So, we've talked many times about the line from gut check through sugar and spice (Turns 15-16-17 going CCW). Some time ago, I ran all 3 "main" lines people run. I ran these in the same session, so there isn't a lot of variance. No traffic for these runs, so the data is about as good as it's going to get (for me).
1) The outside line [red trace]
2) The deep line [green trace]
3) The trail brake line. [blue trace]
The outside line: this line is a result of taking an early turn in at the front end of the gut check. This is the line most/many drivers run. For DE, it's an OK line, but really slow. For racing, you will get passed on the inside every lap you do this with a trailing car. You miss the first apex by at least a car width running this line, but your car is oriented on the right line, just displaced from the apex(pointed towards the middle of the rumble strips).
The deep line: this is the line that is runs farther into the braking zone and uses a portion of the run off area. Some people run 2 tires over the rumble strips. Some people run all 4 tires out there. This is also an OK line for DE, but lateral load at turn in has to increase sharply, so the car isn't set as quickly. You miss the apex by over a car length. Your car is not oriented correctly relative to the apex [poitned towards the first part of the rumble strips] The trail braking line: this appears like an inside line, but it's closer to the middle of the track. You actually clip the first apex running this line.
In the data below, all the traces are essentially equal at the left apex of gut check - so any time differential is solely due to the the sugar and spice segment. The outside line misses apex at the last part of the gut check and the car stays to the right. The deep line hits the apex, but is still pointed to the right. The trail brake line hits the apex, but is pointed parallel to the inside edge of the track.
In short, you brake less, carry more speed and end up saving almost 8/10s of a second over the deep line in just one corner. You save almost 1/2 second over the outside line.
As you will also see, the cars all merge into the same line at the rumble strips. And, mid-corner speed is a few Mph higher - with a flat spot at the bottom - for the trail braking line. The other 2 lines have a dip at the bottom, which is the slowest spot and corresponds to turn-in. What this means is that you have to over slow to enter the corner and your minimum speed is at turn in. Then you get to mid-corner and your speed is increasing slightly. Note that at mid corner all 3 traces have the same speed - BUT, under trail braking, you get that speed at turn in and don't go under it. Every other line requires you to go under mid-corner speed and then accelerate back to it.
For me, in my car, the difference in just this one corner is between .5 and .8 seconds. I've seen the difference as high as 1.5 seconds - just for this corner (for example, driving the way outside line or dive bombing the corner).
Running the blue trace is free time. Literally free. Just don't drive way out to the right.