Omnivore’s Dilemma and Three Point Shots

Now that it’s time for the 2012 NCAA tournament, I will be writing a few posts about college basketball. I think the NCAA men’s basketball tournament is the greatest sporting event of the year by far in many ways. But that’s not what this post is about.

This post is about shot selection – specifically when it is a good decision to shoot a three point jumpshot. It can be a difficult decision to make, and it’s one that I feel players often get wrong. In general, taking a bad shot means that the possession ends with a lower percentage shot than the team would expect to have later in that possession. Passing up a good shot means that the team will likely have to settle for a lower percentage shot or possibly turn the ball over.

Not all players are faced with a tough decision. For elite shooters, the decision is easy. They try to get open from three point range and, whenever they do, they shoot without hesitation. Their role on the team is to shoot threes and everyone expects them to shoot when they get a clean look. They shoot at a high enough percentage that almost any uncontested shot is expected to result in significantly more points than an average possession for that team. For non-shooting post players, the decision is even easier. They rarely try to touch the ball on the perimeter and they know not to shoot threes unless the shot or game clock is extremely low.

Unless there's under three seconds left on the shot clock, of course.

Life is easy, just eat bamboo and don't shoot any long jumpshots.

In the Omnivore’s Dilemma, Michael Pollan discusses how omnivores are faced with the tough decision of choosing what to eat. Omnivores can – and often must – eat a variety of foods, but it is not hardwired in them to distinguish foods that are good for them from foods that are bad or even toxic. Animals in the wild that eat only one thing don’t have this problem. Pandas know bamboo will properly nourish them and not make them sick, just as cows do with grass and lions do with hoofed mammals.

In basketball, average three point shooters are the omnivores. Sometimes it is good for them to shoot, but sometimes it is bad. If they habitually decline to shoot, they neglect a potentially productive area of their game and allow defenders to sag off them to contain dribble penetration. If they shoot too much, they wind up wasting possessions on suboptimal shots.

When players take shots that are considered bad, they may be chided by the coach or lambasted by fans and media for being trigger happy. When players pass up shots that are considered good, they may be chided by the coach or lambasted by fans and media for being passive or timid.

But what will the people on Twitter think?!?

To shoot? Or not to shoot?

There are many factors, in my opinion, that determine whether a particular shot is a good one for a player, including:

  • How good is he at shooting threes?
  • How open is he? A wide open shot is preferable because it can’t possibly be altered and allows time to set up like the shooter would in practice.
  • How much time is on the shot clock? More time means there are more opportunities to get a better shot. A shot that’s good with 10 seconds on the shot clock might not be good with 25 seconds left.
  • How efficient is his team on offense against the opposing team’s defense? A team with a superior offense should be more selective, whereas a team that’s overmatched should have lower standards on their jumpshots.
  • Is his team behind? A team that’s behind by a lot should be more inclined to shoot threes as those increase variance in the game and make comebacks more likely.
  • What kind of rebounding position are his teammates in? When the paint is devoid of teammates, the chance of an offensive rebound is slim and the shot is less desirable.

That is a lot to take into consideration. Players usually have a window of less than a second to decide whether to shoot before a defender gets to them, making their decision even harder. On top of that, I believe confidence to be an important asset for a shooter to have. Second guessing oneself on a shot can only decrease accuracy. Players just don’t have the luxury to process everything or doubt themselves in the heat of the moment.

If you take a three point shot and move it closer to the basket by a foot or two, you get a long two. Long twos are the shots that are 85%-99% as difficult to make as three point shots but are worth only 67% of the points; every player would be wise to avoid them. Yet, players shoot long twos anyway and the ones that I’ve found most prone to doing so are average shooters. I think average shooters may do this to avoid the criticism and mental anguish that can come with shooting (and missing) a potentially ill-advised three point attempt. Or maybe they’re more likely to put themselves in position to shoot long twos because they are not concerned with shooting threes. On the other hand, elite shooters attempt threes with a purpose and make a point to ensure that all their long jumpshots are threes.

