I’m barely halfway through the post, but I am already compelled to advocate the author to start pitching the USGA on using this to replace manual course ratings. Also, OP runs a labor of love in golfcoursewiki that democratizes basic info like green contours that are usually locked away behind annual subscriptions. They deserve a shoutout.

Some info for non-golfers: every golf course has a “course rating” and a “slope.” Course rating is essentially the “true par” of the course for a “scratch golfer” (a golfer who normally shoots par). The “slope” is a measure of how much worse less-talented golfers score compared to a scratch golfer. These numbers are used to compute a golfer’s “handicap,” which lets them compete fairly against more- or less-skilled players in tournaments.

Course ratings are currently assigned by people measuring distances from the tee box to various points of trouble and then to the green. This makes course length the dominant factor by far in terms of course rating. If we adopted something like scoofy’s inverse strokes gained metric, course ratings would become far more accurate, and they would become much cheaper (asymptotically approaching free) for courses to obtain. (Currently courses must pay to have their course rated.)

My previous best idea for fixing this was just to use the scores reported by players every day to nudge the rating toward its “true” value. But that would be subject to a lot of conflation that this simulated approach is not.

My immediate thought is that OP is reinventing dynamic programming/RL from first principles. The final visualization looks exactly like a standard value estimate heatmap. Golf is a MDP over all the physical points on the course, with stochastic probabilities of transition to each one based on golfer skill and physical randomness. Strokes are the cost to be minimized, the colors are the value estimate at each state, and his difficulties with the different maps is because a value function is defined as the expected value of being in that state assuming you will follow a particular policy thereafter (ie. be a golfer of a particular skill level, playing optimally for that skill). This lets you formalize 'strategicness' of a golf course: it is how much the value estimates differ on average across the full range of golf skills; a non-strategic course looks identical for the beginner and pro, while an incredibly strategic course might have completely different values for every point for every bracket of skill. (You could probably automate creation of pathological golf courses this way, where even a slight increase in skill makes the new strategy different.)

OP doesn't seem to explain what the lines are radiating out from the hole? I assume they're some sort of artefact from the simulations. There's no obvious reason for me why it's harder to chip in from these specific, evenly spaced directions.

This is sick. But also i think that stuff like this is making us less human. Before tournaments good players take a book with then and their caddie and do this themself. A model takes all the fun and strategy out of it imo. Like if i suck at 7-9 irons but am good with my 4-6 irons this type of work doesnt take that into account. Also likee the optimal way to play a course isnt very fun. We play at a course where on the fourth hole we always play to the fairway to the left cause of all the trees. If a player were to use this they wouldnt have been able to come up with such a fun way to play the game

Not a golfer but I'm a big fan of the pretty plots.

Someone get this in front of Tom Doak immediately

THIS IS THE COOLEST THING I'VE READ IN YEARS EVEN THOUGH I DON'T PLAY GOLF!

cheers