The PDGA Professional Disc Golf World Championships have concluded, and now that we've come down from the highs of Kristin Tattar's first world title and another dramatic Paul McBeth opus, it's time to look back at the real story: the performance of UDisc Live's new Win Probability model.
OK, OK: We know Win Probability pales in comparison to the week that was, but we're also aware it provided plenty of talking points for disc golf fans and pundits alike. With that in mind, we figured it would be a good time to reflect on its debut in the spotlight, provide a reminder about what it is (and isn't), and share with UDisc Live followers what they can expect from the model in the future.
Replaying the Hits
We don't want to toot our own horns here too much, but – toot toot – here are some predictions the Win Probability model got right:
- The FPO favorite at 58% win probability, Tattar, did end up winning the tournament. By a lot.
- Paul McBeth, who entered the tournament close to the top but not quite the favorite, emerged with the highest winning probability by the end of round 2. In case you have been living under a rock, we now call him McB6ast, as he did end up winning the event.
- Paige Pierce made the Top 5 after starting the tournament with a 78% chance to do so.
- Eight of the 10 best-projected FPO players actually finished in the top 10. They say Cs get degrees, and 80% is a B (in most places, anyway). So we're feeling pretty good about that one.
Swing and a Miss
But before you start to think this article is all about bragging about the model's success, we can also admit when we were wrong (note: we're good in relationships). Here are some predictions the model missed:
- Only three of the 10 best-projected MPO players actually finished in the top 10 (McBeth, Matt Orum, Calvin Heimburg).
- Neither Pierce nor Catrina Allen finished on the podium, despite beginning the tournament with 55% and 52% chances to do so, respectively.
- From the department of "So you're telling me there's a chance," Aaron Gossage nearly won the tournament despite starting the tournament with a <1% likelihood to even finish on the podium. It was the best story of the week.
- Tristan Tanner finished on the podium even though not a single one of the 20,000 pre-tournament simulations had that result. It was probably the 20,001st that would've done it.
Five Rounds vs. Three vs. Two (or, There's a lot of golf left)
There are a lot of pieces that make Pro Worlds a remarkable tournament. One of them is the fact that it's the longest tournament of the season. The five-round, 90-hole format, though, can mess with our intuition. Think about it like this: Two rounds into a typical event means there's only one (or sometimes two) rounds remaining. At Worlds, two rounds in means there are three rounds left – that's an entire standard tournament!
So how does the length of a tournament affect winning probabilities? The answer is the same as the answer to the question "Why is Worlds longer than any other event?" — there is more opportunity for the best player(s) to separate themselves from the pack. Sure, when there are several rounds left to play, there's more opportunity for an underdog to get hot at some point – but also more opportunity for a long bogey streak. And while there's more opportunity for the tournament favorite to have an off round and fall behind, there is also more opportunity for a subsequent bounce back. From a statistical point of view, the more golf there is left to play, the better the chances that the ups are balanced out by downs – and vice versa.
A consequence of this phenomenon, called regression toward the mean, is that if we are near the beginning of an event, small stroke differences have little effect compared to at the tail end. For example, McBeth's first birdie of the tournament only gave him a slight 2% bump in win probability (6% to 8%). In contrast, his last birdie in regulation during the final round rocketed him from 60% to 84%.
To put it another way, ask yourself this question: "Could Kristin Tattar beat me over five rounds even if she spotted me five strokes?" For most people, the answer is yes, definitely. But could she beat me over five holes if she spotted me five strokes? Well – still probably yes. But it would be a lot closer!
Speaking of Kristin Tattar…
The UDisc Live Win Probability model started Tattar out at a 58% chance to win Worlds, which took some folks by surprise – we heard arguments that other sports' probability models never place winning percentages that high. Pro disc golf, though, is still so nascent that neither division features the parity or depth approaching that of, say, traditional golf – a sport whose professional tour has existed for 93 years.
We get it, though. While 58% is far from a statistical certainty, it left only 42% for the remainder of the 75-player field – a field that included the FPO GOAT and a two-time world champ. Tattar did indeed go on to win (we'll take another victory lap, if you insist), but that single data point really isn't enough to say whether 58% was a reasonable number.
Still, there's plenty of evidence that Tattar is an incredibly dominant player right now, from her three Elite Series wins this year prior to Worlds to the fact that she hasn't missed a podium in more than a year (2021 Pro Worlds, 5th place). She is ranked #1 in the world, and her Dominance Index prior to Worlds was nearly twice that of her closest competitor (indicating a near double head-to-head win probability).
Additionally, recall that Worlds was a five-round event. If it was only a three-round tournament, the Win Probability model would not have given Tattar such a large advantage.
What about the model showing Tattar with a massive 85% win probability after she had only played 13 holes? Now that comes naturally from the fact that she was already far outperforming the rest of the field, especially the next two tournament favorites: Tattar was 9-under par through 13, while Paige Pierce was only 3-under and Catrina Allen was 1-over.
Think about it this way: If Worlds was played 100 times, the model thought Tattar would have won nearly 60 of those competitions. After spending mere minutes of the tournament without at least a share of the lead and then coasting to an eight-stroke victory, that feels reasonable.
