It depends…
Ok, not the best answer, but an accurate one. In some venues, the wind blows steady and at pretty much the same velocity and direction at the same time every day. Buckeye Lake is NOT one of those venues! In those places, particularly for “high level” events, a change of 10-15 degrees might be enough for the race committee to change the angle of the next leg. In places that are known for more shifty winds (like most of our region), that threshold is typically higher.
Knowing when to make a change is, very often, more of an art than it is a science. A good Race Officer knows the venue and has a good “feel” for local conditions (or, if visiting, has someone on board the RC boat who does.) One thing that seems to be a truism in race management is that any change will be greeted with both support and criticism. That’s the nature of things and perfectly understandable. Just as with most things rules-related though, I always remember George Fisher’s admonishment regarding the rules… “Don’t let one incident ruin your whole race.” The race committee may signal a change you think was unnecessary (maybe you were on the “lifted” side of the course and had gained an advantage.) Trust that they made the change for good reason, sail the course and keep sailing your race. Once signaled, right or wrong, that is the course you have to sail according to the rules.