My best streak came a few years back. We had already bowled about 1/2 of the league, when one of the younger bowlers ( who was actually leading for high average at the time), made it a point to tell me "I am going to win high average this year, and there isn't anyone that can stop me".
He was averaging around 220, and I was around 212. What he said didn't bother me as much as the way he did/said it, sort of calling me out in front of a lot of guys I had bowled with for years, making it a point to single me out, as I had once been one of the better bowlers at our center.
It really made me mad, so I told him that I could catch him, and thanked him for his motivating speech. High average really wasn't a goal of mine, and never had been really, but I really did want to catch this guy now.
To make a long story shorter, I managed to average a touch over 236 for the second half of the league, which also allowed me to finish the league with a 224avg, beating him by three pins for high average.
Averaging over 700 for over 18 weeks in a row is my best streak. Sure wish I could even get close to that now, lol.