What makes legspin effective in limited-overs cricket?

Why wristspinners are dominating in the shorter formats (2:29)

India have made a trendy move in playing two wristspinners in their series against Australia - there is a reason behind it (2:29)

Why are legspinners so successful in the shorter formats?
There are plenty of factors that go in favour of legspinners in shorter formats.

They have the ability to take the ball away, off the surface, from both left- and right-hand batsmen without bending the elbow or the rules.

Most batsmen, when they try to take the aerial route against spinners, prefer to use the power generated by the bottom hand because there's very little pace available on the ball, and so they target the midwicket region. Which means legspinners have the ability to force the batsman to play against the spin most of the time.

Many legspinners are also short in stature and bowl with a slightly roundarm action (to extract sidespin), which in turn lowers the trajectory of the ball considerably. The lower the trajectory, the tougher it is for batsmen to use their feet to get to the pitch of the ball. Also, the lack of bounce, because of the roundarm action, doesn't allow the batsmen to get under the ball that easily.

It's not surprising that legspinners get a lot of wickets off half-trackers, for the ball often hits the bottom of the bat instead of the sweet spot. The ones like Imran Tahir and Rashid Khan, who bowl with a high-arm action and are quicker in the air, rely a lot on their accuracy and subtle variations in spinning the ball both ways.

Why are India's current legspinners bowling so slow through the air, and is it easy to do so? If yes, why aren't all wristspinners doing the same?
Often the South African batsmen in the current series against India have failed to read the spin out of the hand, and so have been circumspect against India's legspinners. They have been reluctant to use their feet; stepping out is a viable option only if you know which way the ball is going to turn after pitching. Sensing this inability, the two Indian wristspinners slowed the pace down further.

While a little variation in pace is possible, it's not advisable or possible to maintain same effectiveness if you go too far away off your optimum pace. Bowling a lot faster or slower than your optimum pace will lead to lack of control in length, and you'll find yourself bowling too short or too full too often. Fortunately for the Indian spinners, their optimum pace is on the slower side, and slowing it further a tad didn't compromise their accuracy. The likes of Tahir or Rashid, however, won't be as effective if they bowl about 10kph slower than their regular pace.

Why are most modern batsmen, including Asian batsmen, struggling to read the variations from the hand?
Call it the gift of T20 cricket: most batsmen are training themselves to pick the line of the ball, and playing through that line for the big shots. Since a lot of fingerspinners fail to extract turn with the newish ball on placid surfaces, the tactic of playing the line works well. In the absence of help from the ball or the surface, fingerspinners tend to bowl fast, which in turn further encourages the batsmen to stay rooted to the crease and attempt to muscle the ball away. But a few quality fingerspinners have added the carrom ball to their variations, which has made them as effective as wristspinners. Since both offspin and the carrom ball are delivered from the front of the hand, the batsman needs to watch the fingerspinner's fingers very closely. Failure to do so leads to trouble - as we have seen from Sunil Narine's success in T20.

The difference between a legspinner's googly and the stock legspin delivery isn't that subtle, though. You can't bowl a googly without showing the back of the hand to the batsman, and that's why it's puzzling that top batsmen are regularly failing to spot it.

However, legspinners have changed one thing in the way they deliver the ball: instead of delivering with the seam slanting towards third man, they now seem to bowl everything with the seam scrambled. Seam position is no longer a sure giveaway to the direction in which the ball is likely to spin.

A few modern legspinners - Rashid Khan, Imran Tahir etc - bowl mostly stump to stump. What are the pros and cons?
Bowlers with a roundarm action find it a little difficult to finish within the stumps but a number of current legspinners have a fairly high-arm action. While the high-arm action leads to less sidespin, it makes the googly more potent and provides more accuracy. These legspinners are from the Anil Kumble school, and just like the big man, they also finish within the stumps very often.

Have the legspinners who are currently enjoying success peaked early? Will they be as effective in the World Cup 2019?
It has taken a long time for legspinners to take centre stage in the shorter formats. They needed to adapt and become more accurate to survive and thrive. Frequently bowling boundary balls was their weakness, and that kept them on the bench in the initial years of T20 cricket. The new-age legspinners might not be turning the ball as much as their predecessors did, but they are extremely accurate. While they might have compromised a little bit on the sidespin, they haven't lost their wicket-taking length - the fuller length.

The best chance a spinner has to take a wicket is when the batsman is forced to play an attacking shot, and the length that most legspinners bowl forces batsmen to attack. Since the number of legspinners is still relatively few, familiarity hasn't taken a toll yet. While some teams might start playing them a little better than they are doing at the moment, it'll be very surprising if legspinners don't remain relevant in the World Cup.