How Strong Was the Field?
Harmonic Field Strength (HFS) as a New Way to Measure Tournament Toughness
Pool pundits battle about whether the European Open or the World 10-Ball Championship had the stronger field—or which event truly ran deepest in 2025. Or which tournaments should be considered majors.
These debates almost always come down to some version of the same tradeoff:
star power vs.
depth — comparing the top few entrants to the overall quality and density of the field.
Panozzo might argue the star-power side this time, pointing out that Filler, Gorst, SVB, and FSR were all in the field of some tournament. Or he might count how many of the World Nineball Tour top 10 were there. Or how many players were rated over 830.
The other Mike might counter that while Panozzo’s event had a few more marquee names, this
other field, with more players traveling from Asia, ran deeper and included more of the top 100 or more players over 800 or 780.
Both sides have a point. It’s a good instinct to care about
both star power
and depth. How hard it is to win — or just to go deep — really does depend on both. It is more likely for a top contender to get snake-bit early when the field runs deep.
Until now, though, we haven’t had a unified way to balance that tension in a single number.
Introducing: Harmonic Field Strength (HFS)
You’ve probably come across some version of the
80/20 rule, also known as the
Pareto Principle --
20% of the people do 80% of the work. Or
20% of the seals do 80% of the barking.
That idea reflects a deeper pattern called a
power law, where impact isn’t spread evenly but instead tapers off from the biggest contributors to the many smaller ones.
The same pattern appears in tournament field strength.
- We care a lot about the presence or absence of the top five or ten players.
- We care somewhat about the next 30 or 40.
- And we care very little about whether the bottom half of a 256-player field is rated 680 or 610 — or even whether they’re there at all.
To account for that uneven importance we borrow a concept from economics and physics:
A harmonic-style average that naturally emphasizes the top-ranked players while still incorporating the strength of the rest in a balanced way.
What is HFS?
Harmonic Field Strength (HFS) is a single-number summary, a rating-style average that weights each player’s contribution by the
reciprocal of their rank, where
rank here comes from a top-to-bottom ordering of the players in the field by
Fargo Rating.
- The 2nd-highest rating counts half as much as the top rating.
- The 3rd counts one-third
- The tenth counts one-tenth.
- And so on — through the top 64 players.
This produces a number that:
Looks like a player rating
Reflects both star power and depth
Allows clean comparison between tournaments
An Illustration: Bali vs Hanoi
Two overlapping events happened in 2025:
World 8-Ball Championship in Bali (Filler, SVB, …)
Hanoi Open (Gorst, FSR, …)
Which field was tougher?
By average rating of the top 16, Bali is a smidge ahead, by less than a point. But when we reach further to consider the t
op 32 or
top 64, the tide changes and Hanoi looks stronger. The average rating of the top 64 players is 801.3 for Hanoi and 792.2 for Bali. HFS conbines the influence of the top 64 players and reveals Hanoi as the stronger field overall.
Event HFS Score
Hanoi Open 825.2
World 8-Ball 824.6
What About Other Events?
Here’s a taste of what HFS reveals:
- Eurotour events, Derby City 9-Ball and Super Billiards Expo come out comparably tough.
- The Battle of the Bull (Roanoke VA) ranks right alongside Bali and Hanoi, surprising perhaps, until you note its proximity to the US Open
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Which tournament had the toughest field in 2025?
What about these big ones?
- China Open
- Las Vegas Open
- US Open 9-Ball
- World 10-Ball
- UK Open
- Florida Open
- World Pool Championship
- Peri Open
- International Open
Which one do you think had the
strongest field?
What are the
top three picks?
We’ll compile the full numbers and share the results soon.
