a: a force that brings good fortune or adversity
b: the events or circumstances that operate for or against an individual
Chad and Niv brought up some points in the comments to this post, and then I discussed things a bit further with them (in person in the case of Chad!). The biggest problem with that post is that i just basically categorized events as being luckly/unlucky without any real definition of the term. Well, I guess I was using the above definition, but there is way too much room to interpret how that may apply to baseball. In addition, there is a big distinction to be made between luck on an individual play and luck over the course of an entire game – I was confusing the two in a bit in that post, and will try to be a bit more distinct here.
Let us take a step back first and think about a game which is much more simple than baseball: darts. Let’s say you hit a bullseye; if you were to recreate the same exact physiological motion from the same exact location (location meaning physical structure and placement within that structure) and environment (same noise level/people moving around you) with the same exact grip that you used to hit that bullseye, you would with 100% certainty hit it again. You only depend on your own talents for an individual throw, so there is no luck involved whatsoever. Because the game itself is practically unchanging (you might have to aim for a 17 instead of the bullseye, but you are still the same distance away and using the same darts) and is turn-based (as opposed to interactive between the various players), you aren’t really competing against someone else as you play but rather you are competing against yourself relative to someone else competing against themselves (assuming you are not playing with teams). Your own performance can be neither lucky or unlucky; rather, you as an individual reap what you sow. However, because you yourself have no control over the performance of your opponent, the final outcome of the game may be lucky or unlucky based on how they perform relative to what is expected of them: if they hit numbers more quickly than they are expected to then you are unlucky, and if they hit numbers less quickly than they are expected to then you are lucky.
A game that adds an additional layer of complexity to darts is pool: it is turn-based, played in a climate-controlled environment, and uses a consistent set of equipment. However, unlike in darts the placement of the balls creates an infinite set of possible situations in which one can face. A player can repeat the same motion given the same situation and get the same result as in darts – therefore there is still no luck involved on an individual shot – but unlike darts they must be prepared to deal with any number of situations. Since these situations can range in difficulty from simple to impossible, it is possible for one player to face a much easier set of shots than the other. However, since leaving your opponent difficult shots is a skill in itself, this must be taken into account when trying to determine the role of luck. Therefore, one is lucky over an entire game of pool if they face easier shots than expected given opponent quality and/or have more opportunities at shots given opponent quality (due to unexpected misses by the opposition).
Golf seems to be a mixture of these two games to me – while the required shots change significantly over the course of a hole, each player is responsible for where their ball lies and plays no role in shots of the of their opponents. However, weather is brought into play for golf – an unexpected gust of wind blowing a shot off the green, for instance – and this means there is the potential for a slight bit luck on an individual shot (I would say this is slightly more common than someone dropping a glass while you are about to take your shot in pool, but overall it is pretty similar).
However, over the course of an entire tournament golf is a bit different than the other two games due to the fact that: 1) there are many more holes of golf in a tournament, reducing the volatility of the performance of each individual competitor; 2) there are many more competitors playing, reducing the volatility of the performance of all competitors in aggregate; and 3) the weather can change, potentially creating different conditions for the various competitors. Points 1 and 2 lead to the conclusion that, for the most part, you can have a pretty good idea about how the tournament scores will be distributed before it even starts. However, these may be affected by point 3. Also, while the overall distribution of scores are what matter for a tournament, when it comes to winning it is those scores on the end of the distribution that matter, and these will still be a bit volatile. Nevertheless, one can be considered to be lucky over an entire golf tournament if their competitors have performed worse than expected given the weather which they have faced and/or if the competitor has played in more favorable weather conditions than the rest of the competitors overall.
Finally, baseball. Let’s skip over the whole pitch selection part of the equation (which deserves a whole different post in itself) and just deal with balls in play. If you throw the dart/hit the pool ball/hit the golf ball where you want to throw/hit/hit it, then on an individual basis there is very little luck involved (except for dropped glasses/wind gusts). In baseball, however, there is no such guarantee. If you hit the ball exactly where you want to hit it in play, there is some non-zero probability it will turn into an out. And due to the nature of the game, is is much more difficult to hit a baseball exactly where you want it than to throw a dart/hit a pool ball/hit a golf ball exactly where you want it. That means that, on an individual play in baseball, there is some luck involved. A batter is lucky on a single play if the value of the outcome of the play exceeds the expected value of that ball in play. As samples increase in size this luck should even out somewhat – over a career there should be very little luck, but over the course of a game it certainly still plays a role in the outcome.
Note: I extracted some of this post in its original form for this so just imagine this as all being a prequel to that post.
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 isn’t a fun week – in a contracts class from 8-4 every day and then it’s into the office for another few hours to do a ton of work that got thrown at me because the people who are really responsible for it don’t know how to work with huge data sets. So there won’t be as much baseball work to get done this week as I would want, but I still have to keep up the blog posts! And obviously sitting in a classroom for 8 hours will give my mind ample time to wander and contemplate some things for this project.
For instance, today I found myself thinking more about what a true talent level actually means – basically an extension of the second paragraph of this post. As I said there, players have many different talents and trying to collect all of that information in a single statistic is going to be problematic. In what proportions do you mix these different talents? You could just assume that all hitters face pitchers with totally average pitches that they throw at the same rate as the major league average and have handedness in line with the actual breakdown in MLB by innings pitched. But is that meaningful? A left handed hitter that struggles against lefties may face a ton of LOOGYs and therefore face a higher percentage of lefties than normal – but then again he might get lifted for a pinch hitter in that situation or sit more often with a lefty on the mound and therefore face fewer than normal.
Regardless, there is no doubt that I’d rather be thinking about this stuff than the lifestyle of a Federal contract. Which is pretty good motivation to keep thinking about it even further.
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.