Harry Hong has an in-depth look into what he feels is a growing problem: a specter of reductionism specifically dealing with non-contextualised football statistics.
A specter is haunting the world of football-the specter of reductionism. To be more specific, it is the tyranny of shallow statistics explaining away the intricate whys and wherefores of the beautiful game.
Numbers-in the forms of totals, averages and percentages-have been around for nearly as long as the games themselves, representing a cursory outline of its proceedings while serving as the salient entries in its annals. But to the observers and chroniclers of sports who have adopted it as their lingua franca, individual statistics have, perversely, evolved from servant to master; what was purported to be a quick-fire encapsulation of player contribution has glibly become an earnest and authoritative conveyor of player value.
This fidelity is fallacious: when dynamic motion on an excitable field is reduced down to static numbers in an aseptic repository, context is invariably lost. These non-quantifiable elements can be tangible: objective narratives such as the circumstances that surround and the caveats that clarify the quantified action; and intangible: subjective or intrinsic notions like aesthetics, élan, inspiration, grace, grit, leadership, sang-froid, character-that ineffable je ne sais quoi. Though the intangibles serve as many a sports romantic’s raison d’être-punctuating jaw-dropping plays and awe-inspiring players with a mystique and legend that will live on in posterity-the focus of this lamentation is on the tangibles.
By and large, two types of tangible information is stripped during the distillation of qualitative action into quantitative statistics in team sports. The first-and the more important of the two-is the leverage situation. Simply, all goals, points and runs (whatever the scoring unit) are not created equal. Their value is distinguished by three leverage factors: the impact the score has on the game; the impact, in turn, the game has on the wider championship picture; and the quality of opposition that the score came against.
Consider how this applies to the beautiful game. Goals are football’s currency, the plain and pure determinant of each match. But while all goals count equally, they matter differently: a score that breaks a tie in stoppage time, considered a high-leverage match situation, is far more valuable than a pile-on or consolation goal in a blowout, a low-leverage spot.
Just as how goals are the fundamental units that determine matches, matches, in turn, are the fundamental units that determine championships-be it season-long league campaigns and cup competitions, or month-long knockout tournaments. In domestic leagues, matches, much like goals, are fixed in nominal worth but variable in actual value: a contest that impacts the title picture at the season’s climax is more highly leveraged than a run-of-the-mill one at its outset. In tournaments and cup competitions, matches progressively become more highly leveraged with each passing (elimination) hurdle, from the preliminary group stage, where spots in the knockout phase are up for grabs, to the final, where the championship trophy is on the line.
And even if a goal was scored in a high-leverage setting in both a match and a competition context, its value is also contingent upon the ease with which it came about: if it was slotted at the expense of a fairy tale outfit that finally exhausted its pixie dust at the deep end of a tournament, then it would be somewhat cheapened; if, on the other hand, it downed a chief rival during the stretch run of a title race, then it ought to be elevated even further.
For all its omnipresence, raw abstract scoring totals-simply a tabulation of goals that occurred within a certain time frame-do not adjust for these leverage situations: is a hat-trick amassed in a 6-0 romp, for instance, really more valuable than the single score that decided a 1-0 struggle (let alone three times as much, as the crude arithmetic would posit)? While mulling this, bear in mind that league and tournament championships are not decided by the cumulative goal difference across matches but by the goal difference within each match, either cumulatively with equal match weighting (league and group stage of tournament), or singularly with the occasional exception of two-legged ties (cup competition and knockout phase of tournament).
True, numbers don’t proverbially lie. But when non-contextualized goal tallies-omnisciently extrapolated as future performance indicators (a form of “inductive reasoning”, to use statistical jargon)-are utilized as strict proxies for footballing value (a “statistical syllogism”), it is based on the premise of a uniform distribution of scoring, on a player’s behalf, across moments of high and not-so-high leverage, across all matches, and against oppositions of all stripes (a “generalization”). Yet that fundamental premise simply does not hold in the high-pressurized world of professional sports, despite its culture of routine and repetition-hence the statistical fallacy.
Generally, week to week fluctuations can be explained by natural variance; while month-long dry spells during a season or over an entire tournament can be attributable to the occasional form slump-though over the course of a nine-month league campaign, or across multiple tournaments, reversion to the mean typically takes place. But for a certain kind of player, a systematic trend can be discerned: a susceptibility for relatively reduced output in the high-leverage spots.
