For me TOI is nothing revolutionary, but it does offer a unique perspective compared to most techniques.
For every shot, your control of what happens is (effectively) limited to the point on the cue ball you hit, the direction your cue is pointing, and the speed of the cue upon impact. The immediate result is the cue ball moving in a particular direction with a specific amount of spin on each axis. The successful execution of a shot depends on your ability to a) figure out the direction and spin we need to make the cue ball do what you want it to, b) work backwards from that to the impact point, cue direction, and speed necessary, then c) manipulate the cue to reproduce those parameters.
Most beginner pool players learn to pocket balls while simplifying the translation of cue motion to cue ball motion by hitting (near) the center of the cue ball. With center ball hits, the cue ball direction is the same as the cue direction and it continues in that direction until it hits something. Even with draw and follow along the center vertical axis, this holds true. Theoretically, you can actually accomplish quite a lot on a pool table with center, draw and follow. In practice, it makes the game difficult. Hitting the vertical axis on a cue ball, or even close enough to it to get the expected behavior, is tough to do consistently. The way an object ball reacts to a cue ball with no horizontal spin, is erratic because the amount of throw it produces is very sensitive to the angle and whether the cue ball is spinning, sliding, or rolling. Finally, not using english severely limits your possible position routes. Therefore, it's not long before english becomes a part of the game, and...
With english comes deflection/squirt, swerve, massé, and spin-induced throw, all of which are conspiring against you to make you miss the shots that you used to make with center ball. Deflection/squirt means that the initial direction of the cue ball isn't the same as the cue direction, swerve and massé (really the same thing) cause the cue ball curve, and spin-induced throw makes the object ball behave differently. In order to still make balls with english, we develop techniques to compensate for all of these factors. Some do it very well without thinking about it, some think about it a lot, and some use "shortcut" techniques that do some of the compensation for them. TOI is one of those techniques, and it works well for some people.
The unique thing about TOI compared to most techniques is that it doesn't really consider the intended line between the cue ball and the object ball. Instead, it uses a reference line (either center to center or center to edge) and a parallel shift of the cue to create enough squirt to produce the correct line, (hopefully) making the shot. The fact that you can combine it with backhand english (pivoting the cue without moving your bridge) means that if you have arrived at the correct alignment using the TOI technique and pivot back to where the cue is pointed straight through the center of the cue ball, you will have the cue pointed along the correct shot line. From that standpoint, the technique is theoretically sound. There are also some benefits to shooting with inside, arguably more than shooting with outside, the initial alignment process lends itself to shooting most shots with inside english (although, as already mentioned, you can use backhand english to pivot to a shot with outside if you want). Ultimately, you can shoot any shot (contact point, cue direction, and speed) by first aligning using TOI, but the tendency is to play with mostly inside, which often results in lots of stun shots.
Personally, I usually prefer to line up with the intended cue ball path as my starting point and compensate for any english I decide to use from there to find my new aiming point, but there are some shots where I have found it easier to use the parallel shift to change my shot line. In particular, shots that are nearly straight in or nearly a half ball hit seem easier to play this way. I'd like to give CJ credit for it, but I've been using that little mental "trick" since long before he debuted TOI and said you should shoot every shot that way. Now I just know what it's called. :wink: