense can manage. Even when the defense can stall, the sheer numbers built up from the initial push can have a devastating advantage... at least until their focusing messes up and the force builds up in the opposite side.
There are several problems with answering that:
You say you don't like helping your teammates because your tower is unprotected. That means you don't think enough about lane dynamics yet. As AP mid, the way you play is basically you push the lane to the enemy tower and go do other stuff (gank other lanes, take a jungle camp, take blue, etc.). You can do that freely because the lane is pushed, the opponent can't destroy your tower since he has to push the lane back first which takes about 30 seconds to a minute until the minions are at your tower, depending on how strong you pushed the lane and how strong the opponents champion can push.
That is enough time to go to another lane and help them.
If you destroyed the first tower, you can push the lane even further back, giving you even more time to gank other lanes.
Generally speaking, once you destroyed the tower or gained the ability to insta-clear a minion wave, you should spend as little time as possible in your lane and as much time as possible ganking other lanes and then be there just in time to catch the big counterwave coming in range of your tower. In the meantime take your and sometimes even his wraith camp for some bonus farm while you go to top or bottom lane.
Another way to approach this situation with more defensive mids is to freeze the lane, that means let the lane come to you and tank it far enough away from your tower that it doesn't shoot but close enough that the enemy mid can't farm your minions. Then farm very, very slowly which denies the opponent his farm since he can't reach your minions safely and since he has no tower to back him up, it makes him extremely vulnerable to ganks which can snowball your advantage even further. However, defensive mids will rarely get into this situation in the first place.
However, the situation most likely means that the opposing team is just bad, so you could do whatever and still win. It should never occur in a match of equally strong teams of decent skill.
Best Answer
Every champion is different when it comes to last hitting, and some are easier purely because their AA hits harder then other champions. This doesnt make CSing under tower any easier. And if you don't know the champion well enough it'll make it even harder, specially if you play as Anivia who is super slow and doesnt hit very hard and then try to CS with Orianna who AA hurts and has average AS.
I think it comes down to 3 things; Experience, Knowledge of Champion, Patience
Experience of how a tower works is easy enough, you can get a perfect CS score even under tower if you know how to use the tower to your advantage.
Knowledge of Champion, takes time and games. Any champion can be good at last hitting under a tower if you know how much damage your gonna do and when to use that damage.
Patience , dont get flustered that your under your tower; calm down think, plan, and click precisely. Use of the S button never hurt either.
Also if your being supported, how well your support can help you last hit under tower can really help. As a support I will typically hit minions to make it easier for my Carry to get last hits, although this only works if your Carry knows what your doing and times their attacks accordingly.