This underachievement in crunch time can mostly be accounted for by shortcomings in two areas. The first is physical: an imperfect and incomplete technical skillset that is well-suited to devour up the (technically inferior) mediocre squads, but is distinctly neutralized when faced with the (technically superior) elite outfits. This is the embodiment of the flat-track bully, who disproportionately accumulates his statistics against the former but barely makes a numerical dent against the latter. The second factor-at the risk of besmirching the entire amateur psychology industry-is mental: psyches overwhelmed and nerves swallowed up by the magnitude of the moment. The increased frenzy and the bright lights deviate the dainty from their methodically and meticulously practiced habits that is exhibited more or less flawlessly against inanimate cones in training sessions and inanimate opponents in mundane fixtures, and oftentimes induce over-compensating mechanisms-such as over-pressing or overthinking an opportunity-that compound the situation.
The other type of tangible information lost in the translation of action into figures is the context of game-play. As a general precept, the slower and more discrete a sport “plays”, the less that context will be reduced in its quantified actions.
This is manifest in two ways. First, discrete sports consist mainly of independent, mano a mano matchups; the statistics gathered, thus, isolate individual player value from teammates, making them more meaningful for evaluation purposes. Conversely, continuous sports feature more interplay between teammates; its individual numbers, consequently, comprise of a bigger teamwork component. Second, specific discrete actions are easier and more accurately codified than nebulous free-flowing ones. Such a statistical yield from each outing results in a larger sampling over time, and ultimately a more reliable set of empirical data with which to work. Sampling statistical terms might be confusing to those who are not familiar with the terminologies, but these can be understood with some quick research online. Additionally, do note that not every sampling data is 100% accurate and sampling errors are bound to occur.
Consider the two most discrete sports, baseball and cricket. Because both involve solo contests between (specialized) hitters and hurlers, a player’s measured output in these two arenas mainly reflect his contributions to the team’s cause. Moreover, such are the atomized and regimented movements of the hitter on offense that his actions are reflected entirely by the game’s rudimentary offensive measures: singles, doubles, etc. in baseball; runs in cricket-with those same figures symmetrically charged to the pitcher or bowler responsible for giving them up. This minimal amount of informational loss explains why both of these two sedentary bat-and-ball pastimes so closely identify with its hallowed numbers.
Sports that permit hands to control possession, such as basketball and American football, are next on the game-flow spectrum. Since hands are plainly the most dexterous part of human anatomy, possession is more or less nine-tenths of the law as far as offense is concerned-except by artificial means (shot clock, downs) designed to balance offensive (in possession) and defensive (out of possession) opportunities. The advanced level of possession manipulation and the curbs on opportunity engender a greater sophistication in game-play, featuring precise scoring targets (stationary basket, moving catch zone) and deliberate sets and schemes. As a result, tangible actions that can be statistically catalogued encompass not just scoring measures in points and touchdowns, but non-scoring categories like rebounds and assists, completions and yards.
On the continuous end of the spectrum are sports which, for the most part, prohibit hand use, such as football and hockey. Possession in these games, which entails proficiency of an unnatural body part or a foreign object, is challenging to maintain, and thus fleeting. As a result, less emphasis is placed on precision, hence the bigger scoring targets (stationary goalmouths). The difficulty in controlling possession results in a style of game-play that is both more interdependent, which begets less meaningful statistics, and continuously haphazard, which begets fewer discrete offensive plays that can be codified. Scoring, already hard by virtue of non-hand use, is made further difficult by hand-enabled goaltenders. And of the hand-disabled sports, scoring is lower still in football, which forbids even indirect hand use (hockey, for instance, utilizes hand-controlled sticks).
In short, football’s characteristics (continuous, collective and low-scoring) connote that more game-play context is stripped in its numbers than any other major team sport. Put another way, no sport is seemingly more reduced by its statistics than football-which implies, by extension, that no scoring indicator in any sport potentially deceives as much as goals do in football. Yet the fealty to figures has become part of the ecumenical thinking within the beautiful game-and, alas, is not so easily sworn off.
