Assuming you take $\pu{200mg}$ of caffeine, it's half life is roughly 6 hours. So after 6 hours there should still be $\pu{100mg}$ of caffeine in your body.
Then why is it generally said that after six hours caffeine's effect should wear off? Shouldn't it only be diminished since there is still $\pu{100mg}$ of caffeine in your body?
Personal experience: Some years ago, I mowed our lawn on a hot summer day. It took about 2 hours, and I sweated up a storm. To compensate, every 20 minutes or so, I came into the house and swigged down some Pepsi Cola. After I was finished, I noticed that the 2 liter bottle of Pepsi was also finished, and I was tired, so I sat down.
With nothing else going on, I noted that my heart was skipping beats. 1,2,3,skip. 1,2,3,skip. Extra systole. Nothing to get excited about. But never this skippy. So I listened, and checked, and after about 15 minutes, I got 1,2,3,4,skip. 1,2,3,4,skip. Interesting. And about every 15 minutes, my heart would go another beat before the skip. It finally got out to 14 before skipping, then went all crazy: 12, 17, 20, then finally stopped skipping.
It took 2 hours to consume the Pepsi, and about 4 hours to overcome the observable effects of the caffeine. There is certainly a non-linearity involved with the excretion and with the effect of the caffeine on my heart, but yeah, the half life says something, but there is a diminution of effect, not a go/no go.
And I never again drank that much caffeinated beverage all at once.
