Christopher Kempf, the new statistical analyst of the PDC, looks at the sets format which can make the William Hill World Darts Championship so difficult to play - and so much fun to watch!
SET THEORY
Phil Taylor, the 16-time World Champion, can look back at two of the World Championship finals that he lost - in 2003 to John Part and 2015 to Gary Anderson - and justifiably feel that he was the better player on the night.
Despite losing both matches 7-6 in sets, Taylor won the majority of the legs in the two finals, winning 27 in both to the Scotsman's 26 and the Canadian's 25.
But being the better player over 50+ legs is not necessarily of the utmost importance.
Taylor was not crowned World Champion in 2003 because he lost all three set-deciding legs in the match to Part, and because he failed to convert nine of his legs won against Anderson into sets.
When Taylor won and lost his legs mattered more than their overall quantity. Timing matters in set play, and it matters in the World Champonship more than in any other event.
Sets are like funhouse mirrors: a three-leg, five-minute whitewash is equivalent in the calculus of sets to a gruelling five-leg, half-hour-long siege of arrows.
It is possible to lose a match 3-0 in sets in spite of having won six legs, just as it is to win a match 3-2 and lose 11 out of 20 legs.
The vast differences in the effort needed to win different sets of the match confounds players' ability to estimate the size of their lead or of their deficit.
A lead of four legs in the World Matchplay always requires a minimum of two breaks of throw by the opponent to equalize the match, whereas a seemingly larger two-set advantage at the World Championship can be overcome with as few as one or as many as five legs won against the throw.
Set play rewards players who can win the right leg at the right moment, rather than accumulate the most holds and breaks over a particular distance.
Although players alternate between throwing first and second in sets as they do in legs, the advantage of throwing first in a set, compared to the advantage of throwing first in a leg, is almost nonexistent.
At Alexandra Palace in 2017, 64% of legs were won by the player throwing first, compared to a mere 51% of sets won by players similarly advantaged.
Because set play totally changes the importance of breaks and holds - the most important structural element of leg play - it also eliminates the reference points players use to gauge their performances and keep their opponents in the rear-view mirror.
To win sets, players cannot break throw at their leisure as they often can in other events. Even in a set where a player is guaranteed to throw first in three out of a possible five legs, he must make a strong effort to break throw at least once, in expectation that his opponent may break him back in turn.
At the 2017 World Championship, there were no breaks of throw in only eight percent of sets, or roughly two break-free sets for every five matches; the average Ally Pally set features 1.2 breaks of throw.
This pressure to break in every set can prove especially unwelcome for highly-ranked players who have spent the past year winning long-format legs matches on TV and in the World Series, but find themselves forced essentially to win a series of very short matches in which there is no overall advantage to throwing first.
Finally, set play takes an occasional feature of leg play - the deciding leg, or last-leg decider - and transforms it into a regularly recurring feature of the match.
When taking sets into account, 122 'deciders' were contested at the 2017 World Championship, compared to a mere seven played at the leg-format 2017 European Championship.
The nerve-wracking effect of playing multiple deciders in a match can take a substantial psychological toll unlike anything seen in a straight leg format.
Winning a decider can lift a player to new heights of euphoria and relief, and losing can plunge him inextricably into a pit of despair.
A lost decider wipes two of a player's hard-won legs off the scoreboard, putting him back in the same position that he occupied at the start of the previous set, and excuses two legs' worth of mistakes from his opponent.
A true last-leg decider, invoked when both players win five legs in the final set, is even more cruel; it is the only single leg for which the right to throw first is decided by a preliminary throw for the bull.
After a long, tiring battle, the contestants may have only one nervy dart each to determine their fate.
Many players prefer the legs format. Michael van Gerwen, in particular, commented last year that he categorically prefers this to sets, since it allows the player in better form to wear down and defeat his opponent.
After a close shave at the 2016 World Championship in which Rene Eidams pushed him to within two legs of defeat, and countless triumphs in leg-format events, his point of view is understandable.
The World Championship spectator, however, gets to see the odds-on favorites shaken up by the unpredictable set format and overcome by players who, to borrow a phrase of Van Gerwen's, "do the right things at the right moments" by stealing deciders and making the seeded favorites fight for every set.
The set format certainly does not guarantee for the Michael van Gerwens of the world the results they want, but it does for the rest of us: a cracking December at the darts!
Legs Played In 13-Set Format World Championship Finals
2001: 24 (Phil Taylor 21-3 John Part) ** Shortest final since move to 13 sets
2002: 26 (Phil Taylor 21-5 Peter Manley)
2003: 52 (Phil Taylor 27-25 John Part) ** Won by John Part
2004: 64 (Phil Taylor 34-30 Kevin Painter) ** Longest final
2005: 47 (Phil Taylor 28-19 Mark Dudbridge)
2006: 27 (Phil Taylor 21-6 Peter Manley)
2007: 57 (Raymond van Barneveld 29-28 Phil Taylor)
2008: 40 (John Part 25-15 Kirk Shepherd)
2009: 35 (Phil Taylor 23-12 Raymond van Barneveld)
2010: 42 (Phil Taylor 26-16 Simon Whitlock)
2011: 45 (Adrian Lewis 24-21 Gary Anderson)
2012: 43 (Adrian Lewis 23-20 Andy Hamilton)
2013: 50 (Phil Taylor 27-23 Michael van Gerwen)
2014: 44 (Michael van Gerwen 25-19 Peter Wright)
2015: 53 (Phil Taylor 27-26 Gary Anderson) ** Won by Gary Anderson
2016: 45 (Gary Anderson 26-19 Adrian Lewis)
2017: 44 (Michael van Gerwen 27-17 Gary Anderson)