Building a model that visualizes strategic golf

Hacker News · Feb 16, 2026 · Collected from RSS

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For the last month and a half, I’ve been working nonstop on a project attempting to illustrate what I believe to be a new way to look at golf design. And after more consecutive late nights of coding than I’d like to admit to my partner, I’ve finally cleared the first big hurdle. Here, I’m going to walk through the tool I’ve been furiously building from scratch to bring my way of looking at golf architecture – an expansion on Mark Broadie’s foundational strokes gained approach – to life.It’s going to get a bit technical, so please bear with me.For years, I have – simultaneously – been extremely frustrated by the “strokes gained” approach to golf laid out by Mark Broadie,1 while also openly telling everyone that it is both obviously correct and is probably the most important step forward in explaining the game to have been achieved in my lifetime. I don’t want to disparage Broadie or his thesis here: it is sound and rightly influential. By using the benchmark of average strokes to hole, players are able to solve for shot-for-shot performance, find the weakest part of their game, improve, etc. It’s everything golf should be about. Broadie bases everything in analytics, on real world data.But I’ve always felt a constant nagging that something was missing. My frustration was clear: where is the room for strategic architecture in a theory where only distance matters? The frustration was so persistent that I even bought and read through Broadie’s book, Every Shot Counts,2 to make sure I wasn’t missing any aspects of the thesis that might take care of the problem of strategy.The strokes gained benchmarking system requires “like-for-like” comparison, and, to be perfectly honest, using distance is an entirely reasonable way to do a comparison. I just kept thinking about how some positions on the golf course are better than others, even when they are both the same distance from the hole. An obvious example would be two shots of the same distance, but one is taken from the fairway and the other from a bunker. The strokes gained approach would treat these shots as different in kind: hitting off the fairway vs sand vs rough are not like-for-like shots. They must be benchmarked against other shots from the same distance of the same kind.For me though, when looking at golf hole design, this still doesn’t go far enough. If we care about design, then the same shot from two different angles simply can’t be the same shot. If a green tilts left-to-right, it should be easier to approach from the right side than the left side. Why? A shot from the right side hits the green where it’s tilted toward the player, which helps stop the ball. A shot from the left is just more likely to run off the green. When we start averaging these shots together, we lose the strategic positional elements through dilution. So, how can a theory as obviously correct and effective as Broadie’s still be unsatisfying? I sat with this conundrum for years.I finally found my solution by leaning into the theory instead of pushing back against it. Okay, fair enough. Strokes-to-hole is obviously the most important metric we should be looking at, so let’s look at a world where the only thing that matters is distance.Let’s say we have a golf hole with no features: no bunkers, no contours, and everything is a perfectly flat fairway. Playing this hole is effectively an applied driving range exercise. This is a world in which only distance matters. This is a place where I fully endorse the strokes gained approach.Left: a golf hole. Right: a strokes-to-hole heatmap of the same hole, except with no features whatsoever. On this map, the blue is about 2.5 strokes-to-hole, lime green is about 3.5, and red is about 4.5.Here the solution becomes clear: if we play golf in a world where only distance matters, then let that be our benchmark. Forget the real world (I’m a philosopher by training, after all). If we set our benchmark on an idealized plane, then we can use that benchmark to explain the real world. Forget the golfer, and forget measuring the golfer’s shots. Instead, what if we use the golfer’s shots to measure the hole itself?The idea is this:First, set our benchmark as a player’s strokes-to-hole at every point on an idealized plane.Next, calculate the same player’s strokes-to-hole on the actual version of the hole, but we have to do it at every single position.Now, if we subtract the idealized strokes-to-hole from the actual strokes-to-hole, then we can see a map of where that hole is difficult, and where it is easy.That’s it. We can use strokes gained not just as a way to look at player performance, but as a way to look at golf course architecture. I had a new thesis, and at that point, all I had to do to act on it was figure out a way to calculate a player’s strokes-to-hole at every point on a golf hole. The good news is that I have a computer and I know how to use it.So, I literally spent