Consider, first, the two transcendent players of this generation, Cristiano Ronaldo and Lionel Messi. While their personal goal-scoring arms race is what inexorably binds them, team success, especially in the world’s most prestigious club competition, the Champions League, played no small part in certifying their duopolistic supremacy: both have guided their preeminent franchises to the pinnacle three times (Messi has a fourth winner’s medal, from the 2005-6 season, but his campaign was cut short by injury at the round of 16 stage).
Lionel Messi in action for Barcelona in the Champions League. (Photo credit: JOSEP LAGO/AFP/Getty Images)
The duo’s fecundity in front of goal is epitomized by the fact that one or the other led all-comers in scoring during each of their squad’s triumphant European campaigns: Messi in 2009, 2011 and 2015 (all for Barcelona), tallying a total of 31 goals in 38 appearances, including 12 in the knockout phase (21 apps); and Ronaldo in 2008 (Manchester United), 2014 and 2016 (Real Madrid), netting an astounding 41 goals in 34 appearances, with 16 coming in the knockout rounds (18 apps). However, superstars of the highest order, of which Messrs Messi and Ronaldo indubitably belong to, are purchased for record transfer fees and paid sky-high wages by their mega clubs precisely to be the difference-maker on the grandest stage-in the highest leverage circumstances. And when factoring in this essential context it is evident that Messi’s goals have been patently more responsible for his team’s most splendid successes than Ronaldo’s scores have for his.
In his winning runs, Messi has accounted for five goals (in three big-match-winning performances) which ticks all three high-leverage boxes. The first two of these came-opposite his supposed peer-in the opening leg of the 2011 semi-final Clásico at the hostile Bernabéu, where he broke the scoreless deadlock with an adroit volley in the 76th minute; and followed it up 11 minutes later with a virtuoso score, slaloming past four Real defenders and the goalkeeper to all but wrap up the tie. Then, in the ensuing final opposing Manchester United at Wembley, with the match knotted at 1-1 in the 54th minute, he delivered the Champions League winner. Messi’s two other big-time goals came at the expense of his former manager Pep Guardiola’s Bayern Munich during Barça’s treble-winning 2015 campaign, in the first leg of the semi that effectively killed off the tie: the first, after 76 tense minutes, was a strike from a turnover that beat a diving Manuel Neuer to his near post; the second, barely three minutes after the first, featured a balletic penalty box maneuver that broke Jérôme Boateng’s ankles, followed by a delectable chip that left Neuer frozen in time.
For his part, Ronaldo has netted only one such score which satisfies all three clutch criteria-and even then there is an accompanying postscript. Facing Chelsea in the 2008 final in Moscow, he opened the scoring in the 28th minute with a masterly header; but in the shootout, he also saw his cagey spot kick saved. And had it not been for some preemptive John Terry karma (whereupon he slipped on a wet Moscow turf before hitting the post with the potential trophy-clinching kick, all the while opposing keeper Edwin van der Sar had dove the other way), Ronaldo would have been the singular culprit for the shootout loss.
While not categorized as a goal, Ronaldo did conjure up a big moment when he took and (this time) converted the shootout penalty that sealed the 2016 final opposite cross-town rivals Atlético Madrid in Milan. But that, too, requires an addendum. Obscured from the “winning moment” narrative is the fact that his penalty came straight on the heels of Juanfran’s dragged kick that clanked off the post, and consequently turned into the least pressurized of Real’s five spot takes: a guaranteed non-loser and potential glory-monopolizer (or, for the financially versed, the equivalent of owning a limited liability company in a risk-averse world, with limited downside and unlimited upside).
Beyond the caveat-affixed, all of Ronaldo’s otherwise notable goals for his team’s winning campaigns seem to have one of the three high-leverage boxes unchecked. His second-leg hat-trick tallied against Wolsburg this past season was of high-leverage in terms of both the match (it dug his squad out of a 0-2 hole) and the competition stage (the last eight of the Champions League), but not in the level of opponent (a club that finished eighth in the Bundesliga). In a similar vein, his three much-ballyhooed scores in the last two matches of La Décima campaign in 2014 did come on the grand stage opposite elite sides, but in exceedingly low-leverage scenarios: from a 34th-minute counter-attack that made the aggregate score 4-0 against Bayern Munich in the second semi-final, and subsequently, from a 90th-minute free kick that padded it to 5-0; and, in the final in Lisbon against Atlético, from a last-minute penalty in extra time that punctuated the 4-1 score line.
