Looked to me like the times are predetermined beforehand.  Note how the ranges vary wildly between Ninji stages.

 

My friend, you are right on the money. Well, for 10,000. I can confirm the top 10,000 get the gold stars.

However, the rest determines on how good the players do. Remember the squirrely airship speedrun? The times were very close together. The gold was 0:26, silver was 0:32, bronze was 0:40.

Many people did well on that speedrun. The graph went up as the times decreased. However, many people didn't complete the Goombud Bust up really fast, because the graphs went DOWN as the time decreased.

For this speedrun, a lot of people got over a minute, so that's why the silver and bronze cutoff is very widespread.

(If you were wondering, my time was 0:44.516, and I got #4484.)

 At  the time of posting (Jan 5, 2021), the Goombud Bust-Up speedrun just  finished about 7 hours ago. People with a time of 1:45 are in the Bronze  category, 1:23 is silver and 0:55 is Gold. (I managed to go to 0:44.866  and was 4651st in the world, I'm impressed).

My  question is, how were they determined? Was it like, top 50% gets  Bronze, top 30% is silver and top 10% is gold? Or is it by number of  players (Top 30000 in bronze, top 20000 in silver and Top 10000 in  gold)? Or is it something completely different?

Does anyone have any idea? If you do please let me know!

How are the gold, silver and bronze times determined in the Ninji speedruns?