Even though a three and a long two are essentially the same in every way except for how many points they’re worth, they get treated very differently by media and fans. In the box score, threes are their own category while long twos are grouped together with all other shots including layups and dunks. Fans and commentators love box scores because it’s easy and deemed acceptable to draw conclusions based on them alone. If Average Shooter X, who averages two 3PA a game and shoots 35% for a season, goes 1-7 from three point range in a loss, that figure will stick out like a sore thumb in the box score. I mean, what was he thinking missing six threes in a game?

One factor that is not on my list of what determines a good shot above is how many threes that player or his team have already made or attempted that game. Very often you’ll hear basketball commentators on TV saying a certain team needs to make x amount of threes to win an upcoming game. Or you’ll hear them blame a loss on a team or player attempting too many threes when they have taken more 3PA than average. Comments like these are often misguided.

As Ken Pomeroy showed in his blog, defenses have a significant amount of influence over how many three point attempts they allow but very little influence over what percent of those attempts go in. This reinforces the idea that there is a lot of randomness involved in whether three point shots go in or not. More importantly, this data supports the theory that a team that’s committed to and/or effective at defending three point shots can reduce the amount of clean three point looks the other team gets and consequently reduces the number of shots they attempt.

It follows that the number of clean three point looks a team gets in a game is at least partially out of that team’s hands. Therefore, striving to shoot or make an arbitrary amount of threes is counter productive and can only hinder shot selection. A player should never think “I’ve attempted a lot of threes, I should stop shooting threes for the rest of the game.” Likewise, he should never think “I haven’t been shooting enough threes this game, I should start forcing some shots.”

Good thing they lost while shooting so many threes or else they might not have learned their lesson!

28 is a big number. 6 is a small number. Time to draw conclusions.

The tweets above came from media members after Kentucky’s recent 71-64 loss to Vanderbilt in the SEC championship game. Kentucky this season is widely considered one of the best teams in the nation at defense, two point shooting, rebounding, and getting to the free throw line. In this game, Vanderbilt had better offensive and defensive rebounding percentages, attempted 13 more free throws, and shot higher two point, three point, and free throw percentages than Kentucky. Oh, and Kentucky went 6-28 from three point range. You can see which statistic the media decided to make a narrative out of.

I watched the game closely and I did not notice any appreciable difference in the quality of three point shots Kentucky attempted compared to their other games. Most were open looks and most were taken by their best three point shooters. In fact, the shot selection and distribution was quite similar in Kentucky’s 79-49 victory over Georgia a few weeks earlier when they shot 15-27 from three point range. Of course, nobody after that game was lamenting that 27 threes is too many or that Kentucky’s players needed a lesson to teach them to shoot fewer threes. The difference between shooting 15-27 and 5-27 is 30 points, the margin of victory that game.

But what is there that can be learned from all this? In general, I think players should pass up shots more often early in the shot clock but hardly ever pass up decent looks late in the possession. I think time on the shot clock is an important factor in determining shot selection yet it seems to be one that is often overlooked. With lots of time left, teams should be working to get a high percentage shot, preferably a layup or a dunk. Those seconds are valuable, and when a team shoots they forever lose what is left on the clock.

Yet when the shot clock hits single digits, “beggars can’t be choosers” applies. A shot clock violation or a desperate or forced shot are vastly inferior outcomes compared to any reasonable shot attempt that comes in the flow of the offense. As Matt Goldman shows in his study on NBA decision making, the value of holding on to the ball declines gradually for most of the possession and then dips sharply in the final five seconds of the shot clock. Having to create a shot that late is no easy task.

I also think it would be beneficial for players and coaches to discuss what kind of shot selection and three point shooting thresholds would be optimal. This would reduce the amount of thinking about whether or not to shoot that is required during games. And, when a player does decide to shoot, he should shoot with a purpose and with complete confidence… and pay no concern to what negative things people might say on Twitter.


5 thoughts on “Omnivore’s Dilemma and Three Point Shots

  1. Interesting how options contract values approaching expiration deadline have a similar time decay as expected value of possession as shot clock winds down.

    I really like the analogy to omnivore’s dilemma, you can consider each meal a possession. Before each meal you have the decision of what food to eat. If you wait too long to decide, you will get too hungry, and get an upset tummy. If you decide too hastily, you may choose a suboptimal idea for a recipe or dining option. Wait too long and over-think the matter, and you may turn into a Diva like in the snicker’s commercials.

