What is the hardest to achieve? Is it a nine-darter, a 147 break or a hole-in-one? Stats Analyst Christopher Kempf looks at the difficulty and rarity of each feat.

Suppose you were to correctly guess, at random, the month, day and weekday (e.g. Tuesday, 25 April) on which an individual was born.

The odds of this are 2,557 to 1. These are roughly the same odds facing a darter as the referee calls "game on", a golfer at the tee box of a par-3 hole, and a snooker player at the break-off, as they pursue perfection in their particular sports.

It is as astounding a fact that the highest achievement in darts, golf or snooker is as accessible to the trained professional as a highly improbable feat of guesswork, as the fact that the nine-darter, the 147 break and the hole-in-one occur (per attempt) with almost the same frequency.

The question of which is the most difficult is, however, not settled by this probability coincidence, and this article will attempt to compare these wildly difficult achievements.

The probability of a nine-darter is the easiest to calculate because every nine-dart leg is, essentially, the same.

Each player is positioned the same distance from the board when throwing, the boards are, with insignificant manufacturing variations, exactly the same, opponents can do nothing to interfere and most perfect legs are completed in the same way: a player attempts to hit seven consecutive treble 20s, a treble 19 and a double 12.

Even if a player does attempt a 144 finish, his aim is always to finish in nine darts, because an eight-darter is not possible in 501 and there is no advantage to completing a ten-darter.

Thus, because we know that players have contested 69,888 legs across 60 Players Championship events and achieved perfection 48 times, we can say that the odds of a nine-darter being completed in any particular leg are 1,456 to 1, or 2,912 to 1 per player attempt.

Since the average PDC Tour Card Holder contests about 850 legs on tour per year, that player might expect to have a perfect leg once every 3.5 years.

There are strategic reasons why a golfer would choose to not attempt to hole out on a par-3, but it's fair to say that a golfer is trying to place his ball as close to the hole as possible with every shot.

At that point all similarities between hole-in-one attempts end, because not only is every hole of golf designed with different angles, distances, elevations and hole positions in play, but every day, in terms of humidity, temperature, wind, grass length and ground moisture (green "speed") is difficult to compare with the next.

Thus attempting to ace the Island Green 17th hole at TPC Sawgrass in a downpour might be hundreds of times more difficult than holing out on a level, 100-yard par-3 on a beautiful day.

Mark Broadie of Golf magazine has estimated that "the odds of a pro holing out from 200 yards are about 2700 to 1", based on analysis of data from the PGA Tour's ShotLink database.

This understands the probability of holing out as purely a function of distance, irrespective of whether a player is taking his first or third shot from 200 yards away, but with four par-3 holes per round, and a PGA player playing in the vicinity of 80 rounds of golf on tour per year, this puts the odds of a player having an ace at some point in a year at 84 to 1.

Of the three crowning achievements of darts, golf and snooker, the likelihood and difficulty of the 147 break is the most difficult to evaluate.

It is a simple matter to count the number of official maximum breaks on the World Snooker Tour in a particular time period (33 since the beginning of the 2022 World Championship), divide by the number of frames played (more than 46,000) and arrive at a probability of 2,825 to 1 per player attempt, and conclude that it is almost exactly as difficult as a nine-darter or an ace. But it is not so simple.

We cannot compare the maximum break on equal footing because a 147 break, unlike the other two feats, has no additional competitive value in the course of professional snooker to any other century.

A 147 is just as devastating to an opponent's hopes in a frame as a 146 or 145; once there are no longer enough balls on the table for the opponent to make up the score deficit, a maximum break becomes a matter of pure exhibition.

Moreover, depending on the orientation of the balls at the beginning of a clearance, lower-value breaks may actually be much more difficult than the maximum.

A theoretical 72 break in which a player pots 15 reds and 15 yellows, potting the same number of balls (36) but scoring 72, would be substantially more difficult than a break of more than twice its point value.

Thus, because there are often easier routes to victory in a frame involving colours other than black, only a fraction of those 48,000 frames could actually be said to feature a bona fide 147 'attempt'.

Once we consider that there have been at least 200 36-ball breaks on the World Snooker Tour, and the number of frames in which clearing the table is a sensible strategic play (without recourse to snookers or safeties) is far less than the total, the odds, though impossible to determine, become much less intimidating.

Even though snooker players contest fewer frames per year than professionals in darts or golf do legs or par-3s, the true difficulty of a 147 break, being so dependent on the frame's unique distribution of balls across the baize, is limited because it often is not a player's objective.

Follow Christopher on Twitter @ochepedia

Stats Analysis: Nine-Darter, 147 Break Or Hole In One. What's Harder?