To be able to gauge the line and length of a ball hurled in your direction at 140kph, and then respond, all in the space of about a quarter of a second, you need a huge amount of training.
A batsman has three pairs of options to choose from for every delivery - front foot or back, aggressive or defensive, off side or on side. Once he has made his picks, he must move his body accordingly, and since there just isn't enough time to think about the best possible response, instincts must take over. But what we call "instincts" here are things batsmen acquire over a long period of time.
In his book Bounce, Matthew Syed explains how the mind learns to pick up cues to decipher what to expect. As an international table-tennis player, he could handle the ping-pong ball travelling at 110-120kph across the table, but he couldn't get the racket to a tennis ball served by a professional at the same speed from across the tennis court, which is many times bigger than the TT table. This was because his mind couldn't pick up cues from the tennis player, and he didn't know how and when to react.
Similarly, in cricket when you play against a bowling machine for the first time, balls coming down at a modest 125kph are tough to handle because the machine doesn't give you any hints. You can practise facing balls at high speeds only after trying out the machine a few times over.
If you ask a professional batsman what he's looking for in a delivery and what leads him to choose certain movements over others, he might not be able to explain himself, because the choices are made at a subconscious level. That's precisely why unorthodox bowling actions are effective.
Even a straight ball delivered by a bowler with an unorthodox action looks like a bag of mystery. That's because the mind has failed to read the hints. And losing even a fragment of the fraction of a second you have in which to make your response makes a difference between judging the line or length well or misreading it.
For years he kept befuddling the batsmen around the world because they didn't know what to expect. Over 90% of the balls you play in your career are bowled by bowlers with a high-arm action, and so the mind learns to pick up cues from that. The earlier the release, the fuller the ball; the later the release, the shorter. But with Malinga's extremely round-arm action, gauging the point of release is never easy, especially for someone facing him for the first time. And if you fail to successfully judge the time of release, you lose crucial moments. Add to that his accuracy and clever use of variations, and you have a very difficult task at hand.
It's rare for India to have an unorthodox bowler like Bumrah, which is why he's proving to be quite a handful for batsmen at the moment. Batsmen are accustomed to begin preparing for the release of the ball when they spot the non-bowling arm descending (the arms are like the pedals of a bicycle - when one starts moving down, the other goes up). But in Bumrah's case, the non-bowling arm never rises, so its downward movement is really late and hardly noticeable. The bowling arm starts moving up without the requisite clue for the batsman to get ready. That's why Bumrah looks faster than he actually is.
Different unorthodox actions create different kinds of illusions. Most bowlers initiate the jump with the back leg, but Tanvir does it with his front leg, which is why they say he delivers wrong-footed. Since there aren't many of his kind around, his early T20 success wasn't surprising: a spell that lasts no more than 12 balls is too short for batsmen to go after him.
In an ideal world, batsmen would only be bothered about what the ball does after it has left the bowler's hand, but in reality it's not that simple. Bowlers with unorthodox actions aren't exactly mysterious but they create an illusion. Sooner or later batsmen figure them out and then playing against them is no different than facing the rest. But till that happens, unorthodox bowlers enjoy an edge that's not proportional to the quality of their skills.