Getting Luck Properly Under Control

GETTING LUCK PROPERLY UNDER CONTROL

RACHEL MCKINNON

Abstract: This article proposes a new account of luck and how luck impactsattributions of credit for agents’ actions. It proposes an analogy with the expectedvalue of a series of wagers and argues that luck is the difference between actualoutcomes and expected value. The upshot of the argument is that when consider-ing the interplay of intention, chance, outcomes, skill, and actions, we ought to bemore parsimonious in our attributions of credit when exercising a skill and obtain-ing successful outcomes, and more generous in our attributions of credit whenexercising a skill but obtaining unsuccessful outcomes. Furthermore, the articleargues that when agents skillfully perform an action, they deserve the sameamount of credit whether their action is successful or unsuccessful in achievingthe goal.

Keywords: luck, metaphysics, epistemology, expected value, control, modal,chance.

1. Introduction

A randomly selected fan, Bill, at a basketball game is selected for amillion-dollar half-time contest requiring a full-court shot (from one sideof the court to the other). Bill has never played basketball, but he makesthe shot nonetheless and is a million dollars richer. At an NFL game, thequarterback makes a Hail Mary pass in the closing seconds of the game.The receiver, Terrell, under heavy coverage, bumbles the pass and jugglesit repeatedly while falling but ultimately catches the ball for the winningtouchdown. Jane is watching the televised draw of a large lottery, towhich she holds a ticket, and realizes that she holds the winning ticket.Vincent, while wanting to plant a rose bush on the island he inhabits,finds the best location for growing roses and, while digging, finds someburied treasure.

All of these cases seem to be instances of luck: Bill making the shot,Terrell making the catch, Jane winning the lottery, and Vincent finding thetreasure. Providing an account of luck that captures each of these caseshas, however, been surprisingly difficult. In this article I offer an accountof luck that captures each case, along with some important intuitions,which will have some fortunate upshots for topics in both ethics andepistemology. I propose that we separate important metaphysical ques-tions about the nature of luck from equally important epistemological

bs_bs_banner

© 2013 Metaphilosophy LLC and John Wiley & Sons LtdMETAPHILOSOPHYVol. 44, No. 4, July 20130026-1068

© 2013 Metaphilosophy LLC and John Wiley & Sons Ltd

questions about when we can identify the presence and influence of luck.The upshot of my argument is that when considering the interplay ofintention, chance, outcomes, skill, and actions, we ought to be moreparsimonious in our attributions of credit when exercising a skill andobtaining successful outcomes, and more generous in our attributionsof credit when exercising a skill but obtaining unsuccessful outcomes.Furthermore, I argue that when agents skillfully perform an action, theydeserve the same amount of credit whether their action is successful orunsuccessful in achieving the goal.

I make the case that we can better understand the nature of luck bydrawing an analogy with the expected value of wagers. A long series ofwagers, each with a determinate expected value, itself has a determinateexpected value. It’s unlikely, however, that the outcome of the series willbe the expected value. I argue that the difference between the actualresults and the expected value is what we call luck. When we considerhow actions, especially when exercising a skill or ability, are similarlyprobabilistic, we can call the expected results of a series of actions “skill.”Then, mutatis mutandis, the difference between the expected outcomesand the actual outcomes of a series of actions is what we call luck.Moreover, like a single wager viewed as part of a series of wagers, Ipropose that we view the outcome of an individual action as one elementof a larger series of trials. Its status as creditable or lucky depends essen-tially on its place within that series. I subsequently argue that agentsdeserve credit for an outcome proportional only to their skill. Insofar asan agent’s obtaining an outcome involves good luck, we should removecredit proportional to the good luck; similarly, insofar as an agent’sobtaining an outcome involves bad luck, we should attribute credit pro-portional to the bad luck.

2. Luck out of Control

There’s a strong intuition that lucky events are those that are somehowout of our control. Jane’s winning the lottery, for example, is luckybecause the outcome is out of her control. As Thomas Nagel notes, “Priorto reflection it is intuitively plausible that people cannot be morallyassessed for what is not their fault, or for what is due to factors beyondtheir control” (Nagel 1976, 58; cf. Williams 1976). Daniel Statman offersa definition of luck that captures this intuition. He writes, “Good luckoccurs when something good happens to an agent P, its occurrence beingbeyond P’s control. Similarly, bad luck occurs when something badhappens to an agent P, its occurrence being beyond [P’s] control”(Statman 1991, 146). If we supposed that Jane rigged the lottery so thatshe would win, then we’d cease to have the intuition that her winning waslucky. The explanation is that the outcome is under her control and that,therefore, events under our control are not lucky. There’s an important

497GETTING LUCK PROPERLY UNDER CONTROL


terminological point to make at this time. Although it’s common to use“luck” to refer only to good luck, I will use “luck” or “lucky” as a neutralterm to describe the concept of luck irrespective of the outcome beinggood or bad.

