The Sloan Sports Analytics Conference is under way in Boston and, though we sent no intrepid reporters to Dorkapalooza this year, the conference happily made its research paper finalists publicly available on its website. Let's blearily page through and see if we can't learn a few things. (We're focused on the SSAC's primary muse, the NBA, but this year they also have football, baseball, tennis and soccer papers, for those interested.)

Some of it is conventional wisdom backed up by new metrics, some of it is new wisdom backed up by new metrics, but all of it is far more mathematically supported than any argument you've ever had about NBA players or basketball strategy. Let's get to it.

#### 1. Teams that are winning let their opponents back in the game by playing too cautiously.

Matthew Goldman of UC San Diego and Justin M. Rao of Microsoft looked at play-by-play data over four years and studied risk as it relates to how a team chooses between 2-pointers and 3-pointers. The theory goes that a risk-averse offense will feature more twos, while a risk-loving offense would shoot more threes; related, the study hypothesizes (and finds) that teams that are winning are risk-averse, while teams that are losing tend to get trigger happy. So why isn't a lead ever safe in the NBA, if the risk calculation seems so obvious? Because teams with diminishing leads play like teams with stable or increasing leads:

As a lead decreases, the leading team should become more risk-neutral, but teams in this circumstance actually tighten up and become more risk averse, contrary to what their risk preferences ought to be to maximize the chance of winning the game [...] 3-point usage does increase with the trail team's preference for risk, but actually falls for the leading team. Teams get it right when losing and wrong when winning.

It's not all good news for the losing team. Though they generally make the right decisions with respect to risk, Goldman and Rao found what you might expect about offenses that need to take chances: "[A]s a trailing team gets in a more desperate situation (becomes more risk-loving), the efﬁciency of their 3-point attempts falls." That's why some leads are safe.

#### 2. A good defensive big man doesn't block shots, he reduces the efficiency of the opposing offense.

Eric Weiss of Sports Aptitude, LLC and Kirk Goldsberry of Harvard (whose work has been featured here and on Grantland) wanted to develop metrics for evaluating defense, a portion of the game that's often ignored even by supposedly comprehensive statistics. The duo doesn't think that tallying blocks and steals says much about a defensive performance:

The NBA's most prominent defensive metrics can be misleading, but this is not a problem unique to basketball. Until very recently, the dominant conventional defensive metrics in baseball were "errors" and "fielding percentage," which do not frequently correlate with a player's true defensive value. In the NFL, the best cornerbacks never lead the league in any conventional stats because quarterbacks are too afraid to even throw in their direction; they don't even get chances to defend passes. Basketball exhibits similar issues; our conventional defensive metrics fail to accurately reveal the NBA's most dominant defenders.

As with a cornerback that's frequently the focal point of a play, blocking a lot of shots isn't always positive; it means the opposing team is testing you, which isn't a particularly flattering game-plan. A guy like Serge Ibaka may rack up blocks but, the paper notes, "coming out of nowhere" means that the other team doesn't have a consistent sense for where you are. In all probability, that's because it doesn't much care.

So who are the good defensive big men? Weiss and Goldsberry used tracking data to determine the efficiency of the opposing team while a given defender is in their area, and the disparity between an opposing team's normal shot selection and its shot selection when it faces a given big man. It turns out that Larry Sanders and Roy Hibbert are excellent at disrupting a team's shots in the paint, while Dwight Howard is good at deterring shots in the paint from even happening. Conversely, teams shoot a great percentage in the paint against David Lee, and Serge Ibaka is a magnet for players driving and posting up.

Overall, NBA shooters make 49.7% of their field goal attempts when qualifying interior defender is within 5 feet of the basket; however, this number drops to 38% when either Hibbert or Sanders are within 5 feet. In contrast, we found that Phoenix's Luis Scola and Golden State's David Lee were the worst defenders in these situations [...] When Howard is protecting the basket, opponents shoot many fewer close range shots than average, and settle for many more midrange shots, which are the least productive shots in the NBA. Furthermore, out of centers who have faced at least 100 total shots in the basket proximity study, Serge Ibaka ranked last; when he is within 5 feet of the basket, opponents shot 74% of their shots in the close range area.