Ronaldo’s much-extolled seasonal marks also bear some context scrutiny. His record-breaking 17 goals in 2013-14 were, for the most part, superfluous: it comprised of nine in the group stage which contributed to some points, though without any of them his highly prolific squad would still have topped its group; and eight in the knockout phase which were all lodged when his side was up by at least two goals, and, barring one, bore no influence on any tie’s outcome. While his 2015-16 tally, encompassing an unprecedented 11 in the group stage, epitomizes the playground bully: exhibiting might versus the also-rans-netting 16 times in eight feastings against Shakhtar Donetsk (21 in the 2016 UEFA Team Rankings), Wolfsburg (36), Roma (51) and Malmö (104)-while turning meek opposite the blue-chips-shut out in four tilts against Atlético Madrid (4), Paris Saint-Germain (7) and Manchester City (11).
While putting the ball at the back of the net is the principal measuring stick for a talisman, non-scoring contributions that go mostly unappreciated by the statistically minded-such as producing the pass that leads to a goal (assist), producing the pass that leads to a pass that leads to a goal (so-called “hockey assist”), making the on-the-ball maneuvers and off-the-ball movements that create positional and numerical advantages for teammates, tracking back for defensive shifts, and any other number of “one-percenters”-also undeniably shape a forward’s value. And when these aspects, specifically ones that keyed their respective European triumphs, are taken into account, the chasm between the two titanic figures become wider still.
Messi’s pivotal non-scoring plays include a perfectly weighted pass that teed up Andrés Iniesta’s one-touch winner in the controversial 2009 second leg semi-final at Chelsea (which symbolized the beginning of Guardiola’s Barcelona reign); and vital touches that led to all three Barça goals (though not directly, hence no assist credit) in the 2015 final against Juventus in Berlin. For the first, his pinpoint diagonal long ball disrupted the defense which ultimately left Ivan Rakitić unmarked in the box; for the second, his enterprising dribble (picked up from the halfway-line) and potent shot (from the edge of the box) drew a Gianluigi Buffon save that caromed the ball into the path of Luis Suárez (as well as a trailing Rakitić); and for the third, his stab outlet ball in the dying seconds initiated the three-on-two Neymar breakaway capper.
On the other side of the ledger, a legitimate case can be made that Ronaldo’s non-scoring contributions in high-stakes situations, on balance, may actually have hindered more than helped his team’s cause during its European successes. His lone positive contribution entailed a telling pass that led to Karim Benzema’s opening goal in the first semi-final leg versus Bayern in 2014. But in both finals dates with Atlético, in 2014 and 2016, Ronaldo was either non-existent or extravagantly wasteful in front of goal. Admittedly injuries compromised him; but the fact that Real prevailed both times was a testament not so much to its larger-than-life totemic presence as to its under-appreciated key cogs in Sergio Ramos, Gareth Bale, Luka Modrić, Ýngel Di María, Toni Kroos-and to Atlético neglecting to man their posts. As for Ronaldo’s maiden Champions League crown, for United in 2008, his shootout failure in Moscow wasn’t the only big stage blemish from the spot that his side had had to overcome: his miss in the opening leg of the preceding semi-final tie with Barcelona was only mitigated by a wonder-strike from Paul Scholes in the return fixture.
This juxtaposition of the two leading lights also hints, writ large, an observation on the field that mere figures on paper cannot discern. It is that Messi’s preternatural ability to dribble in traffic, perhaps the single most important skill in the game, is a technical element that can be, more or less, deployed in spaces both open and tight, all over the pitch. Comparatively, Ronaldo’s considerable strengths, power and pace, are physical attributes that, while can be exploited in open spaces (when darting into the box to receive a feed or a cross, say, or when lax defenders switch off or sag off him, or when the opposition commits its bodies forward), renders him rather more ineffectual in tighter spots (except for when in the air, where his leaping ability springs him “open”)-which, due to more disciplined and technically sound defenses, occurs with much more frequency in the high-leverage circumstances.
Cristiano Ronaldo of Real Madrid gestures during the UEFA Champions League Group F match between Real Madrid CF and Borussia Dortmund. (Photo by Gonzalo Arroyo Moreno/Getty Images)
This goes some way in explaining Ronaldo’s modest performances in the contests most consequential to his club’s greatest glories-at least vis-à-vis Messi. Yet by virtue of his flattering but stupefying goal totals in the football annals, Ronaldo has been fallaciously granted the numerical license that lumps him with Messi as two inseparable footballing entities.