There are, however, a number of problems with this sort of naïvecontrol view of luck. First, the concept of control is fraught. Whatexactly does it mean to be in control of a situation? One might think thatto be in control means that an agent performing some action guaranteesan outcome. Jane’s rigging the lottery so that she wins, for example,seems to guarantee that she will win. We have to grant, however, thateven when we intuitively consider agents in control of their outcomes,their actions don’t guarantee an outcome. We’re all subject to unforeseenevents that influence outcomes, after all. For example, an asteroid maystrike Earth just before the drawing of the lottery such that Jane’s planscome to naught. It’s difficult to conceive of outcomes of which anyone istruly in control.

There are, however, more philosophically troubling issues with thenaïve control view of luck. A number of philosophers have objected thatcontrol is neither a necessary nor a (jointly) sufficient condition for luck.1

As Andrew Latus notes, “An event such as the rising of the sun thismorning was entirely out of my control, yet it is not at all clear that I amlucky the sun rose this morning (although it is surely a good thing that itdid)” (Latus 2000, 167). In such cases, the mere lack of control, even forevents significant to agents, is not sufficient for the presence of luck.

There seem to be other cases that count against control being a neces-sary condition for the presence of luck. Jennifer Lackey presents a case ofa demolition worker, Ramona, attempting to detonate explosives (Lackey2008, 258–59). The requisite wiring is in place, but, unbeknownst toRamona, a mouse has chewed through the relevant wires such that Ramo-na’s pressing the detonation button won’t be effective. But luckily, alsounbeknownst to Ramona, her co-worker has hung his jacket on a metalhanger right at the point where the mouse chewed through the wires suchthat the electrical circuit is closed and Ramona’s pressing the detonatorbutton will be effective. Ramona presses the button, and the building issuccessfully demolished. The purpose of this case is twofold. First, the caseis riddled with luck. Second, Ramona’s action (pressing the button) iscausally efficacious in bringing out the (desired) outcome and the outcomeis in Ramona’s control. However, her being in control seems to be a matterof luck. This case thus seems to be an instance of luck where control ispresent, so lack of control is not a necessary condition for the presence ofluck. In section 4, I return to the question of whether a more sophisticatedcontrol view of luck can be advanced.

1 For example, see Latus (2000), Pritchard (2005 and elsewhere), and Lackey (2008).

498 RACHEL MCKINNON


3. That Normally Wouldn’t Have Happened

Along with the control intuition there’s a strong intuition that luckyevents are unlikely. Bill’s full-court basketball shot is exceptionallyunlikely, even for the best professional player, let alone an amateur suchas Bill. Likewise, we consider Jane’s winning the lottery lucky not so muchdue to it being out of her control as due largely to her winning being sounlikely. Nicholas Rescher advances a view of luck “as a property ofevents that varies inversely with the likelihood of the event and propor-tionally to the value of the event” (Latus 2003, 465, discussing Rescher1995). Naturally, someone who wins a lottery holding ten thousand ticketsis proportionally luckier than a person who wins a lottery (with the sameprize structure) holding a hundred tickets. And moreover, someone whowins a lottery holding a thousand tickets with a prize of a million dollarsis luckier than someone who wins a lottery holding a thousand tickets witha prize of ten dollars.

There have been criticisms of this sort of chance view of luck, though.For example, as Latus writes, “Suppose I have the ability to bring aboutsome rare event of great value and I make use of this ability. An unlikely,valuable event therefore takes place, but it does not seem correct todescribe me as lucky that the event occurred” (Latus 2003, 467). We canimagine Albert Pujols, who is a prodigious home-run hitter, hitting ahome run in a situation where the probability of success is only 15percent. His hitting the home run is a result of his ability to hit homeruns, his skill. Moreover, some events can seem highly unlikely to anagent while being predetermined by initial conditions and the relevantphysical laws. Or, additionally, perhaps something that seems unlikely(such as sixty golfers all getting a hole in one on a hole) is actually theresult of a rigged system.2

I think that there is a more serious problem with the chance view,though. It might be tempting to think that an advocate of the chanceview of luck could respond to the foregoing concerns by noting that theunlikely but determined counterexample seems to hinge on cases whereoutcomes are somehow determined, and hence aren’t lucky, even thoughthey seem lucky from the agent’s perspective. Moreover, the other coun-terexample also seems to hinge on an outcome being importantlydetermined—this time by the agent’s ability to bring about the outcome—and hence isn’t lucky. I think, however, that there are a large number ofcases where an outcome is not determined (that is, it’s the result of astochastic process), is unlikely, and yet doesn’t seem lucky.

For the sake of argument, suppose that the outcome of flipping a faircoin is random (that is, inherently stochastic). In infinitely repeated trialsof flipping a coin we statistically expect an outcome of a ratio of 50H(eads)

2 This is a reference to the “Heartbreaker” case of Vogel 1990, discussed at length inHawthorne 2004.



to 50T(ails), or 50H:50T. In a trial with a given number of flips, say athousand, we still statistically expect a mean of 50 percent heads, 500H(and, therefore, 500T), but we can calculate the probability of obtainingthis as the outcome of a given trial. The probabilities are calculatedaccording to a binomial distribution, and the probability of a trial result-ing with exactly 500H is 2.52 percent. We can refer to the mean as theexpected value of the trial. The key point is that although the expectedvalue of a trial is statistically unlikely, we wouldn’t consider obtaining thatresult as lucky. To see why, if one had to place a bet on a single outcomeof the trial, the only rational (even money) bet would be to bet on themean, since it’s the most likely outcome compared to any other individualalternative outcome (that is, the trial is more likely to result in 500H than498H or 502H, for example). The upshot is that in all sorts of probabilisticsituations an unlikely event that isn’t predetermined may occur and yetnot seem lucky in the salient sense.

So I think that we can jettison the chance view of luck and lookelsewhere. Responding to these sorts of worries, some have more recentlyoffered a modal view of luck, most prominently represented by DuncanPritchard. Pritchard argues for the following two necessary (but notjointly sufficient) conditions for luck:

L1: If an event is lucky, then it is an event that occurs in the actualworld but which does not occur in a wide class of the nearestpossible worlds where the relevant initial conditions for thatevent are the same as in the actual world.

L2: If an event is lucky, then it is an event that is significant to theagent concerned (or would be significant, were the agent to beavailed of the relevant facts). (Pritchard 2005, 125, 132)3

This view captures the intuition supporting the chance view: events thatlack counterfactual robustness (those that fail L1) tend to be unlikely.Moreover, Pritchard suggests, his modal view of luck captures the controlintuition: outcomes in our control tend to exhibit counterfactual robust-ness (and so aren’t usually lucky), and outcomes out of our control tend tolack counterfactual robustness (and so are often lucky).

There have been some criticisms of Pritchard’s view, though. JenniferLackey is a prominent critic of modal accounts of luck. She offers a casethat purports to show that L1 is not a necessary condition for luck(Lackey 2006, 285, and Lackey 2008, 261–62). Consider Vincent, whowants to plant a rose bush on the island he inhabits. He’s adept at findingthe best growing area and, while digging, finds some buried treasure.

3 Although Pritchard seems to offer them as jointly sufficient, Riggs notes that Pritchardhas communicated that L1 and L2 are not offered as jointly sufficient. See Riggs 2009, 207n. 3.

500 RACHEL MCKINNON


Unbeknownst to Vincent, the treasure was left there a month ago by hisneighbor Sophie. Sophie wanted to bury some treasure shortly before herdeath in a sentimental spot on the island that she knew would be a goodarea for growing rose bushes. Because she’s also adept at spotting loca-tions good for growing roses, and because there’s only one spot on theisland suitable for this purpose, she finds the same spot that Vincentlater finds.

The key point of this case is that Vincent’s finding the treasure is clearlylucky, but in most nearby possible worlds Sophie will bury the treasurein that spot and Vincent will find it. So this seems to be a case of luckthat involves counterfactual robustness, thereby violating condition L1of Pritchard’s view. Lackey’s diagnosis of the case is that although thecase exhibits counterfactual robustness, the fact that it’s counterfactuallyrobust seems to be a matter of luck. She writes, “The fundamental pro-blem with such modal accounts [of luck] is that counterfactual robustnesscan be ensured through a combination of features that is entirely fortui-tous. For instance, an event that appears in both the actual world and allof the relevant nearby worlds can none the less be lucky because therelevant counterfactual robustness is achieved purely through a luckycombination of external factors” (Lackey 2006, 289).4

This appears to be a decisive criticism, as far as it goes. I think,however, that the coin-flipping comments above also militate against amodal view, and particularly against L1 and L2 providing jointly suffi-cient conditions for luck. The single most likely outcome of flipping afair coin a thousand times is five hundred heads. But the probability ofactually obtaining this result is merely 2.52 percent. Suppose that this isthe outcome: it doesn’t seem lucky, but in most nearby possible worldswe wouldn’t have obtained a result of five hundred heads. The coin-flipping case seems to satisfy both L1 and L2 (if we assume that theoutcome is significant for an agent, such as in a wager) without therebybeing a case of luck. So Pritchard’s modal view, at least as presented, isinadequate as an account of luck. Below, I return to discuss the possiblemerits of a modal view, even if we ultimately reject a strictly modal viewof luck.

