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Fair Ways For Statistics: Part 1


The iconic Toboggan course in Milford, Michigan. Photo: Matt Gregoire

Editor's note: This is the first in a three-part series from Disc Golf Hall of Fame member and PDGA Ratings Committee Chair Chuck Kennedy that explores and analyzes how historic performances can be compared.

How do you feel about the number 3? It’s just a number, right? But as disc golfers, we all have different feelings about 3 that can change with the wind: Sometimes it feels like a bogey on an easy hole; others it feels like a great save on a tough hole. Maybe a 3 just feels…meh. There’s also the common sentiment that “all holes should be par 3.” It’s as much how we feel about the situation beyond just the factual number 3.

Now, how do you feel about 45? Earlier this year we witnessed Paul McBeth throwing a score of 45 – 18-under par – on the Great Lakes Open's Toboggan course that was rated 1108. Many are calling this the greatest round they ever watched, and they’re right: Our perception is our reality.

“Congrats to Paul McBeth on shooting the best round of all time. It’s not even close. Unreal. Hats off brother. I love seeing history made in sports. Nobody will ever forget this round.” – Paul Ulibarri via Facebook

Numbers and statistics simply provide the foundation to help shape our perceptions. Better understanding of our disc golf numbers and stats – including their limitations – can help, but still won’t supersede what each of us may see, think, and feel about an athletic performance.

I threw a 47 in league, “amazingly” just two throws more than the highest rated player in the world. However, 45 and 47 are just lifeless numbers without context. We need to know level of competition, watch the kinds of throws being made, take the weather into account, and determine how long and challenging the holes are. You didn’t see my round – or, for that matter, most of the great rounds thrown in our sport before regular video coverage.

Current PDGA membership continues to increase by around 15 percent annually. More than three out of four current members joined or renewed sometime after the PDGA started tracking record round ratings and social media became an important form of communication. The primary ways to compare exceptional rounds before this time were looking up scores on established courses, sometimes with commentary in a few disc golf publications and word-of-mouth from other players who witnessed those rounds. Here are two examples of early records before all rounds were rated:

We’ll step through the evolution of our numbers and stats – not only for the ones used in golf, but also a few unique to disc golf. As much as we get some of our information from tweets and posts, we’ll dive deeper to gain a better understanding of the terms and metrics we toss around every day like under and over par, course length, scoring averages, course ratings, and round ratings. Veteran players may discover something new about the numbers they’ve used for years. The hope here is to improve our ability to discuss numbers and stats from the same framework and perhaps reshape our perceptions when great performances are witnessed.

Stroke or Throw – Let’s give it a shot

The scoring unit for any form of golf is one stroke or throw. Using stroke count alone, my 47 looks awesome next to McBeth’s record 45. That would be an accurate perception if we had played the same course at the same time; scores are how we rank players in direct competition. But we didn’t play the same course at the same time. Simply comparing round scores on different courses is not a very effective way to compare performances.

A basic problem for comparing performance in golf is each shot counts once, whether it’s a five-foot putt or 500-foot ace. A cut-through or bounce-back costs one throw. Every penalty counts as one, or even two if the drop zone is too far back. There’s no extra credit for amazing escape shots. A throw-in, circle 1 or circle 2 putt (thanks, UDisc!) scores the same with no extra credit for the foliage or elevation challenge.

The beauty of golf scoring is there are many ways to score a 3 on many types of holes. The failure with golf scoring is how impressive each 3 looks cannot be determined by simply looking at the scorecard. You must watch the round closely – hopefully with knowledgeable eyes – and know the context, event, and weather. If you could watch my round compared with McBeth’s, you would see a significant difference between the two – although I did hit the basket on a 275-foot ace run. But then, McBeth almost skipped in for a 2 on a 915-foot hole.

“Dude’s a monster. We all know what happened today cannot happen every day.” – Z.W. commenting on McBeth’s Toboggan round (Facebook)

What about par?

If comparing total round scores on two courses does not provide enough information, perhaps another golf metric like par could help us compare rounds? Paul’s 45 was 18 strokes under the par 63 set by the tournament director. My 47 was seven below a default par of 54. We’re now able to see a bigger difference emerge when meshing total par with total scores to compare performances.

Digging a little deeper, we also discover top pros would likely score 2s at least half the time on several holes on the course I played. However, assigning a hole as par-2 is currently not considered acceptable (despite scoring data that supports it). This artificial constraint has led to inflated pars on some tournament courses, undermining the ability to use under/over par as a reliable reference for comparing rounds on different courses. For example, if an elite pro par of 46 was assigned to my course by including eight par-2s, my 47 would have been a 1-over par versus the 7-under par 54 default.

Using tournament scoring data to adjust par on holes for future events when the same layout will be used is not a regular practice, nor required by the PDGA. ESPN announcer John Buccigross may have cleverly suggested this practice should be considered with his Shakespearean Macbeth quote following McBeth sinking his eagle putt on hole 2: "False face must hide what the false heart doth know."

Our sport has followed tradition by assigning pars in a manner consistent with ball golf. But even if we would feel comfortable assigning the most appropriate par value on each hole, that single digit par may still only fall within a half stroke of the calculated scoring average which is typically shown with one decimal digit. So even if our sport tries to assign more accurate single digit pars, they’ll only get us a bit closer for reliably comparing challenges on two holes, let alone two courses.

Scoring averages to the rescue?

Consider Course A with 18 holes, where each hole averages a score of 2.6. Course B has 18 holes where each one averages 3.4. Every hole on each course would typically be assigned par 3, making both Course A and Course B par 54. Now, multiply the scoring average on each hole by 18 to get the total scoring average on each course.

  • Course A: 18 x 2.6 = 46.8      
  • Course B: 18 x 3.4 = 61.2     
  • Course Scoring Average Difference: 61.2 – 46.8 = 14.4

We have two courses where the scoring difference between the two is more than 14 throws, and yet we call both courses par 54. Shooting 6-down on the tougher Course B would be significantly more impressive than shooting 6-down on Course A. But how would we know? Under/over par calculations can fail to properly compare performances between two courses. Watching the players shoot each course is still key for comparing performances – especially exceptional performances – along with support from more useful stats.

Despite potential problems using course par to compare two courses, we discover using scoring averages could be a better way. Even though both courses were par 54, Course B had a scoring average of 61.2 and Course A was 46.8. Course B clearly appears tougher, but is it really 14.4 shots tougher than Course A? We’re still not sure until we know the skill level of players producing those averages.

 “Reality is merely an illusion, albeit a very persistent one.” – Albert Einstein

If it’s the same player pool as in a tournament, then we know Course B is about 14 throws tougher for that pool of players. However, if one pool played Course A and a completely different pool played Course B, we could be fooled if sixth graders shot the 61.2 average on Course B and a pool of top pros shot the 46.8 average on Course A. It’s probable that Course B with the 61.2 average for sixth graders is easier than Course A where top pros averaged 46.8 since the pro skill level is likely more than 15 throws better than the youngsters.

Course scoring averages get us closer to a better stat for comparison. However, we need a way to account for the different skill level of players producing the averages. Then, we must adjust those numbers to the same skill level so we can properly compare one course with another.

This is the first step done in the ratings process. More on this coming next in Fair Ways for Statistics: Part 2.

Comments

Great story on helping you understand a course round rating for that course on that day and why a tournament round rating is worth more or less on a any given day on the same course during the year.When you understand that every put you miss in a tournament round that you should make or could make cost you 10-12 points per putt missed its easy to see the best way to improve your game and player rating.

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