The ironclad obsession with headline statistics also speciously canonized one of the most prolific seasons in recent memory by a player not named Messi or Ronaldo. It was turned in by Messi’s current teammate Suárez, in his final campaign with Liverpool, before he set off for Camp Nou in 2014 to complete Barça’s forward triumvirate. He cranked out 31 goals in 33 matches, the highest scoring rate in Premier League history-and the main impetus for his sweep of the player of the year awards that season. However, what Suárez’s numerical accomplishments did not betray was his distinct lack of scoring punch in the uber-high-leverage spots, a leading factor in his side’s agonizing failure in breaking its 24-year title drought.
After blazing in 19 goals in his first 12 matches back from suspension, Suárez was shut out in back-to-back top-line fixtures, a pair of 1-2 defeats at Manchester City and at Chelsea. Had he merely found the back of the net once in 180 minutes of high-leveraged action, he would have earned Liverpool a point-a vital one, in retrospect-while taking away two from a key rival.
Then came the fateful day at Anfield when Liverpool hosted Chelsea in its third-to-last outing of the season-a triple box high-leverage circumstance. Steven Gerrard’s ill-timed slip (which was, by definition, accidental) directly led to a Demba Ba score shortly before the break. This meant that Liverpool needed (at least) a goal in 45 minutes to salvage a point to keep themselves in the driver’s seat. But for an entire half, the Reds, and Suárez in particular, the supposed player of the year, could not conjure up an equalizer, which consequently left them short on goal difference vis-à-vis City in the title race, which City duly clinched on the season’s final day.
True, Gerrard’s wretched “accident” cost Liverpool a critical goal. But to glibly attribute that as the main reason for Liverpool’s title failure is misguided; as it turned out, the “culprit” was not Merseyside hard luck so much as the “31 in 33” talisman: a single Suárez score in any of the three crucial clashes would in all likelihood have won his club its long-awaited league title. (Of course, subsequent events would likely turn out differently as a new timeline would have been created, but that is always the case when engaging in counterfactual thinking-in sports or any other arena.) What’s more, a forensic dissection of Suárez’s match log that season finds that the player unanimously adjudged the best was anything but that when opposing the best: shut out in all six encounters against fellow top-four sides. And a lightly contextualized post hoc analysis posits that Suárez wasn’t even Liverpool’s most valuable player throughout the entirety of their close-but-no-cigar campaign: Daniel Sturridge’s 21 goals, 10 less than Suárez knocked in, had actually netted his team a greater number of points (20 to 16), exemplified by the dichotomous snapshot that Sturridge’s first three scores (in three 1-0 victories), which had jump-started Liverpool’s season in Suárez’s absence, were in many ways more valuable than the 10 goals accumulated in Suárez’s three hat-tricks (in blowouts of 4-1, 5-1 and 6-3).
In any event, both exhibits illuminate what is known as the “availability heuristic”, a mental short cut whereby the evaluation of success (or failure) is ostensibly a function of what can be immediately recalled or retrieved: the memorable moments palpably etched in the minds (Ronaldo’s penalty that secured the Champions League, Gerrard’s slip that squandered the Premier League, Iniesta’s blast that launched a dynasty, Suarez’s pounce that sealed the treble); or the context-free statistical accomplishments immutably etched in the record books (Ronaldo’s historic European tallies, Suarez’s 31 goals in 33 matches). Those that weren’t “available”, either in actuality (Suarez’s grand total of zero goals in the six top-four fixtures, including the three ultra-high-leverage ones) or in the annals (Messi’s set ups at the Bridge and in Berlin), are, alas, consigned to the dustbin of history. To repurpose George Bernard Shaw: We see things as they happen and say, Wow! Yet we don’t dwell on things that never were and wonder, What if?
