I think I'm like WR, except with a much smaller N (twss). My best 1 minute power is like 70% of my best 5s power. I won the race both times I committed to a 1k attack. Both times were out of the pack, and there was a corner in the final 1k.
Several times I have started a 1k attack and completely chickened out. A minute can be a really long time.
Several times I have been in good position but not felt like I had enough gas left to launch a 1k attack, but I also didn't have enough gas to sprint, so I should have just tried it anyway.
Several times I have been in a small break and tried to game out the finish, and not won.
Many times I have been in no position to launch a 1k attack.