You need to read his book Obedience to Authority: An Experimental View. He goes into greater detail. I think that one experimental condition is critical. The degree of obedience varied a a function of proximity. When the so-called teachers heard only the voice of the "learner" (actually an actor who never was shocked), about 70% administered the maximum shock. That percentage reduced when they could see the user through a one way mirror. It became even less when they were in the same room. Finally when the teacher had to physically put the learner's hand on the shock plate, the majority refused to comply.

Now for the depressing part. Recently the original study was replicated, in the context of a game show. Instead of an experimenter in a white lab coat, the experimenters used a game show host. In this context over 80% complied and ended up giving the learner the maximum, fatal shock. In the original study, when the teachers had social support for refusing to comply with the experimenter most if not nearly all refused to proceed. In contrast in the replication despite the social support to refuse, nearly all complied with the instructions.

You can read the journal article about this replication here:

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.600.9375&rep=rep1&type=pdf

And there's a more plain English explanation here:

https://behavioralscientist.org/how-would-people-behave-in-milgrams-experiment-today/

Again well worth the read.