About Ella Hansen
Let's look at one other point-in-time projection for the FPO field: the end of round 2.
Tattar was leading the tournament with Ella Hansen trailing by 2 strokes, Ohn Scoggins and Missy Gannon down by 3, and Pierce behind by 4. What puzzled some people was why, despite being in second place two rounds in, Hansen had a lower win probability (1%) than Scoggins (4%), Gannon (4%), and Pierce (9%).
The short answer here is that the three remaining rounds (aka an entire standard tournament!) provide ample opportunity for regression to the mean, i.e., small stroke differentials are more or less dominated by player strength. We can illustrate this using a head-to-head simulation methodology, sampling 54 holes and spotting players strokes according to their actual positions at the end of round 2.
Just to make it clear how to read the table, if you start at "Tattar" on the left and move to the right, you learn that in the position Tattar was in at the end of round 2, our model predicts she would finish ahead of Pierce 82.6% of the time over 54 holes, ahead of Scoggins 90.9% of the time, and so on.
As you can see, even with a two-stroke advantage against Pierce and a one-stroke advantage against Scoggins and Gannon, Hansen only comes out on top in simulated head-to-heads around 30% of the time.
Probabilities, Not Odds
The goal of UDisc's Win Probability is not to serve as a basis for gambling. Instead, the goal is to enhance the spectator experience by providing win (and other) probabilities as accurately as possible. Our model is independent of human opinions (we know you've got 'em), under-reactions (and those), and overreactions (oh, and definitely these).
Still, we know how many disc golf fans like to talk about betting odds and gambling, so let's dive into it anyway.
If a bookie used our model out of the box, a $100 bet on Gossage to win (had he pulled off the upset) would have been worth $462,000. But no sportsbook would actually give you those odds. Why not?
Remember that any sportsbook is engaging in a balancing act between core economic incentives:
- Make money
- Mitigate risk
To see how these incentives affect the odds presented by a sportsbook, look no further than Simon Lizotte. The German superstar and hero to all dads has won three times on tour this year, including the most recent event prior to Worlds. He is also a generally well-liked and respected player. UDisc's Win Probability put Lizotte at a 3% chance to win Worlds. A bookie doing their job well would consider the popularity of a player like Lizotte (65.4% of Grip6 Pick6 entries had him on the roster, compared with just 4% of entries containing Kyle Klein, another player with a 3% pre-tournament win probability) and adjust the offered odds to discourage Lizotte wagers to mitigate against unbalanced betting action that is super risky for the house.
Another technique that sportsbooks use to make money is the concept of incoherent odds. Go to any Tournament Winner wager on any sportsbook, and convert the odds to probabilities. The sum will always be greater than 1. For example, the DraftKings "Tournament Winner" wager for the BMW PGA Championships slates Rory McIlroy as the favorite at +600. This means that a successful $100 bet on McIlroy will net you $600 (on top of being refunded your $100 stake). In other words, DraftKings offers 6:1 odds against McIlroy, implying a 1/(6+1) = 14.3% winning probability. Repeating this for the 144 players and adding up the resulting probabilities yields a whopping 134%!
You might argue that math is math, stats are stats, and any accurate winning probability model should output essentially the same results as one might find on their favorite betting site. UDisc's Win Probability wasn't built with gambling in mind – the simple fact that it always adds up to 100% is proof in the pudding.
Where Can We Improve?
While the UDisc Live Win Probability model is already delivering on our goal of enhancing the spectator experience, there is always room for improvement! Here are some of the elements we'd like to incorporate and iterate on in future versions:
- Weather and course conditions (in particular, wind speed and precipitation)
- Momentum and streakiness
- Probability updates in the middle of a hole (if a player has gone OB twice, their best possible score is now a 5; this is not something the current model is aware of)
- Past performance at specific events
To elaborate on weather and course conditions, we were slightly concerned about the fact that, because Worlds was played on the same courses as the Dynamic Discs Open but that DDO had experienced winds of up to 40 mph, this might cause the model to expect that the courses would be much harder than they are in reality. Fortunately, since everyone is playing the same courses under (mostly) similar conditions, this shouldn't have a big effect on pre-tournament and between-round win probabilities.
However, we did see some evidence of this behavior during the middle of rounds. In this screenshot for players on feature, lead, and chase cards, we see that before they even begin to play each round, their top 5 probability gradually drops. This is due to the model believing the courses to be more difficult than they actually are and therefore thinking that the rest of the field is playing far better than expected.
This problem was particularly egregious for Worlds due to wild DDO weather conditions, and we expect that this is about as bad as it will get. But we do see an opportunity to improve the model by explicitly including information such as wind speed and precipitation.
On the whole, though, we've loved hearing the feedback from fans – the good, the bad, and the in-between – about Win Probability. And if you're ever frustrated with what it's projecting, remember: It's not disrespecting your favorite player, and it's not always going to be right.
Unless it's projecting Kristin Tattar to win Worlds. On that one, it's batting 1.000.