4. Luck, Control, and Credit

Although there are some prominent objections to a naïve control view ofluck, such that one might think that all is lost, there’s been a resurgence ofa more sophisticated version of the control view offered by Wayne Riggs(see, e.g., Riggs 2007 and 2009). Central to an adequate control view is tofocus instead on what outcomes are creditable to agents. Consider Shari,who is terrible at pool and is faced with a nearly impossible jump shot to

4 This feature is also present in the Ramona case.



pocket the 8 ball. She doesn’t actually know how to hit a jump shotproperly, let alone how to do so with any accuracy. But buoyed by thetaunting of her friends, she attempts a jump shot and makes it. Thisoutcome seems incandescently lucky. One explanation for this is that theoutcome isn’t adequately a result of Shari’s (limited) skill at pool, at jumpshots in particular. Were a professional pool player to make this shot wewould be more inclined to credit the player for the outcome manifestinghis or her skill rather than being the result of luck, as is the case withShari’s shot.

Riggs offers the following as a definition of luck:

[Event] E is lucky for S iff it is not the case that S brought E about (where thisimplies that either E was not the result of the application of S’s powers,abilities, or skills, or E was inadvertent with respect to S). (Riggs 2009, 219)

He goes on to argue that this is incomplete since satisfying these condi-tions is not sufficient for E being lucky. Although I will not discuss thedetails, he offers the following as a more complete specification:

E is lucky for S iff

a) E is (too far) out of S’s control, andb) S did not successfully exploit E for some purpose, andc) E is significant to S (or would be significant, were S to be availed of the

relevant facts). (Riggs 2009, 220)

What’s important is that what it means for an agent to be in control of anevent is for the outcome to be sufficiently the result of an agent’s ability inorder for the agent to deserve credit for the event. The pocketing of the 8ball isn’t sufficiently the result of Shari’s ability to make the shot; thisexplains why it’s lucky. In contrast, pocketing the 8 ball would be suffi-ciently the result of a professional’s skill, which is why it wouldn’t be luckyin that case.

It’s important to note, however, that it isn’t for the lack of counterfac-tual robustness that Shari doesn’t deserve credit for her shot’s success.Even though she will miss the shot in nearly every nearby possible world,we could imagine a case where the game is rigged for her to make the shotin nearly every nearby possible world. We’d still have the intuition,however, that her success is due to luck, rather than her ability to exploitthe game being rigged.5 If, on the other hand, Shari knew the game was

5 It’s unclear whether Riggs would consider the outcome lucky. According to the tripar-tite definition, it seems that the outcome is lucky for Shari. This seems, however, to run afoulof our intuitions of outcomes in rigged situations being “lucky” for the agent.

502 RACHEL MCKINNON


rigged for her to make the shot, then even exercising her limited abilitywould properly bring about the outcome for her to deserve credit (inthat she exploited the game being rigged, thus failing condition b forbeing lucky).

Central to what it takes for an agent to be credit-worthy is for anagent’s action in bringing about E to be causally efficacious. Recall thecase of Bill and his full-court basketball shot. Of such a shot Riggs writes,“[T]hrowing the basketball the length of the court [is not] an efficaciousway to make a basket (though, once again, it’s better than not throwing itat all). Note that merely being in the causal chain that leads to an event,even being a necessary element of the causal chain leading to the event, isnot sufficient to make an agent causally efficacious in bringing somethingabout. So one way for an event to be lucky for an agent A is for the agentto be causally inefficacious in bringing about the event” (Riggs 2007, 334).Although Bill is obviously a necessary part of the causal chain, and hethrew the ball at the hoop rather than, say, the crowd, he doesn’t deservecredit for making the shot, since his success isn’t sufficiently the result ofexercising his (limited) basketball skills. Rather, the result is attributableto luck. I have more to say about this, however, in section 5, where I arguethat Bill deserves some credit for his success.

It’s important to note Riggs’s contribution to the debate over thenature of luck. His account clearly captures the control intuition: luckyevents are lucky in part because they are sufficiently out of our control. Hisview also captures the chance intuition that lucky events tend to be thosethat are unlikely. Although it’s not a necessary condition that lucky eventsare unlikely or that they lack counterfactual robustness, they do tend to beunlikely and they do tend to lack counterfactual robustness. The upshot ofLackey’s examples, particularly the buried-treasure case, is that a lackof counterfactual robustness can’t be a necessary condition for luck. AsRiggs puts it, such views are simply “not looking in the right place for theappropriate conditions for luck” (Riggs 2009, 210). What explains thelucky nature of the buried-treasure case is, instead, that Vincent’s findingthe treasure is not a manifestation of his treasure-finding ability; instead,it’s an inadvertent result of his skill in locating good areas for growingroses.

The sort of sophisticated control view that Riggs proposes is notwithout problems, however. First, it’s unclear how the account will treatcases like Lackey’s Ramona and her pressing the detonation button. Theaccount doesn’t adequately address cases where that an agent is in controlseems to be a matter of luck even when the event is sufficiently the resultof an agent’s actions. Riggs argues that there’s some ambiguity in suchcases. On the one hand, one intuition pushes us in favor of creditingRamona with the outcome (the demolition of the building); on the otherhand, we don’t fully credit her because she wasn’t in control of herco-worker fortuitously (that is, luckily) hanging his coat on a metal hanger



in just the right spot to close the circuit in order to allow Ramona toexercise her ability in demolishing the building.