Weiss and Goldsberry also looked at who tends to get near shots (within five feet), and who tends to affect shots when they're close by—for all his pugnacious posturing, Tyler Hansbrough has a habit of getting out of the way, while Larry Sanders again proves good at inserting himself into the play. Click over for full tables, some pretty pictures, and a first look at defensive metrics that will likely be standard on advanced stat sheets soon. (The strangest finding? Andrea Bargnani spooks inside shooters as much as anyone but Sanders.)

#### 3. Cutting hard during set plays probably means you're a good player.

Philip Maymin of NYU-Polytechnic Institute sought to explain why some set plays work in their execution, and some don't. As it turns out, when making an algorithmic language to describe basketball plays (??), "Important inputs to the language are the frequencies and locations of player acceleration." In figuring out which players move most quickly from one spot on the floor to another during a team's half-court set, Maymin found that, with some exceptions (Alabi, now in the D-League, couldn't survive on acceleration alone), the overall quality of the player does have some correlation to his tendency to accelerate in the half-court:

Generally, it seems like the people that stay moving and tend to move quickly during half-court sets are better, but the rule doesn't always obtain (Mark Gasol and Tyson Chandler are both high quality big men, but they're on opposite ends of the spectrum in terms of acceleration), and you can see on the above chart the Spurs' preference for slow-moving—maybe because they're careful and unobtrusive—swing men. Click through for more pretty pictures and a visual breakdown of the play that got the Thunder past the Spurs in last year's Western Conference finals.

#### 4. Hustling for offensive rebounds is a gamble, but it's probably a good one.

MIT's Jenna Wiens, Guha Balakrishnan, Joel Brooks and John Guttag tried to figure out when the cost/benefit analysis of crashing the offensive glass tips from benefit to cost, and found that aggressive offensive rebounding usually pays off, but the scale will slide depending on how many people you send to the boards and whether those people play smart transition defense:

Moving toward the basket immediately following a missed shot seems to increase a team's probability of getting the offensive rebound, but still even the best offensive rebounding percentage is much less than 50%. I.e., following a missed jump shot, a defensive rebound by the other team is always more likely [...] Still our results suggest that in general focusing on the offensive rebound immediately after the shot goes up seems to trump the gain a team gets with a head start on getting back.

This last bit comes with the caveat that, for whatever reason, sending two players to crash the boards is a better way of mitigating the damage on the resulting offensive play—when you don't get the offensive rebound—than only sending one. One explanation may be that, when two players crash the offensive glass, they instictively understand the importance of finding their man and sticking to him instead of just trotting back on defense:

Simply retreating to the defensive end of the court is not sufficient [...] The first time an offensive player is within a threatening distance to the basket in the first five seconds of his team's possession, we measure his distance (in feet) to the closest defending player. We compute a distance for each offensive player that becomes a threat during the possession and use the maximum of these distances as the MDET [Maximum Distance to Early Threats] score. The maximum distance represents the most "open" player during the early portion of the possession. Note that a lower MDET score indicates better neutralization [...] We computed the MDET score for each defensive possession and recorded a binary outcome (1 = opponent did not score, 0 = opponent scored or got to the free throw line). Figure 9 plots the MDET distribution for each outcome. Using the Kolmogorov-Smirnov test, we found that the two distributions were significantly different (p < 0.01). Looking at the distributions, we see that outcome 1's distribution is shifted toward lower MDET values than outcome 0 [...] These results are consistent with the intuition that better threat neutralization can prevent transition baskets on defense.

As it turns out, the trade-off between crashing the boards and playing good transition defense is pretty stark, but teams can offset that problem by playing offensive rebounders who are aware enough, and athletic enough, to neutralize quick guards that might be trying to lead a fast break off a defense rebound.

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Ahh, feels good to have gained usable knowledge based on shallow interpretations of data sets acquired by methodologies we don't understand. Next time someone in your pick-up game asks why you didn't get back on defense, carefully explain that you were well within your Maximum Distance to Early Threats, and then prepare to get punched in the mouth.

Picture via.