I had a lovely argument with Chris Lusto about luck yesterday. If you’re going to take the time to dig into this, read his post first.
As I see it, we have outlined two stands on the meaning of luck.
- Luck describes the fact that what happened is not what we expected to happen. When what happened is better than we expected, that is good luck. When it is worse, that is bad luck. In this view, luck is not causal. It doesn’t make stuff happen. It simply describes the size and direction of variation from the mean.
- Luck causes things to happen, or at least makes them more (or less) likely to happen. When what happened is better than we expected, we don’t just describe this as lucky, we attribute the cause of the event to luck. In this view, luck is viewed as a semi-controllable bias; a property with which some people or objects are imbued.
I argue that (1) is a probabilistically sophisticated view, but that (2) is much closer to the commonly held meaning. Furthermore, I argue that probability and statistics instruction that doesn’t directly address (2) is unlikely to make useful shifts in people’s thinking about probability and chance.
I got to thinking about all of this in reading Thinking Fast and Slow by Daniel Kahneman this summer. Kahneman doesn’t define luck. But he uses the term.
A few years ago, John Brockman, who edits the online magazine Edge, asked a number of scientists to report their “favorite equation”. These were my offerings:
success=talent+luck
great success=a little more talent+a lot of luckThe unsurprising idea that luck often contributes to success has consequences when we apply it…
He goes on to describe a common scenario in which a golfer scores very well on day 1 of a tournament and more poorly on day 2.
I don’t question whether Kahneman himself understands luck in the sense of either (1) or (2) above. I do think, however, that he is writing in a way that supports (2), and I think that’s unfortunate (heh).
The key for me is that Kahneman doesn’t write: “success=talent+random variation from the mean”. He writes “success=talent+luck” and he writes “luck often contributes to success”.
Luck contributes. In the same sense that talent contributes. That’s causal, and that’s conception (2).
Failing to see eye-to-eye with both Lusto and Kahneman (two formidable minds, to be sure), I went to my next favorite source of wisdom.
Me: What is luck? What does it mean to be lucky?
Griffin (8 years old): Well, if you found five dollars on the street, you would be lucky. Or if I opened my drawer and there was a bunch of gold in there, that would be lucky.
Me: Why would that be lucky?
G: Cause five dollars is a lot of money. And because gold is very valuable.
Me: What if you found a penny? Would that be lucky?
G: If it was heads-up it would be. Some people think that finding a penny heads-up is lucky.
Me: Right. But what would that mean for it to be lucky?
G: Well, if it was New Year’s Eve, you could make three wishes and they would come true.
Me: OK. And what if it weren’t New Year’s Eve. What if it’s just a regular day and you’re walking up to Romolo’s [our neighborhood pizza joint] and you found a penny on the ground, heads-up. What would it mean for that to be a lucky thing to have happen?
G: Well maybe only one wish would come true.
Me: So if something is lucky, it makes good things happen, like wishes coming true. Is that right?
G: Yeah, pretty much.
Overthinking my teaching 
Did you find an answer for this? It seems like an obvious error. So much detail on terms everywhere and then a huge jump to an undefined term ‘luck’? And this undefined ‘luck’ has a presumably greater weight than talent in deriving expectations for peformance?
Do you mean did I ever get an answer from Kahnemann on his meaning? I never asked (except here on this math teaching blog) so no. Reading this more than four years later, I still agree with my claims though!
Thanks for writing back. I just covered this section. I think he uses ‘luck’ to summarize the net effect (positive or negative) of individual independent forces acting on the system represented by a golfer in a tournament. (He’s using a non engineer definition) There’s so many independent factors/forces and the bucket ‘luck’ catches the net effect. But like you mention the term ‘luck’ has baked in assumptions because it’s complex to quantify. Talent as an input ‘force’ must have heavier weight than ‘luck’ because luck is not a force. If we removed the golfer, we wouldn’t get a score – the ball wouldn’t be transported by birds to each hole. It carries with it an expectation of an outcome which is unquantifiable and is based on hindsight – rearward thinking- it’s value changes based on association. An equation with an undefined variable isn’t an equation. If we replaced ‘luck’ with ‘sum of the effects of the environment on talent’ it may be more accurate. Talent can be measured as the ability to adapt to and overcome the environment – meaning ‘enviromental forces generally subtract from capacity of talent as a force’. Human capacity has a maximum talent threshold. This would alter the equation for success to success = talent – net environmental forces. All would have to be weighed in a common measurable unit. The outcome is a balanced force equation where the level of success remaining is how much talent force overcame the environment. His error is in assuming there exists a definite mathematical ‘mean’ for ‘success’ across the event before it occurs. The ‘mean’ is only defined after the event based on the sample at which point ‘luck’ can be assessed and erroneously applied to justify the level of success achieved or not….. this means success has more to do with an individuals capacity to exert talent on the specific environment than the enviroments capacity to ‘aid’ or ‘hinder’ the player through ‘luck’. This judgement happens in real time with every shot taken during the game. He may be steeped in academia which uses ‘luck’ and ‘chance’ as grab bag explanations to avoid underlying quantification.