A much more important problem with a sophisticated control viewsuch as Riggs’s is that, like its predecessors, it unduly treats outcomes asthe result of an exclusive disjunction between luck and skill (or ability, andso on). Although parts of the view seem sensitive to many of the successfuloutcomes of our actions involving a little of both luck and skill, often oneis strongly privileged over the other. For example, when an archer skill-fully hits his or her target, we tend to forget about the possible presence ofluck, and when Bill makes his unlikely basketball shot, we tend to forgetabout the role that his skill, albeit limited, plays in his success. Hence, inthe next section I argue that we ought to be more parsimonious in ourattributions of credit when exercising a skill and obtaining successfuloutcomes, and more generous in our attributions of credit when exercisinga skill but obtaining unsuccessful outcomes.

5. Just as We Expected

In this section I present a new view of luck that builds on the credit view inRiggs’s sophisticated control view while avoiding talk of control. In theprofessional online poker-playing world, there are some sophisticatedviews on luck. Online poker sites create histories of all the actions taken ineach hand, record them, and offer them to the players. Knowing this,a number of highly sophisticated software programs (such as Hold’emManager and Poker Tracker) have been created that take this informationand allow players real-time sophisticated statistical analyses of their play aswell as the play of their opponents. One particular statistic is relevant to ourdiscussion of luck: all-in expected value (or AIEV). Poker inherentlyinvolves a great many probabilistic judgments made by players about theprofitability of a play (the expected value, or EV). It’s rare, however, thatplayers can know the exact EV of a play, since this requires knowing theiropponents’ cards, which is often impossible. One situation in which playerscan know their EV is when both players are all-in with cards to come (e.g.,in Texas Hold’Em before the river card has been dealt).6 When a player isall-in pre-flop (before any board cards have been dealt), for example, witha pair of aces against a single opponent with a pair of twos, we can preciselycalculate the player’s probability of winning (it’s roughly 80 percent). Whenwe know the value of the bets and how much has already been wagered,calculating the exact EV for each player becomes trivial. We can thencompare the actual results to the EV (what I’ll call the expected results).

Due to the software available, players can view the AIEV over theircareer (or any period of time) and then compare this with their actual

6 The reason it can be known is that the hand histories indicate an opponent’s hand onlywhen that player reaches showdown. This always happens when two players are all-in.

504 RACHEL MCKINNON


results in these situations.7 For example, over a year playing two millionhands a player may be in these sorts of all-in situations twenty thousandtimes. Suppose that Shannon has an AIEV of +$20,000 (a positive numberindicates that Shannon makes good decisions about when to go all-in withcards to come; the higher the number, the better she is at making thesedecisions).8 Her actual results from these situations, however, are that shewon $23,500. So her actual results are $3,500 better than expectation. Myproposal is that we can attribute $20,000 of her earnings to skill and$3,500 to luck.

This is related to the coin-flipping example from section 3. In probabi-listic events, we can determine the “expected” outcome. In flipping a coinit’s a ratio of 50 percent heads to 50 percent tails. We recognize, however,that, in any reasonably sized trial of repeated flips, it’s unlikely that theoutcome will be the expected ratio. Instead, it’s more likely that we’llobtain an outcome other than the expected one, though one fairly close tothe mean. In a binomial distribution of outcomes of flipping a fair coin athousand times, most will be within about 16H of the mean (that is, withinone standard deviation). In probabilistic events, I argue, outcomes of themean (the expected outcomes) are what we attribute to skill, and anydeviation from the mean is attributable to luck. Outcomes with moresuccesses than expected are what we call “good” luck (positive deviation),and outcomes with fewer successes than expected are what we call “bad”luck (negative deviation).

Let me explain with a more familiar example. Take Bill’s unlikelybasketball shot. Admittedly, there is some nonzero probability that he’llmake the shot (there must be, since he makes it in the case). Suppose thathe’ll make the shot 1 percent of the time. If we were to let him have aninfinite number of throws, we’d expect an outcome where 1 percent of histhrows were successful. This is the degree to which Bill is skilled at makinglong-distance basketball shots. A professional, by contrast, might be ableto make the shot 5 percent of the time.9 And when Bill makes the shot, thesuccess manifests his ability: he was successful because he has some abilityin making such shots. So Bill deserves at least some credit for making theshot: it wasn’t entirely due to luck. But how much? Since his ability is onlyto make the shot 1 percent of the time, we don’t attribute all of the creditto Bill’s ability. Instead, we should attribute most of it to luck. In fact, weshould attribute 1 percent of the credit to Bill’s skill, and the rest to luck.

7 In order to generate useful statistical conclusions, large sample sizes are required. Sincethese all-in situations may only happen a few times per thousand hands, players often requirea long period of play before analyzing their play with any confidence.

