I have a really big post coming, but I’m driving to cleveland tonight and there’s no chance I’ll be able to finish it. So here is a little digression from the middle of it all that pretty much stands on its own. I hope to post the rest sometime this weekend.

Chad wondered: can we look at luck on individual plays or does it only make sense in aggregate? We discussed this over brunch for a while (our fiancé’s were thrilled), and I think the answer is yes, you can look at individual plays. In my original post, I didn’t specify what the odds were that the shortstop got to the ball, but in my head I was imagining a play that would be a hit maybe 90%-95% of the time. Now is that 5%-10% unlucky or just unlikely but inevitable? How about this play? That’s a home run 99.999% of the time, and I think we can all agree the guy who hit that was unlucky.

After a lot of thought, I realized that any cutoff is an arbitrary cutoff and in reality we should only be talking about degrees of luck rather than bucketing everything into categories. From a batter’s perspective, every hit is lucky and every out is unlucky. It’s a bit like win probability added insofar as every hit increases the chances of a win and every (nonproductive) out decreases the chances of a win.

A ball in play which is a hit 50% of the time that is turned into an out is unlucky, and that same ball when it is a hit is equally lucky. A ball which is a hit 99% of the time that actually results in a hit is lucky, but just a little tiny bit lucky. A ball which is a hit 99% of the time but is turned into an out is about as unlucky as you could be. getting 6 hits on 10 balls in play with an expected hit total of 3.6 is lucky, but not as lucky as getting 7 or 8 or 9 or 10 hits on those same balls; 5 hits in that situation is still somewhat lucky, but relatively less lucky than what actually happened. And if you’ve got a 30% chance of a ball in play turning into a hit and it does, that’s equivalently lucky to getting two hits on balls each with a 54.8% chance each of turning into hits or getting three hits on balls each with a 66.9% chance each of turning into hits (using the binomial distribution: 30% = 54.8% * 54.8% = 66.9% * 66.9% * 66.9%).

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 post by Dave Cameron at FanGraphs does a pretty good job at pointing out the difficulties that arise when trying to separate talent from results. Trevor Cahill has certainly had a very strong year by “traditional” measures (ERA, WHIP), but in other ways (GB%, K%) has performed worse than even Jason Justin Masterson. I’m not very concerned about whether the Cy Young vote should be based on wins and losses or K-rate or SIERA (although if I did have a vote, it would probably be for Cliff Lee despite witnessing this in person). It’s not the perception of talent that I care about, but rather actual talent. More precisely, the probability that a particular player has talent level X on a given day (see here for a very good background). Using all of the wonderful information available from MLB.com, it is possible to begin stripping away park and luck and quality of opposition and come closer to some distribution of true talent level for that player.

However, of course a player doesn’t have just one talent – a pitcher might have great fastball velocity but no command, or a wonderful change but a curve that gets pounded. On the other end of the pitch, a hitter might crush high and tight fastballs from righties but couldn’t hit a curve from a lefty to save his life (and in the case of switch-hitters, they likely behave like two totally different hitters depending on the side of the plate they are on). My goal is to use what we do know based on what has happened in the past to construct a better measure of player talent.