Bracket racing is a mind game. Like any other sport, if you work on the part that you're not that good at, it will improve your overall performance. To over-simplify, there are three things to being a successful bracket racer.
1. Cut a good light. It doesn't need to be a double oh light to win. Get a practice tree. You can easily make 100 runs per night. It will improve your R/T. Do not try to cut a perfect light every time. If you do, and you're a tad quick, you go red. I aim for a .015 light. If I'm quick, it's a double oh. If I'm a bit late, it's a .030 or so.
2. Know your car and hit your shift points. Short shifting or late shifting will change the E.T. of your car.
3. Take the stripe by as little margin as possible.
Keeping records of your runs is extremely helpful when bracket racing. If you have good notes, you can estimate your E.T. even if you peddal, brake, or just flat out beat the car you raced in the prior round. Even if you lifted before the stripe, going to your notes to find a run with a similar 60 foot, 330 ET, and 1000 foot time should get you close. A machine (your car) will repeat it's performance over and over if the variables don't change. As a human, you will struggle to repeat if you leave too much "in the bag". My game plan is to run my two time trials as similar as possible...hitting launch RPM and shift points throughout the run. If I do that, I'll dial one hundredth slower than my fastest pass. That way, I'm pretty sure I'll run very close to the ET dialed. If the next round is in better air (getting towards nightime), I'll dial one hundredth faster than my best pass. If i cut a good light, i should be able to back into my opponent in order to not breakout.