How to research about professors wisely? The application season is coming, and I'm going to spam the mailbox of every professors. 

OK, just kidding, but not completely untrue. Of course I will do my homework. As Anonymous said, it is fine to contact a professor if you are:


  asking detailed questions about the professor's research, or questions about the research group beyond what you can discover on the Internet


Does that mean that I need to spend time to dig into their papers (actually beyond the internet), or just reading the descriptions in their website is enough? I mean, sure, just like asking questions in SE, the more detail you give, the more likely you get the answer. But I cannot only concentrate on some particular professors, I need to increase the chance of being accepted by, erm, spamming other ones. One PhD student says that he had to contact 17 professors in order to find the best for him (good fund, good research, etc). I think contacting 17 professors, with all emails are careful prepared and worth to reply, will drain my energy soon. 

Not to mentioned that in the email setting, you don't have to be obligated. If the email require you to spend a lot of energy to answer it, and if you are super busy, you will likely to ignore it. This will waste my effort.

Q: So, how likely is a professor to ignore an email even when the sender does their homework? How many professors should I contact in order to find the best one? And how much effort should I spend for a professor?

Also, there is a probability that after I read some papers of the professor, 


the paper is easily to follow, that I don't have any question. How should I email in this case?
the paper is hard to follow, and I meet my limit of knowledge. Is this the gold chance for me to ask, or should I self-teach me this? This could be a trivial question, and asking it may bother them, increasing the chance to be ignored. Especially that I want to switch my field (a little bit).



Anonymous' comment on  Is it unwise to contact the professor directly before getting admitted to a program in US?
Related: How to contact professors for PhD vacancies?
Does that mean that I need to spend time to dig into their papers (actually beyond the internet), or just reading the descriptions in their website is enough?


I strongly suggest you at least look over 2 to 3 recent, important papers of this professor. Not only will this allow you to write a mail that has a higher chance of being taken seriously, it will also inform you whether this kind of research is actually what you want to be doing for the next few years. This will indeed take time, but frankly, you should be willing to spend one or two hours to look over the work of a professor that you consider working with for your PhD. You don't need to read their papers end to end. Just figure out what research problems they work on, what methods they use, and so on.


  I cannot only concentrate on some particular professors, I need to increase the chance of being accepted by, erm, spamming other ones.


Here's the thing: for me, if your mail even remotely looks like you have been spamming professors with applications, your mail moves directly to my "Will never be answered" mailbox. Seriously. I have a keyboard shortcut for that. I assume similar things are also true for most other people in PI-y positions. Avoid spamming people at all costs.

Edit:
I will answer Ooker's follow-up questions here as they seem related enough to me.


  "How likely is a professor to ignore an email even when the sender does their homework?"


Very likely. Cold mailing somebody about a position is always a long shot. The difference between doing your homework and spamming, from personal experience, is that the former has a small chance of success while the second seems completely pointless to me.


  "How many professors should I contact in order to find the best one?"


I am not sure I understand. Given that your success rate with cold mails will be very small anyway, you (a) need to have a fallback plan anyway (this can't be your primary strategy to get into grad school, right?), and (b) it seems rather unlikely that you will have multiple offers that you then need to choose from.