For those interested in a deeper dive into the methodology underpinning UDisc's newly released Precise Power Index (PPI), you've come to the right place. Before reading ahead, make sure you've checked out our introduction to PPI article.
This new statistic aims to capture a dimension of a professional disc golfer's game that commentators talk about frequently: being able to throw a disc accurately from long range, or "on a golf line." But it's a tricky concept to measure, and we tried a lot of different ways before settling on a definition that we think is best.
Read on if you want to look at the equations behind PPI for yourself or if you want to know more about how we think about developing sports statistics here at UDisc.
Setting the Stage for PPI
First things first: PPI is not just measuring how far pros throw. If you're looking for that, go check out the results from the Long Drive at 2022 Pro Worlds (oh hey, Ella Hansen and Garrett Gurthie).
Instead, this is about who can throw both far and accurately at the same time. If you now find yourself asking:
- But how far is far?
- What does it mean to be accurate?
- Are we talking internet distance here?
We'll answer most of these questions in a bit… but we like where your head is at.
One crucial feature of this metric is that it deals with only a player's throwing ability. In an ideal world, having a high PPI should give competitors a lot of chances to get birdies (or even better), but we won't penalize them if they don't make their putts.
We also wanted to ensure that a player's PPI is not dependent on other factors from the tournaments they play in. For instance, we spent some time toying around with the idea of including Strokes Gained: Tee to Green in our formulation. But Strokes Gained depend on the strength of the field at a given tournament, so comparing it across events isn't all too meaningful (as we discussed when we introduced the statistic). We came to the conclusion that how everyone else plays shouldn't determine if someone possesses precise power.
Instead, we aimed to make PPI consistent across all tournaments so that fans could compare players' performances over the course of the season. The definition we created should allow for just that.
A final point: We approached this problem with a healthy dose of skepticism around course par. What is considered par varies from course to course, and we don't want to just reward players who always find a way to eagle soft par 4s. The only time par is used in this definition is as a signal as to whether the hole is designed to test distance or other factors – but more on that soon.
How is the Precise Power Index Calculated?
The Precise Power Index is a hole-level statistic that is calculated by using the landing zone data captured by UDisc Live volunteer scorekeepers (thanks for all of your hard work!). It can be broken down into two parts:
- Determining whether a hole allows players to showcase their precise power skills
- Measuring how much precise power a player demonstrated on that hole
What Holes Do We Include?
In order to gain Precise Power Index points, a player has to get into scoring position on specific holes they play at UDisc Live events. 'Scoring position' means reaching the Green in Regulation (GIR) – 'green' defined as either Circle 1 or Circle 2 (C1 or C2) – or throwing in their shot for birdie or better from outside C2.
Remember, though, that this is the Precise Power Index. And while we love all types of hole designs equally here at UDisc, not every hole matters for figuring out who can throw a disc accurately at long range.
Instead, we only look at holes that require elite distance shots for the player's division. That's what we call meeting the division distance threshold.
How do we figure out what this threshold should be?
We looked at the average shot length it took to reach the GIR for all events on the 2021 UDisc Live schedule. In other words, we were looking for, on average, how far a player must throw their disc to reach the green in one shot for a par 3, two shots for a par 4, and three shots for a par 5.
From there, we selected the upper 20% of holes on tour by average shot length to reach the GIR.
- For MPO, these are holes with an average shot length of at least 400 feet/122 meters.
- For FPO, this came out to roughly 350 feet/107 meters.
Now that we have set a distance threshold for each division, what does it mean to meet the division distance threshold? In order to do that, at least one of two tests must be passed:
- Player Test: Did a player's average shot length to reach the green meet or exceed the distance threshold?
- Hole Test: Did a hole require an average shot length that meets or exceeds the distance threshold?
Again, passing just one of these tests means a hole counts toward a player's PPI.
Let's showcase how this works with a few examples from Finnish phenom Henna Blomroos' performance at 2022 Pro Worlds:
Avg shot length > 350ft / 107m?
|Include in PPI|
|ECC Hole 2 (R4)
Par 4 | 582ft / 177m
|291ft / 89m||FW -> C1X||No|
|ECC Hole 3 (R4)
Par 4 | 466ft / 142m
|233ft / 71m||C1X||Yes|
|ECC Hole 6 (R4)
Par 3 | 300ft / 91m
|300ft / 91m||C1X||No|
|ECC Hole 11 (R4)
Par 3 | 404ft / 123m
|404ft / 123m||C1X||Yes|
|ECC Hole 15 (R2)
Par 3 | 353ft / 108m
|353ft / 108m||OB||Yes|
- HOLE 2
At 582 feet/177 meters, hole 2 demands an average shot length of just 291 feet/89 meters to reach the GIR. Since Blomroos took two shots to reach the green (one to fairway, one to C1X), this doesn't pass the Hole or Player test, so we ignore it for PPI.
