In the late 1980s, STATS, Inc. started collecting pitch by pitch data, which included pick-off attempts. They discovered that one pick-off attempt was enough to deter the running game. Runners stayed a bit closer to the bag if the pitcher showed they were paying attention. Subsequent throws did not reduce steals any further.

Tom Tango shows today that the pick-off limit turns that on it’s head:

Once a pickoff attempt happens, things change radically.  Players at 26-26.99 ft/s jump up to +0.7 net SB per 100.  This puts them squarely at the equivalent of 29 ft/sec with no prior pickoff attempts.  In other words, it’s like adding 2.5 ft/s of speed, simply by having a prior pickoff attempt.

And it gets worse.  Players at a speed of 27-28.99 ft/s have a net SB of +2.9 per 100 pitches (with 1 prior pickoff attempt).  That is similar to the speedsters of 30+ ft/sec with no pickoff attempts.  Again, it’s like adding 2 or 2.5 ft/s of speed.  That’s what the prior pickoff attempt does.

TangoTiger.net

Of course, there is no increase in speed, there is an increase in the runners lead since the next pickoff throw puts the pitcher at a disadvantage.

In the first situation, there was almost never a good reason to make the second pick-off throw. In the current situation, there is almost no reason to make the first pick-off throw. In each case, you had to make the superfluous throw to keep the runner guessing.

Now that this is in the hands of managers, I believe the correct strategy is for catchers to make the second pick-off throw. With a bigger lead, snaps throws should catch more runners leaning.