One of my econ professors from Northwestern, Jeff Ely (Econ 380-1 Winter quarter 2003 – I have no idea how I remembered the course number but I do), has a pretty fun blog that I highly recommend if you’re into that kind of thing. Strangely enough, this post from earlier today is very much in the spirit of what I’ve been thinking about recently.
Now there is certainly some role for luck in golf, and it’s actually potentially able to be calculated: it would be “lucky” for a tournament winner if his competitors finished with worse scores than they would have been expected to finish with (taking into account weather/injury, etc.) entering the tournament.
However, on an individual level I cannot see there being a great deal of luck over the course of an entire tournament. Luck would involve shots ending up in better position than would be expected given the velocity/spin/trajectory which the golfer put on the ball. Examples of this would be getting a perfect lie when hitting it into the rough, hitting the pin instead of racing past the hole, or bouncing the ball over a bunker.
Luck is certainly not the residual of some estimate of overall skill. Over the course of a tournament, some players are going to outperform their ability while others will underperform – that’s just what happens over a 72 hole sample of golf. But assuming no flukey balls or silly penalties for not realizing you’re in a bunker, it’s pretty likely that the guy who wins the tournament actually played the best golf over the course of the tournament.
So is drawing a favorable sampling distribution luck? I don’t think so – you get the outcome you deserve given your own personal contributions over that time period. To bring this back to baseball, I’d say that a Yuniesky Betancourt line drive up the middle for a single is not luck – it’s just a low-probability outcome of him showing considerable skill. If the shortstop makes a diving stop and throws him out on the same ball that’s in fact bad luck for Betancourt, despite the very low ex-ante probability of him getting a hit in the first place.
I’ll certainly take a look through that paper at some point, but just at first glance I think I have to agree with my trusted professor (and not just because he gave me an A).
this trips me up a bit – so it’s bad luck if Betancourt’s liner up the middle is caught, but wouldn’t that be within the range of defensive possibilities of the player who caught the ball? Is that implying there is skill for one side and luck for the other side of the same outcome, and if so, is that ok? It might be ok, I am not sure.
Or is Betancourt’s screamer up the middle that is nabbed by a 2B within the range of possibilities for Betancourt?
so, i may not be understanding this perfectly either, but it seems to me that the luck we are talking about cannot really be seen in an individual play, but over the course of a season or a career. betancourt’s line drive up the middle maybe gets caught, maybe not – but we can say with a reasonable level of confidence that it SHOULD get caught about X% of the time. But, if liners up the middle should get caught at a certain rate, on average, we would expect to see a normal distribution of rates for players around that average. and a player who is a couple standard deviations above the average is likely just getting very unlucky.
now, that luck may be a result of poor luck in timing (he always hits his line drives against the teams with the best defensive shortstops) or just plain poor luck (for some reason, shortstops happen to just make their best plays against him). it could also be a sign that he is predictable or easy to defend (teams recognize that he never hits the ball in the hole between short and 3rd, so they play him more up the middle).
but the point is, that i think it is really hard to say that a player had good or bad luck on a single play – it makes far more sense to think about it in aggregate. betancourt hits 20 line drives up the middle over the season, on average 4 should be caught, instead 8 are…that is bad luck.
does that make sense?