- HOLE 3
As a par 4 demanding an average distance of 233 feet/71 meters for players to reach the GIR, this also doesn't pass the Hole Test. However, Blomroos unleashed a massive drive here during round 4, putting herself into C1X for an eagle bid on this 466-foot/142-meter hole. That means this hole did pass the Player Test, so it's counted toward Blomroos' PPI.
- HOLE 6
This hole is simply below the 350-foot/107-meter mark that's the lower limit for FPO PPI, meaning it can't pass the Hole or Player Test.
- HOLE 11
Unlike the other three holes so far, the 404-foot/123-meter hole 11 requires a player to throw a shot of more than 350 feet/107 meters in order to reach the green for their birdie chance. Regardless of how Blomroos played that hole, we'd have counted it for PPI. But, as she seemed to do time and time again during round 4 on her way to a second-place finish at Pro Worlds, she landed her drive in C1X for a birdie chance. This one passes both the Hole and Player Tests.
- HOLE 15
A 353-foot/177-meter par 3, hole 15 is another one that meets the Hole Test. Unfortunately for Blomroos, she threw her drive OB when she played this hole during the second round. Since she did not reach the green on her drive, it would not pass the Player Test. But since it passed the Hole Test, we still count it toward PPI.
Now that we've walked through what holes count for PPI, let's put it all together in an equation.
In mathematical terms, this is what we call a piecewise function. If the Player or Hole Test is met and the player is in scoring position, then the player scores p points. If the Hole Test is met and the player is not in scoring position, the player scores 0 points. Otherwise, the hole is not counted at all.
How Do We Judge How Much Precise Power a Player Demonstrates?
In the last section we introduced the variable p, the amount of points a player receives for a qualifying PPI hole in which they find themselves in scoring position. This variable depends on two factors: how far they threw their shots to reach the green and how close they landed to the basket.
While we are only including a limited number of long holes, it is still better to park your drive on a 600-foot/183-meter hole as compared to a 500-foot/152-meter hole. So the first factor we include here is the average shot length to reach the green.
The second factor deals with how close a player lands to the basket. We are trying to measure precision, after all, so it's better to be closer to the basket than farther away from it. But how much better is it, for instance, to be C2 versus C1X versus Parked?
To quantify this, we looked at each division's putting statistics from the previous season and calculated the average player's C2 and C1X percentages. This effectively gives us a multiplier of how much worse it is to be C2 versus C1X versus parked (we just give you a value of 1 in this case).
We take these two factors, multiply them together, and – tada! – we have a player's value for p for a given hole. Here's what that looks like in math terms:
Higher values of p mean that a player demonstrated more precise power on that hole and landed their long-range shot closer to the basket.
Let's return to the example of Blomroos during Pro Worlds. We just need one more piece of information in order to calculate her p value for the qualifying holes: the 2021 FPO putting percentages. Last year, the global FPO putting rates were 64.4% from C1X and 10.1% from C2. This time we are going to work in just meters for simplicity.
|Hole||Include in PPI||Player avg shot length||FPO avg putting rate||p|
|ECC Hole 2 (R4)
Par 4 | 177m
|ECC Hole 3 (R4)
Par 4 | 142m
|ECC Hole 6 (R4)
Par 3 | 91m
|ECC Hole 11 (R4)
Par 3 | 123m
|ECC Hole 15 (R2)
Par 3 | 108m
We see that of these five holes, the one which maximized p came from Bloomroos' impressive drive on hole 3 during round 4, telling us that she displayed more precise power on that hole compared to the other four.
Why Is It Only Available at the Season Level?
Currently, we think it's better to show PPI at the season level rather than the tournament (or even round) level. Why is that?
Thinking back to how we've formulated this metric, it's unlikely that many holes during any given round will qualify to be included in PPI. After all, roughly 20% of all holes played are eligible to be included – that's 4.5 holes per round on average.
With that few holes qualifying, we've found that PPI doesn't really tell the story of a single round. Some courses, such as the FPO layout at the Waco Annual Charity Open, even have 0 holes that pass the Hole Test. A course like that isn't designed to test a player's precise power – and that's OK – but this metric doesn't make sense for that tournament.
As a result, we are more interested in capturing who showcases the most precise power over the course of the season. As of today, a player has to have played 100 eligible holes in the 2022 season in order to be ranked, which comes out to roughly 8 or 9 tournaments out of the 36 UDisc Live tournaments that have already happened this season.
You can find each player's average PPI across all of their eligible holes played on the UDisc Live under the Stats tab.