8 There are some confounds, but I ignore them for the sake of simplicity. For example, aplayer who is unduly cautious will have a highly positive AIEV but will likely be passing upother good opportunities.

9 As Bill moves closer to the basket, we’d expect his probability to increase to the pointof being nearly 100 percent if he were standing right next to the basket.



That we should attribute credit in this way is a point about how creditought to be attributed. In many cases this is different from our actualpractice in attributing credit to agents for obtaining outcomes. Insofar asthe two come apart, my view is revisionist.

My view of luck importantly differs from Riggs’s in that I jettisondiscussing skill in terms of being causally efficacious in bringing aboutcertain outcomes. Part of the reason for this is that it’s unclear what ismeant by something being causally efficacious. On the one hand, in dis-cussing a low-probability action such as Bill’s shooting a full-court shot, itmakes sense to say that anyone—even a professional—attempting to do soisn’t a good way of attempting to make a basket. This just seems to beanother way of saying that it isn’t a sufficiently likely way of making abasket. But there’s a problem for Riggs’s view when we consider highlyskilled athletes making highly probable attempts, such as Steve Nashtaking a free-throw shot.

Elite National Basketball Association players can have a probability ofsuccess in making free throws that is around 90 percent. When Steve Nashsteps to the free-throw line, we expect him to make the shot most of thetime. Suppose that Steve is truly a 90 percent shooter: let’s suppose thathe’s constituted such that his success rate at making free throws in normalgame situations is inherently 90 percent. This requires a number of heavymetaphysical assumptions about abilities and actions. Many will thinkthat in a given instance of a shot, given the mechanics of the shooter, thelaws of physics, and the initial conditions, a shot will either surely succeedor surely fail: it’s not fundamentally stochastic. I propose, however, thatwe view the individual event as one element of a larger series of trials. Itsstatus as creditable or lucky depends essentially on its place within thatseries. Moreover, it is important that we treat agents’ abilities to performactions as fundamentally stochastic, at least epistemically speaking.

It’s also important to restrict the specification of a player’s skill to, insome important sense, normal conditions of the skill’s application.10 Animportant feature of a skill is that a more skillful agent will be able tosuccessfully exercise a skill in a wider range of cases with slightly differentcircumstances. A professional basketball player, for example, will remaina 90 percent shooter when a crowd is loud and using distraction devices,whereas a novice will lose whatever skill she or he has in such conditions.But even professionals will not be able to shoot well if stones are hittingthem as they’re trying to shoot.

With these background assumptions in place, suppose that Steve sinksa free throw: do we attribute the success to his skill or to luck? Here I thinkwe need to separate the metaphysical from the epistemological question.Metaphysically speaking, I think that the question is ill formed. Since

10 For a good, recent discussion of skills and normative assessments of performances, seeSosa 2011.

506 RACHEL MCKINNON


Steve’s ability is only to make the shot 90 percent of the time, we expecthim, even when he’s exercising his ability, to miss some of the shots.Consequently, on my view, even when he succeeds, in exercising hisability, Steve doesn’t deserve all of the credit for the success manifestinghis ability. He’s only entitled to 90 percent of the credit. Returning to thepoker case will help explain why.

Suppose that Shannon and Bonnie are playing a game of TexasHold’Em poker. They both have $1,000 to wager and, with one card tocome, they both bet all of their money (with nothing already in the pot).It so happens that Bonnie is 95 percent likely to win (given that we don’tknow what the next card will be). In poker, we calculate the EV of the playaccording to the following formula:

EV Probability of Winning Amount WonProbability of Losing

= ∗( ) −∗∗( )Amount Lost

In this case, Bonnie’s play carries an EV of +$900. EV can be positive,neutral, or negative. For Shannon it’s -$900. She stands, on average overthe long run, to lose $900 on her play, whereas Bonnie stands to make$900.

Poker has a concept of pot equity, where players “own” a portion of thepot proportional to their probability of winning. Here Bonnie owns 95percent of the total pot ($2,000), which comes to $1,900. If we were to playout this hand an infinite number of times, we’d expect Bonnie to end upwith $1,900 on average. However, since she either wins the full $2,000 orloses, this is an impossible outcome for a single hand.11 So suppose thatBonnie wins and thus has $2,000. Poker theorists would say that she’s only“entitled” to $1,900 of that. If she were only to play this hand once, they’dsay that she’s “lucky” to the tune of the extra $100. Critical in this analysisis that the value of Bonnie’s play is +$900 regardless of the actual outcomeof the hand. So the normative assessment of her performance is based onputting herself in a highly positive EV situation (the application of her skillas a poker player), not the outcome of the hand. Were Shannon to win, wewouldn’t credit her for her masterful play in winding up with $2,000;rather, we’d say that most of her winnings are due to luck ($1,900 of them,in fact).

