WAGR Files: Cracking the WAGR Power Rankings

For better or worse, the World Amateur Golf Ranking is the de facto ranking for amateur golf around the world. It is used extensively for earning exemptions and setting fields for USGA, R&A and other top amateur events. It is used in junior golf as well, as the top 100 age-eligible juniors are exempt to the U.S. Junior Amateur (top 50 for U.S. Girls' Junior).  The bottom line is, if you are a competitive junior or amateur player, it is your best interest to understand how WAGR works.

At the most basic level, WAGR ranks players on their average performance (WAGR Points) in 54+ hole tournaments over the last two years, with the last 12 months weighted more heavily. WAGR Points for a given event are going to be a function of two things: finish and strength of the field. The strength of field is expressed in terms of a Power metric.

And while WAGR's mission statement says it is run by the R&A and the USGA as a "global service to golf", the formulas for how the Power ratings and points distribution by finish position are shrouded in mystery.  Frustratingly little information is provided in the FAQs section of their website. We'll get into the points distribution at a later date, but here we'll try to pull the veil on the Power formula.

This article publlshed in 2021 sheds (just) a little more light on the Power rating:

"The strength of events in WAGR® is determined based on the ranking of all the players who make up the field. This includes any professionals who are participating in the competitions. For professionals, their ranking in OWGR or the Rolex Ranking is used. Unranked professional players are assigned a contributing value below the lowest ranked player in the applicable ranking.
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Within WAGR®, the strength of an event is expressed as a Power with values starting around 10. Events with only amateur players will not have a Power exceeding 1000. Events with professionals have Powers starting around 15, but can extend past 1000 and go up to the high 3000s, depending on how many top-ranked players from each ranking are participating. Generally, this will only happen in majors and with the very strongest tours."

Outside of that, that is all the information that the R&A provides, even though in the same article they confess the importance in understanding how it works: "For the highest ranked players, those generally ranked around 400 or better, care might be taken in selecting events in which to participate, as the maximum points on offer to the winner in weaker events may not meet their current average." DRVN.Golf reached out to the R&A to get more information, but was shut down: "(we) cannot share any further information in regards to how to how the power formula works, this is part of our intellectual property"

One could question the logic for protecting the intellectual property of a free service that is literally used exclusively throughout golf and is firmly entrenched in the fabric of the tournaments run by the same organization. It's not likely that someone would replicate or try to build a version to replace it. The R&A and USGA would never adopt it.

However, if you take the R&A's comment at face value, can we shed more light on how on the WAGR power formula works based on their publicly-available published information? Here is what we know and have at our disposal (for simplicity sake, we'll only focus on amateur events)

• Power ratings start around 10 and max out at 1000 (think U.S. Amateur)
• Unranked players are assigned a contributing value below the lowest ranked player in the ranking
• 2+ years or tournament results and published Power rating for each event

Admittedly, that's not a lot to go on.  But there is information there that we can start to piece together.

First Puzzle Piece: Non-Ranked Players

It's difficult to make heads-or-tails of the Power Rating of any one tournament because there are multiple degrees of freedom: the total number of players in the field, the total number of ranked players in the field, the WAGR ranking of each of those ranked players and the total number of non-ranked players in the field. However, there is a subset of tournaments that provide valuable clues into the Power rating: those tournaments that have no ranked players in the event.

Rather than publish the complete standings of a tournament, WAGR only publishes the scores of the ranked players entering the tournament plus any newly-ranked players as a result of the tournament (typically the winner and sometimes 2nd place in junior events). Occasionally, you'll see a lower-level AJGA or Hurricane Junior event where only the winner's scores are published. This typically means that there were no ranked players coming into the tournament week. This proves to be extremely valuable in cracking the code because it eliminates many of these degrees of freedom. We know each player in the field is assigned the same 'replacement-level' WAGR rank for the Power calculation.  Therefore the only degree of freedom is the number of players in the field, with some small variation in the total number of ranked players on WAGR in a given week (typically around 4500 for men, with some seasonal variation).

Taking a handful of these tournaments with no ranked players from the 2023 season, we definitely see a pattern with respect to Power Rating relative to field size:

From this information, we can make two primary assumptions:

1. The Power Rating uses a weighted diminishing return formula where the highest ranked player in the field has a full 100% weight of his Power contribution to the tournament's Power rating, the second best player in the field contributes slightly less than 100%, etc. downward until...
2. The Power Rating goes flat right around 60 players, so we can assume that the Power Rating only counts the contribution of the top 60 WAGR-ranked players in the field (or if they do count the players after 60, it is effectively flat and the impact is immaterial)

Based on this data and other tournaments, we can deduce a smooth formula for the weight of each of the top 60 players in the field:

Second Puzzle Piece: Men's vs. Women's Events

Looking at women's events, you'll generally see the lowest-ranked events are higher than the lowest-ranked events on the Men's side.  After controlling for the number of WAGR ranked players in a given week, the next two assumptions are obvious (and are facts rather than assumptions):

3. Mens and Womens events use the exact same Power rating formula
4. The Power Contribution of a given player is an inverse function of the WAGR ranking of that player

[Note: The shared formula for men's and women's WAGR creates a lot of unintended and undesirable consequences, which we'll get into in later blog posts]

Third Puzzle Piece: Solving for the Inverse Constant

Using the above assumptions as foundations of the Power rating, the other tournaments start to make more sense.  Taking each tournament as a data point, these pieces of the puzzle start to form the picture.  The Power contribution of any one player is an inverse to constant of approximately 5950. Therefore, the unweighted Power Contribution of the 595th ranked player would be 10 (5950/590). The Power contribution of the 2000th ranked player is twice the Power Contribution of the 4000th ranked player, the 1000th ranked player is worth twice the 2000th ranked player, etc. For reference, the value for a replacement level player is approximately 1.3 and 1.95 for Men's and Women's, respectively. For players in the top 200, the formula turns from inverse to linear, to prevent the Power Contribution on any one player from going astronomically too high. Based on this spline in the formula, I estimate the maximum contribution of Gordon Sargent to a tournament field as 59.32.

Putting the Pieces Together

Putting all of this information together, the Power Rating for a given tournament is the weighted sum of the Power Contribution x the Player Weight for each of the top 60 players in the field.  For example, assume a 10-player tournament with the top 10 WAGR-ranked juniors in the U.S.:

It's easy to see how much the Power rating is driven by the highest WAGR-ranked players in the field.  For reference, if the tournament included the next 20 best juniors (which would be epic, by the way), the Power Rating only increases from 219 to 275.

The Driven Golf Podcast WAGR Power Estimator

We've put a WAGR Power Estimator on Google Drive to help you estimate the Power Rating for any amateur tournament that you or your son or daughter might be playing in (please save a local copy and edit as you please).  Just enter the WAGR ranking of the players in the field (sorted from best to worst) and other basic information about the field size and you'll get a reasonably accurate (within a point) of the Power Rating.

Like the R&A says, it is important to know the WAGR-implications of the tournaments that you select.  Hopefully this blog post and the calculator help take the mystery out of the Power Rating.  The Driven Golf Podcast WAGR Power Estimator is provided as a service to golf.

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