Games Outside of [Board] Games: Disc Golf, Par, and Risk Aversion

I’m stretching the title of this series because disc golf is definitely a game, but rules were made to be broken, so here we go.

I am fortunate enough to live about an hour’s drive away from Maple Hill, one of the best disc golf courses in the world, and one that hosts a fantastic pro tournament every summer. I’ve played regular golf since I was a tiny child but only recently have started to play more disc golf, a game both similar and distinct from its spherical cousin. Some of the nomenclature and ideas feel forced in, like the idea of a “green” which doesn’t make a ton of sense in a disc golf context and may hinder course innovation.

But I digress.

One similarity both golfs have is the idea of “par”, which is simply a scoring goal for each hole. At the 2019 MVP Open at Maple Hill the course was largely the same as the previous year with one exception: they changed the par of hole nine from three to four. Now, this hole in the past was always the most difficult relative to par, and the commentators always mention that it’s “really” a par four. In 2018 there were exactly three birdies over ~450 plays, which is extremely low for disc golf where scores are typically much lower relative to par than with regular golf.

Looking from the left side of the basket

So it made sense for the tournament director to switch the par of the hole, even though ultimately par is completely arbitrary and has no direct effect on anything at all. It’s a way to create a relative scoring system, mostly. But as I watched the pros play this hole in person last year I noticed they seemed to be playing much more cautiously and I wondered if this had any effect on scoring. 

First, a bit about this hole, which is both beautiful and wickedly challenging. The drive begins on a wooden pier of sorts, which is required to extend the length because you need to throw up and over a steep, intimidating hill. Many players opt for an overhand throw to avoid the risk of flaring out a more traditional toss. If you go for the backhand or forehand you need to somehow try to get distance and enough height to avoid plowing the edge of the disc into the side of the hill. Personally I think I’ve always managed to hit one of the many trees. Once you get to the top of the hill it’s a more gradual decline down to the basket, which is situated on a near-island with water everywhere but back left. You’d love an angle in from the right but that’s where the thickest forest is. From the far left angle you’ve got maybe 8 paces between the front edge and the lake behind.

Lay up your second shot before the water and a pro will have a decent shot at converting the ~50 foot putt, except for the fact that the area immediately before the water is rocky and uneven with a trickle of a creek running through it during the wetter months. In short, you need to execute a very difficult drive followed by a precise approach to capture the three. No one is making it to the green in one shot, or even attempting that.

You’d think the strategy for this hole among pros wouldn’t change regardless of par: make the drive, approach, putt. If you miss the drive, lay up to 80 feet or so and try to toss it in or take the four. However, after watching a couple of groups play through from a position just at the bottom of the hill, I noticed many of them layed up unless their drive was excellent. Even those managing to make it cleanly to the top of the hill on a mis-throw were taking the safe route. I hypothesized at the time that this was irrational loss aversion. Last night I finally checked the numbers. Click here if you want to see the slapdash spreadsheet I made.

Working the numbers

This is noodling around and far from anything like scientific rigor, but here’s what I did: I compared the scores from 2018 and 2019 for each hole and worked from there. I thought about going back further but I know there were some course changes that might make the numbers more unreliable as I go back in time. The 2018 and 2019 setups were mostly identical with only a couple small changes from what I remember. I also didn’t want to have to worry about the strength of the field affecting the data. As a relatively small professional sport, there are more and more “tier 1” players moving up each year and it’s possible the strength of field differences from five years ago might overwhelm the psychological effect I’m looking at.

Comparing the scoring average on each hole, number nine is certainly the most affected between the two years, with it scoring just over 0.2 strokes higher on average in 2019. The second biggest change was hole eleven, with a 0.13 score increase. Three others (10, 1, and 3) were at or above a 0.1 increase.

The course as a whole played a couple strokes more difficult, and as I thought about it I did remember that the conditions seemed more windy this past year than in 2018. Looking at the holes affected most seems to support this as a contributing factor, as holes one and eleven both play downhill from an exposed lie–the kind of throw where wind plays the biggest factor. I watched probably ten groups tee off from the first hole and I can tell you many players were surprised by how much the headwind was pushing their discs to the right. However, hole thirteen has a similar shot (it tees off within 50 feet from eleven’s tee going the other direction) and it was one of four holes to play easier in 2019, so I might be over-speculating among statistical noise.

Still, the disparity in the scores for hole nine seem like more than noise to my eye so I’m somewhat confident in my explanation for why. We know that people are prone to over-react to loss aversion. When confronted with equal losses or gains they valuate the losses as more significant. In the context of board gaming Geoff Engelstein talks about this quite a bit. Can a change in par affect expectations enough that, when combined with this loss aversion tendency, players actually perform worse? I think so.

But there’s an element I’m missing. Average score doesn’t paint the entire picture for someone competing in a tournament atmosphere. There are at-the-moment level decisions that might be affected by unquantifiable metrics, like how comfortable the player is at that moment in time, with that disc, with those playing partners, with that particular lie, etc etc. But there are broader tactical decisions that can be factored in, like how risky you’d want to be at a particular point given your position relative to the leader. As I say frequently, if your singular goal is to win you need to adapt your decisions to be more variable as your odds of winning decrease. 

This calculation isn’t quite as severe in a game like disc golf where money prizes are given on a sliding scale as you move down the rankings. In a football game where the outcome is either win or loss, changing tactics based on the context of the score should be significant. Still, I can imagine a pro disc golfer reading this and offering the counterpoint that while average score may have increased, that was only because players were playing more intelligently, preferring to avoid high scores like five or six even if the chance of a three is decreased. 

This is a reasonable response, so I checked the numbers.

The standard deviation for scoring on hole nine increased from 0.89 to 1.01 from 2018 to 2019. Very high scores were also more frequent, with just over 20% of players scoring a five or more in 2018 compared to over 25% in 2019. The percentage of people scoring six or more doubled from 5% to just a hair under 10%.

Again, while this is far from scientific, it lends support to my hypothesis that something as directly ineffectual as a par change caused a noticeable change in risk-averse behavior that harmed the pro player’s performance on this hole.

What can we learn from this? As players of games we can understand this weakness in our cognition and take active steps to counteract it in order to improve our performance at games. As designers we can use it to nudge players in certain directions, affect the game on an experiential level by threatening loss, or create, perhaps, a deeper strategic experience where people who can overcome mental inefficiencies best are rewarded. 

As game bloggers we can remember that another cognitive tendency is to create narratives out of noise and not overreact to things like this. So, where have I gone wrong? Did I miss a factor in my analysis? Do the laws of math and statistics dictate that the chances of this actually being pure noise are high? I’m also curious, if anyone in or connected to the disc golf scene reads this, can you lend any anecdotal support to a change in the players decision making on hole nine at Maple Hill?

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