the last month and a half building a golf simulator, with a built-in algorithm whose sole purpose is to calculate the strokes-to-hole at every point on the golf hole you give it. And now I get to show you all the pretty pictures this program makes.After the simulator runs, you end up with some images that look like the ones above. So, let me explain what we are looking at here. From left to right:First, the regular hole map. This is just how the vast majority of folks see a golf hole.Next, we have a perfect Broadie map: strokes-to-hole captured at every point. If you can beat the strokes-to-hole on this map, you’ve gained strokes.Next, we have the functional Broadie map. Since there is no practical way to measure strokes-to-hole in the real world, we just average all the fairway numbers together, and what we are left with is a strokes-to-hole map where distance is the only variable.Finally, we have the Schoolfield map. We’ve subtracted the actual strokes-to-hole from the idealized strokes-to-hole, and we are left with the strokes-to-hole penalty. Here, the redder the area of play, the more difficult it will be to finish the hole compared to an idealized scenario.What is most interesting about this last heatmap is that it shows the net effect of all the hazards and contours on the player’s position. So what do we see here?First, we see the water hazard is dark red. It is dark red because being in the hazard means you need to drop, and that drop is costing you a full stroke – importantly – when compared to an idealized scenario, because if that water were fairway, you wouldn’t need a drop.Next we see that both of the greenside bunkers are bright red, because the model suggests that playing out of those bunkers will likely add about a half a stroke (compared to if they were just flat fairway).Next, we notice the yellowish-orange centerline bunker. The model here suggests that this bunker will cost us around 0.2 strokes compared to if it were fairway. This is much less, because the green is reachable from the sand, and the penalty is mostly wrapped up in a wider dispersion pattern.Finally, we see a ring of orange. This is the distance where the model has the player hitting a three wood or four iron in. The player can’t quite reach the green comfortably so the dispersion pattern is large, and the greenside bunkers are heavily in play. If they weren’t there, in the ideal world, a player would just hit it as close as possible without concern. But because so much sand is in play, the player should have 0.15 added strokes when finishing the hole.It’s important to note here that this map is only relevant to a player of this skill (this map is simulating a “5 HCP” but that is intentionally vague and effectively unrealistic for real world conditions). This isn’t “the way the hole looks to everyone” because not everyone is going to consistently hit the same strokes-to-hole from the same location, or even from an ideal location. For better players, hitting out of a fairway bunker is more recoverable than for beginners, and any greenside bunker will in play for a higher handicapper, but scratch players are rarely affected by them with a wedge in their hands.The hole above has very obvious hazards and the resulting image is not particularly surprising. This process is most interesting when we look at strategic design features that are hard to parse in the real world. So, let’s look at a case study from history.Often considered the first instance of strategic golf, the fourth at Woking is an excellent candidate to look at how golf course architecture can be visualized via this method. Fried Egg Golf has a fantastic article about the history and strategic interest of the hole, and in that article you can see Tom Simpson’s sketch that I have used here.Generally, the hole is defined by two hazardous areas: out-of-bounds along the right side and the bunker complex in the middle of the fairway. Though, by the green, there are also two small greenside bunkers short-left, and a larger bunker that shots should roll towards on the right.Here, I’ve added some length to the historic hole to help it fit longer modern distances. I’ve also added some topography, which is based on the note that Simpson has under his sketch:WOKING, No. 4.The carry from the tee on the direct line is 220 yards. The green slopes away from the player and has a sharp tilt left to right, which makes it extremely difficult to stay on if approached from the left, which is the safe line from the tee. The scratch player attempts to reach A with tee shot. The moderate player will get as near B as he can.I’ve also overlaid the “A” and “B” markers and some parts of his illustration:While it may seem obvious on the strategic player or skilled golf architect, by using this mapping process we can just see exactly why the shot to “A” is so advantageous, and even why playing to “B” is a good idea . However, assuming the model accurately approximates how a person plays, we can also see that there is only a tiny advantage to playing to “B” rather t