I argue that the case is the same for more familiar cases of successthrough ability, such as Steve Nash making the free throw. In probabilisticactions, which I think applies to most of our actions, agents are onlyentitled when successful to credit for the expected value of their action; therest is attributable to luck. If an agent is 1 percent likely to be successfulwhen exercising his ability, such as Bill’s full-court shot, then he onlydeserves 1 percent of the credit for being successful; likewise, if an agent is

11 Consider that the “average” roll of a die is 3.5, even though such a result is impossiblein a single roll.



99 percent likely to be successful when exercising her ability, then she onlydeserves 99 percent of the credit for being successful.

There’s an interesting consequence of this view, though: when agentsexercise an ability but fail to achieve the desired outcome, they deservesome credit. Often our practices of applying credit don’t do this: when askillful player misses a shot, we don’t give her any credit. Instead, she’soften rebuked for her failure. This seems mistaken: this would be to forgetthat our skills are fallible and probabilistic. That is, even when a skillfulagent is exercising her skill in shooting an arrow, sometimes she’ll miss,and the failure will be merely because she’s expected to miss at least someof the time. And, conversely, when she’s successful, she doesn’t deserveall of the credit. Returning to the all-in EV example, if Shannon’s careerAIEV is $20,000 but her actual results in these situations are $19,000, thenshe deserves some extra credit for the $1,000 she’s missing due to some badluck. Likewise, if Steve Nash is truly a 90 percent free-throw shooter andhis results for the year are only 83 percent, we can give him credit for beinga 90 percent shooter and recognize that he’s had some bad luck to the tuneof the missing 7 percent.12

All of the preceding discussion is about the metaphysical questionsregarding what luck is. I’ve suggested that we should keep these separatefrom epistemological questions about when, whether, and to what degreewe can determine that an outcome is due to luck. I argue that in a givensituation we can’t know whether this shot was due to mostly luck or mostlyskill. Suppose that Steve Nash makes ninety-eight of a hundred free-throwshots in a season (98 percent). If he’s truly a 90 percent shooter, we can saythat eight of these shots were due to luck, but which ones? We can’t know.We can only determine that some eight shots were due to luck. Determiningthe presence of luck (and to what degree) in outcomes thus requires abig-picture view of a series of trials. We have to zoom out, as it were. Whenwe focus on a particular performance, whether successful or unsuccessful,we lose the ability to determine whether the outcome was due largely to skillor to luck. Instead, we’re left with the probabilistic attribution of creditdiscussed above based on expected value: for a given successful shot, SteveNash deserves credit for 90 percent of the shot due to skill.

It’s important to recognize that neither luck nor skill is an all-or-nothing affair. It’s often been the case in the debates on moral or epistemicluck that the presence of problematic forms of luck removes moral respon-sibility or impugns one’s knowledge of a proposition. How should weunderstand the natural idea that luck undermines credit or responsibi-lity? For example, it’s been argued that, in a sense, the presence of luck

12 There’s an important distinction, however, between exercising an ability—and deserv-ing the attendant credit for an outcome—and exercising an ability well—and how exercisingan ability poorly or well will impact the attribution of credit. I avoid that discussion for mypresent purposes.

508 RACHEL MCKINNON


undermines responsibility. Or, in epistemology, the presence of luck under-mines one’s knowledge. A good way of understanding luck is that it’s partof an equation including outcomes, skill (that is, credit), and luck. For anyoutcome, it is the result of a combination of luck and skill whereby,

1 = +% % Credit Luck

so that luck undermines credit because:

% % Credit Luck= −1

As the presence of luck increases, the amount of credit that an agentdeserves for an outcome decreases. Therefore, the extent to which an agentis lucky deprives him or her, to that same extent, of earning credit. Thus,it’s natural to say that luck undermines credit.

Now, one might think that in many cases, the intuition supporting theattribution of luck to an outcome seems to come from the unlikelihood ofthe outcome. For example, Bill’s making the shot and Jane’s winning thelottery both seem lucky partly because the outcomes are unlikely. But weshould be careful. Suppose that we’re comparing two baseball players:Albert Pujols is a professional with a track record of hitting home runs,and Bob is a neophyte. Suppose that we place both in an identical situa-tion facing one of the best Major League Baseball closing pitchers,Mariano Rivera. Suppose that, on average, Albert will obtain a hit only 25percent of the time, and a home run only 15 percent of the time. Supposefurther that Bob will obtain a hit only 5 percent of the time, and a homerun 1 percent of the time. Now suppose that both players hit a home run.Many will have the intuition that Bob’s home run was lucky, whereas,albeit unlikely, Albert’s is due to skill. The example is meant to showthat merely because an outcome is statistically unlikely is insufficient toattribute luck.

