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In drag racing a split second lag is definitely not good, especially at the beginning of the run. TC should always be off when you're drag racing.
When I use the TC I get slower times, you want to launch at the threshold of when the tires just start to break loose, you don't want the TC coming on it will brake and detune the engine and slow you down.
You can leave the active handling on, that will help you if you start to go sidewise, if you do let off the gas and don't worry about the run.
I am so scared to leave the TC off, I have no active handling -
my heart skips a beat before I know she is gonna go into 2nd, the tires scream in to 2nd scared I will spin out
People drag race all the time in cars that are considerably more powerful than ours, with no traction control, no active handling, and they do just fine. Just think about those guys with 9 second manual transmission cars that are dumping the clutch at 7000rpm and the car comes out of the hole like a bat out of hell!
In the case of a high 12/low 13 second car on street tires, if the tires start to spin then just let off the gas and try again next time. If it keeps happening too much, you either need a better set of tires, or to find a better gripping dragstrip! Don't be scared of it though, it's very rare that anyone gets into trouble in a street driven car. I've been drag racing since the early 90s and the only accidents I've seen are with very high powered race cars. I've never seen a street driven car get wrecked.