After reading so many cases here, and according to mine and my friends' experience of being banned, i came to a conclusion: this's a ban base on a period of statistics, the starting time is earlier than 2 weeks ago.
Here's the
proofs:
1.I got 6 accounts, and all of them got banned one by one in 3 days, not immediately at a same time;
2.My friend stop botting two weeks ago, and got banned this morning when he tried to log in at phone, he doesn't play the game for two weeks long;
3.I have tested myself to prove that 1000 pokemons or 2000 pokestops is the limited amount in 24 hours,more will got two kinds of soft banned;
So,here's the
conclusion:
1.There's two main kinds of banned,one is period perm ban, the other one is temp ban(including the softban people have found and an immediately perm ban which is not known so well);
2.Niantic started to collect players' statistic at least two weeks ago, and decided to ban those against the 1000/2000 rule one by one;
3.If 14 days ago (just for example,not exactly) your statistic is more than 1000/2000, you got banned today; if 12 days ago, you'll got banned the day after tomorrow, and so on;
4.I guess, no matter what you do or not do, if you against the 1000/2000 rule in any 24-period of your playing time since two weeks ago(maybe earlier), you'll got banned one day sooner or later.
And here's a very precise method that Niantic may use to find out those snipe:
Create a rare pokemon at an impossible arrived position like "Bermuda" or somewhere in the sea or desert something, normal players wont be able to reach the place but snipers caught it very easily and without any deep thought.(i hope i don't remind Niantic to use this way if it dont find out at all

)