We should be equally careful about another source of problems fromsuch examples. One explanation for why we shouldn’t attribute Albert’shome run to luck is that, although the outcome is unlikely, the outcome isa result of his skill: the success manifests his home-run and hitting ability.Note, however, that Bob’s home run is also a result of his, albeit limited,skill. Since he successfully hit a home run, we know that Bob has someability to hit home runs. And when he succeeds, his success manifests his(limited) hitting ability no less than Albert’s home run manifests his pro-digious hitting ability. The difference in the cases is that we expect Albertto hit home runs much more often than we expect Bob to hit home runs.

This is where the probabilistic analysis offered above is particularlyuseful. If we were to place Bob in the hitting situation and give him aninfinite number of attempts, we expect him to hit a given number of homeruns proportional to his ability (that is, 1 percent of the attempts will resultin a home run). If we were to offer him only a single attempt, then being



surprised at his success makes some intuitive sense: we expect him to hitsome home runs given many trials, but with only one trial, it’s veryunlikely that he’ll succeed. We can’t be surprised every time, however, orwe’ll commit a fallacy akin to the lottery paradox: although it’s unlikelyfor a given ticket to win, and we may be justified in believing that ticket nwill lose, we can’t make that judgment about every ticket or else we’ll bejustified in believing that all tickets will lose, which is absurd (since oneticket must win). So I think a better attitude to adopt toward Bob’s successin a given trial is not to attribute it entirely to luck: instead we shouldnotice that Bob has some (albeit limited) hitting ability and we should givehim credit for his ability. But he doesn’t deserve full credit for his homerun. However, Albert deserves more credit than Bob. How much? Again,we should attribute credit proportional to Albert’s ability, which is greaterthan Bob’s.

6. Conclusion

In this article I’ve presented a new theory of luck based on a probabilisticunderstanding of abilities and expected value. Skill is what we call theexpected value of an ability, and luck is any deviation, whether positive ornegative, from this value. This answers the metaphysical question of whatluck is. I’ve also argued, however, that we should separate this fromthe epistemological question regarding when and to what degree we canattribute an outcome to luck or to skill. I’ve argued that we can onlydetermine that some number of successes (or failures) are attributable toluck (or to skill) only when we take a big-picture, long-term view of anumber of performances. We are epistemologically blocked from deter-mining whether, and to what degree, a given performance is due to luck(or to skill). In such cases we are left with a probabilistic judgment wherewe attribute credit proportional to the agent’s skill, and the rest to luck.

The upshot of my argument is that when considering the interplayof intention, chance, outcomes, skill, and actions, we ought to be moreparsimonious in our attributions of credit when exercising a skill andobtaining successful outcomes, and more generous in our attributions ofcredit when exercising a skill but obtaining unsuccessful outcomes.Moreover, when agents skillfully perform an action, they deserve the sameamount of credit whether their action is successful or unsuccessful inachieving the goal.

University of CalgaryDepartment of PhilosophyCalgary, Alberta T2N [email protected]

510 RACHEL MCKINNON


Acknowledgments

I would like to thank Tim Kenyon for feedback at various stages of thisproject.

References

Hawthorne, J. 2004. Knowledge and Lotteries. Oxford: Oxford UniversityPress.

Lackey, J. 2006. “Pritchard’s Epistemic Luck.” Philosophical Quarterly56:284–89.

. 2008. “What Luck Is Not.” Australasian Journal of Philosophy 86,no. 2:255–67.

Latus, A. 2000. “Moral and Epistemic Luck.” Journal of PhilosophicalResearch 25:149–72.

. 2003. “Constitutive Luck.” Metaphilosophy 34, 460–475.Nagel, T. 1976. “Moral Luck.” Proceedings of the Aristotelian Society

76:136–50.Pritchard, D. 2005. Epistemic Luck. Oxford: Oxford University Press.Rescher, N. 1995. Luck: The Brilliant Randomness of Everyday Life. New

York: Farrar, Straus and Giroux.Riggs, W. 2007. “Why Epistemologists Are So down on Their Luck.”

Synthese 158:329–44.. 2009. “Luck, Knowledge, and Control.” In Epistemic Value, edited

by A. Haddock, A. Millar, and D. Pritchard, 204–21. Oxford: OxfordUniversity Press.

Sosa, E. 2011. Knowing Full Well. Princeton: Princeton University Press.Statman, D. 1991. “Moral and Epistemic Luck.” Ratio, new series, 4:146–

56.Vogel, J. 1990. “Are There Counterexamples to the Closure Principle?”

In Doubting: Contemporary Perspectives on Skepticism, edited byM. Roth and G. Ross, 13–27. Dordrecht: Kluwer.

Williams, B. 1976. “Moral Luck.” Proceedings of the Aristotelian Society76:115–35.



Copyright of Metaphilosophy is the property of Wiley-Blackwell and its content may not becopied or emailed to multiple sites or posted to a listserv without the copyright holder'sexpress written permission. However, users may print, download, or email articles forindividual use.

Getting Luck Properly Under Control

Documents

Transcript of Getting Luck Properly Under Control