  2. Hey, Dan. Great post. There absolutely is a lot of variance in whether or not the ball goes through the hoop. Variance is def the most overlooked factor in deciding basketball games and if you make about 35% of your 3s, then 5-27 (or worse) is gonna happen from time to time (~5% of the time).

    Generally 3s are awesome shots in college basketball. They go in an average 35% of the time, you negate the possibility of turning the ball over prior to a shot, you get a ~30% shot at an oreb, and you have 35 seconds to try and create a decent look, while the other team usually scrambles around in a zone. I’m not a huge college bball afficianado, but I would guess a lot of the belly aching over Kentucky’s shot selection is the same kind of results oriented crap you hear from beginning poker players. In fairness, if Kentucky is a huge favorite over Vandy, it may behoove them to cut down the variance on the outcome a little by looking for 2s early in the game.

    Additionally, marginal 3PA with a defender draped over you are terrible shots for all but a few NBA guys (Jamal Crawford’s ability to make 1/3 of these just earned him 8 figures). Long twos (especially off the dribble) are often terrible shots but in the NBA you mostly only see teams shoot a lot of them when they are forced to try and create something off the dribble at the end of the shot clock because they could not put enough pressure on the D earlier. Most NBA players (and I would hope most college players) know better than to pass up a nice look at a 3 for some type of (slightly higher percentage) pull up jumper. But they know that a pull-up off the dribble 3 is generally not a viable option and have to try and “create” when the shot clock is low.

    1. Thanks Matt. Threes are comparatively better in college than the NBA because the three point line is closer to the hoop, and consequently long twos are even worse. On the other hand, with a 35 second shot clock (which I think should catch up with women and get reduced to 30 seconds) there’s also more time to try to create an even better/more efficient shot. That’s why I think there’s an argument for average shooters to pass up decent 3 point looks early in the shot clock but not late in the shot clock.

      Kentucky was a 6.5 point favorite over Vandy, so definitely not huge. There’s no way teams can eliminate eliminate all but 6 points of variance even if they shoot no jumpshots at all. Also, I’ll pick Vandy every time in a game where UK is not allowed to shoot threes.

      It’s worth noting that in Kentucky’s only other loss all season, at Indiana, they shot 2-7 on threes; many fewer 3PA than their season average and only one 3PM away from shooting above their 3P% average. They were about 5-6 point favorites in that game as well.

      In other news, I lost AK to a small pocket pair like three times IN A ROW the other day. Clearly either poker is rigged or AK is a garbage hand.

  3. “In other news, I lost AK to a small pocket pair like three times IN A ROW the other day. Clearly either poker is rigged or AK is a garbage hand.”

    lol at chasing pairs…I thought you were good at poker

    “Kentucky was a 6.5 point favorite over Vandy, so definitely not huge. There’s no way teams can eliminate eliminate all but 6 points of variance even if they shoot no jumpshots at all. Also, I’ll pick Vandy every time in a game where UK is not allowed to shoot threes.”

    Kentucky shouldn’t stop shooting 3s and they certainly can’t ELIMINATE variance, but every 3 they shoot introduces more variance to the game. If they are favorites then there is a second order effect where they are a little bit more inclined to shoot 2s than a marginal 3. I worked this out in one of my papers because we are trying to evaluate how good nba players are at assessing these changing incentives toward risk. If you are 7 points better than the other team over the next 70 possessions (length of a college game?), than the premium on the reduced variance of a 2 is like .07 points. So at the beginning of the game, for Kentucy a 50% 2 = 35.666% 3 and for Vandy a 31% 3=50% 2. Assuming some reasonable distribution of the quality of 3 point shots (this is the part that is really hard to quantify), its entirely plausible that Kentucky should shoot fewer 3s when they are a bigger favorite.

    1. That is good stuff and makes sense. However, the premium on reduced variance isn’t static over the course of a game. For example, if the favorite before tip-off trails by double digits in the 2nd half, then increasing variance works in their favor.

      Your logic also works in favor of emphasizing defending threes if you’re a significant favorite, which is something I think elite college teams (including Kentucky) often don’t focus on enough. Especially when you have the best defender in the country in the paint, force teams to beat you inside.

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