Navigating the Luck Skill Continuum

Disentangling Chance and Expertise From Achievement

In the domain of skill building, a fundamental question looms: How can one learn from mistakes if the nature of the game is shrouded in mystery? It's akin to trying to perfect a golf swing while blindfolded, uncertain whether each shot's outcome stems from technique or the whims of the wind. You need to take off the blindfold.

In fact, it’s necessary to disentangle luck and skill to get any lessons from history at all.

For example, was the Allied strategy of storming the beaches of Normandy to get a foothold in Nazi occupied Europe good strategy or dumb luck? If luck was the dominant influence, the lessons are limited.

This is the limitation of the case study teaching model omnipresent in medical, legal and business education. To glean any actionable lessons from case studies you must know whether the company was lucky or good, which is not self evident. The behavior of patients, markets and clients is rarely textbook.

To answer this conundrum is no mere academic exercise. It is a lodestone for navigating the treacherous waters of decision-making. To know whether luck or skill holds sway is to possess a map of sorts, one that guides not just the distribution of capital, but the very approach to life's inevitable challenges from which no one is spared.

This knowledge seeps into every crevice of strategy, coloring risk assessments with the hues of probability and tempering expectations with the cool touch of reality. It whispers in the ear of the ethicist, suggesting where true merit may lie. And in the crucible of choice, it stands as a silent partner, its presence felt in every decision, large or small.

In a world where the flip of a coin can sometimes carry as much weight as years of study, understanding the balance of fortune and faculty becomes not just an advantage, but a necessity

The Luck Skill Continuum

In most games the influence of luck and skill falls somewhere along a continuum, presenting the challenge of disentanglement.

The Luck Skill Continuum

Games of skill are the domain of the craftsman, virtuoso and expertise. Skill is hewn from countless hours of practice and iteration in the pursuit of mastery. In this domain, players are in full control because actions produce predictable results.

Games of luck are domains inhabited by a capricious spirit that defies prediction. It is the wind that shifts without warning or the deadly rockfall from a rapidly warming mountainside. It is an external force as neutral as it is powerful. It’s the pebble that diverts the course of empires. It’s a chain of historical events that will never be replicated even under identical starting conditions.

Luck is what’s left over after subtracting skill from an outcome.

Luck = Outcome - Skill

In “The Success Equation” Michael Mauboussin illustrates the luck skill continuum using a sports frame. Consider the following chart.

At one end is the realm of pure chance—a cacophony of clicking slot machines, the whir of roulette wheels, and the flutter of lottery tickets. Players in these games are mere spectators to their own fortunes, their skills as relevant as a snowflake in a blizzard.

Opposite this chaos stands the domain of pure skill, where chess pieces move with the precision of military campaigns and tennis balls arc through the air like guided missiles. In the theatre of expertise, an amateur's lucky move is as futile as bringing a knife to a gunfight—the grandmaster's strategy an impenetrable fortress against the siege of chance.

Between games of pure chance and pure skill lay more nuanced games. Consider the following chart from the Success Equation.

There is a 40% spread between the influence of luck in basketball compared to hockey. This suggests resource allocation to skill development in basketball has a higher payoff than in hockey.

But Mauboussin’s research paints a curious picture here, one that defies intuition. He calls this phenomenon the paradox of skill. ^.

“"Okay, you have gotten the memo on improving skill: 10,000 hours, hard work, deliberate practice, grit, and attentive teacher. We've all heard it. You also recognize that in many of life's activities, the results you achieve combine skill and luck. No debate there. Now, what if I told you that in many cases improving skill leads to results that rely more on luck? That's right. Greater skill doesn't decrease the dependence on luck, it increases it. If you have an interest in sports, business, or investing, this lesson is for you.”

The principle is that, as players abilities converge towards perfection the influence of skill diminishes while the role of luck increases.

It’s analogous to harmonic cancellation, where two sine waves smooth into a third, lower amplitude wave. If skills match with absolute precision, the wave flattens entirely.

Said another way, in games with perfectly matched skill the outcome becomes entirely driven by luck.

Disentangling Luck and Skill Based Games Using Indicators

For games at the extremes of the luck skill continuum, the dominant influence is obvious. For example, it’s mostly intuitive that casino games like roulette are pure luck while a board game like chess is pure skill.

But step outside the casino or away from the game board and it’s apparent that (a) most games are influenced by both factors and (b) it’s not at all obvious how to disentangle their individual influence.

Since luck and skill exist on a continuum it means they are continuous variables and are practically uncountable with any precision. The best we can do is use tools to approximate the coordinates.

Use the following indicators to estimate in what direction on the continuum a game leans. The more indicators you can tick under a column the more likely it is a given game is more dominantly influenced one or another variable

For example, if you cannot intentionally lose a game it is likely you are playing a luck dominant game.

The Treacherous Importance of Sample Size

Picture a vast, snow-covered mountain range. At its base, a group of backcountry skiers huddle around a tiny pit dug into the snow, peering intently at the layers revealed in order to forecast their risk of death or disability by avalanche.

This scene, seemingly innocuous, encapsulates a profound dilemma faced by decision-makers across all fields: the treacherous interplay of sample size, skill, and luck.

The question is, where does the game of avalanche forecasting fall on the luck skill continuum? In my view, it ticks most of the luck based indicators.

So if avalanche forecasting is a primarily luck based game and you have only a small snow pit sampling of the larger mountain slope, one cannot reliably describe the avalanche risk profile from this information alone.

In the realm of skill-dominant pursuits, small samples can be nuggets of gold, each observation a concentrated lesson. But as we venture into territories where Lady Luck holds greater sway, these limited glimpses become as unreliable as mirages in the desert. It's here, in this nebulous zone, that our snow pit reveals its limitations. The skiers, armed with their tiny window into the mountain's mood, are unwitting players in a game where the rules of chance overshadow their expertise.

The avalanche pit predicament is the same as that faced by the use of case studies in academics, which are a small sampling of a much larger spatiotemporal structure. Unless the approximate location of that structure on the continuum can be identified you must be cautious applying any lessons learned. Otherwise, it’s a potentially false signal of trend continuation when the outcome may in fact fatally mean revert.

To extend the mountain the analogy further, enter the gambler’s fallacy. The gamblers fallacy is a siren song that lures even the most rational minds onto the rocks of misunderstanding.

Imagine a coin flipper, convinced that after a string of heads, tails must surely be due. This belief, as persistent as it is misguided, ignores the fundamental independence of each flip. It's the same flawed logic that might lead our skiers to declare a slope safe based on previous descending ski tracks - a sometimes fatal misreading.

The summary principle is that small sample size is useful in skill dominant games but is misleading and dangerous in luck dominant games.

The interplay between luck and skill shapes outcomes across a vast spectrum of human endeavors, from games of chance to professional sports and beyond. Understanding where an activity falls on this continuum is crucial for strategy development, risk assessment, and decision-making. As Michael Mauboussin's research illustrates, even in highly skilled domains like professional sports, luck can play a surprisingly significant role. The paradox of skill further complicates this picture, showing how increasing expertise can paradoxically amplify luck's influence. To navigate this complex landscape, we must learn to recognize indicators of luck and skill, understand the pitfalls of small sample sizes, and guard against fallacies like the gambler's fallacy. Ultimately, disentangling luck from skill is not just an academic exercise—it's a vital tool for setting realistic expectations, allocating resources effectively, and making informed decisions in an uncertain world. By embracing this nuanced understanding, we can approach challenges with clearer insight, whether we're analyzing business case studies, evaluating avalanche risks, or simply trying to improve our performance in any domain.