And even accounting for the prevailing cognitive biases, not all goals have the same isolated contribution component: some are created, while some are merely taken. As a final example, consult the top of the scoring charts of football’s showcase event, the World Cup. If legacies were solely shaped by numbers, then Miroslav Klose would indeed be deemed a marginally better World Cup performer than the Brazilian Ronaldo-a notion that even the most fervent Nationalmannschaft adherents will snicker at. While Il Fenomeno himself created many of the chances that led to his 15 scores, Klose merely took the opportunities that were presented to him to help craft his 16-goal tally. This is not to imply that poaching instincts in front of goal isn’t a much prized skill-particularly for a squad as clinical as Germany that creates an abundance of chances in the box, many of them of the tap-in variety. It merely acknowledges that the ability to create goals, for self as well as for others, is a manifestly more valuable trait that cannot simply be discerned by cold hard statistics.
Miroslav Klose in action during the 2014 FIFA World Cup Brazil Final. (Photo by Julian Finney/Getty Images)
(Nor do plain goal tallies adjust for other eluding factors such as penalties: of which Messi and Ronaldo are the sole beneficiaries from team-created opportunities, while Suárez and Sturridge, at Liverpool in 2013-14, were not; leagues: which, even among Europe’s Big Five, have incongruous standards of competition; and the ever-evolving game: where advances in business and economic theory, sport science and proprietary know-how precipitate fundamental changes to the laws of the game, to club structure, to diet, equipment and training methods, and to overall game-play.)
To be sure, progress in sports statistics has meant that the nuance and minutiae that previously went uncaptured in its traditional measures, such as clutch situations, isolated individual contributions and era adjustments, are now being encapsulated by an “advanced” set of numbers. In an environment as fiercely competitive as professional sports, any form of edge is actively and rigorously pursued. And within certain sports, namely baseball, with its isolated plays, and basketball and American football, with its well-delineated plays, advanced metrics have been embraced as an essential component of the analytical evaluation toolbox; baseball in particular, the first sport to usher in this advanced form of analytics (due to its discrete and independent game-play), has actually seen some of its traditional rudimentary numbers being supplanted by the more sophisticated measures. But in a helter-skelter sport like football, whose games are disproportionately determined by a select number of momentous, game-changing plays, the shift away from its outsized (and context-free) core statistic is seemingly still a long ways off-if it occurs at all.
Yet despite the unremitting statistical reductionism it is worth noting that the vast majority of the numbers gathered in football-and in all sports, for that matter-are offensively oriented. The reason seems simple enough: attacking players are tasked with creating scoring chances; and it is those offensive actions that can be more readily quantified. But in a numbers-obsessed culture which conflates stat-accumulating with winning, the on-field measurements are trickling off the field, being leveraged into a benchmark for prosperity (salary and endorsement) while concomitantly serving as a leading indicator for popularity (fan adulation), before looping back onto the field to perversely-and bountifully-incentivize offensive players to pursue their own numbers at the expense of the broader team goal. The hapless defenders, on the other hand, are shut out of this vainglorious and avaricious conceit: their primary responsibility entails preventing opposing offenses from creating chances. There are no headline stats to pad, only to prevent; about the only time a defender would find himself in the spotlight is after he commits a howler that leads to an opposing score.
While this skewed offense-defense dynamic isn’t all that incongruous with humanity’s penchant to count how much stuff was made, rather than saved, it is worth appreciating the essence of how wins materialize in football: outscoring the opposition, most in this offensive age (in both a statistical and a cultural sense) will be conditioned to proffer; however, from the often-neglected defensive standpoint, conceding fewer goals than the opposing side does the trick just the same.
All this Cassandra-like wailing on the tyranny of numbers, it must be acknowledged, is not to suggest that all statistics mislead all the time-or, indeed, that all stats mislead some of the time, or, necessarily, that some stats mislead all the time. But it does mean that slavishly devoting to them can have a corrosive narcissistic effect. This is amplified in the binary social media era, where more vigilance than ever is required in, first, the information gathering in a hyper-partisan post-truth world where facts are ignorantly misconstrued (at best) and willfully distorted (at worst); and, second, its subsequent dissemination in an instant gratification zeitgeist which gravitates towards the flashy instead of the fundamental, and the piercing instead of the prosaic.
Elementarily, goals are the salient events that ultimately determine the salient unit of football: the match. But blind statistical faith, accepting quantitative production at face value and sans any context, at the expense of qualitative performance, is intellectually lazy-legacies of talismanic goal-scorers, foremost, shouldn’t be reduced to the number of times they appear on banal goal-scoring sheets. Football fans of all countries ought to unite and exorcise this specter of reductionism in a most irreducible and beautiful game.
