Not as much an "amazing thing" as "stroke of dumb luck", but still...
The other day, I was SR-ing for an Azelf in OR. The Smogon analysis says that a Naive nature is preferred for it, but I didn't have a Naive Synchronizer, so I decided to go for Jolly instead.
However, I was out of luck. It seemed like I got a Calm or Careful nature half the time, and whenever Synchronize kicked in and I got a Jolly one, its 3 good IVs were placed in something like HP and Sp. Def. After much ado, however, I got a Jolly one with good IVs in HP, Attack and Defense, and I had really gone tired of soft-resetting, so I decided to go for that one. Just as I was marching towards the PC to deposit it, my phone started ringing, my mom was calling me, and I pressed the "Start" button on the 3DS to pause the game and turn off the sound.
Except that wasn't the Start button. It was the Power button. Buh-bye, decent Azelf!
After the phone call, I decided to give Azelf one last chance before I went to bed. I booted up the 3DS again, put my hand into that hole in the Nameless Cavern, and met and captured another Azelf. I then flew to the Battle Resort to see if its stats were any decent.
Naive with perfect IVs in HP, Attack, Defense, Sp. Atk and Speed.
Thanks, mom!