A systems biologist looks at basketball games through the prism of graph theory
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Steven Cherry: Hi, this is Steven Cherry for IEEE Spectrum’s “Techwise Conversations.”
Have you ever looked at a diagram of a network, with its circles and lines connecting them? The circles are called “nodes,” and the lines are called “links,” or “edges.”
Have you ever looked at the diagram from a playbook in a sport like basketball? They share some similarities. If you draw circles for the players and then draw a line for every time the ball is passed from one to the other over the course of a complete play, you get something that looks quite a bit like a network diagram.
That insight, or something like it, seems to have been the inspiration for a clever and fun mathematical research paper. “Basketball Teams as Strategic Networks” is its name, and it was published by the open-access online journal PLOS ONE back in November.
Network theory has been around since the 1700s, but with the rise of the Internet, it’s become tremendously important. It can explain the winner-take-most popularity of our largest websites, how information spreads through a cocktail party, and the strong and weak social ties through which most of us will get our next job. Maybe it was inevitable someone would use it to see which style of basketball play—get-the-ball-to-the-point-guard, or a more distributed passing game—is more successful.
My guest today is the lead author of “Basketball Teams as Strategic Networks,” Jennifer Fewell. She’s a professor at Arizona State University, where, among other things, she studies ant colonies as self-organizing networks. She joins us by phone.
Jennifer, welcome to the podcast.
Jennifer Fewell: Thank you.
Steven Cherry: Jennifer, I was guessing about the genesis of the research. How did you detour from insects to basketball teams, or is that not a detour at all?
Jennifer Fewell: It’s not actually that much of a detour. I joked to a friend of mine that I think sometimes of basketball players as premarked ants because, you know, they have their names on their backs and they’re running around interacting with each other. I’m interested in the coordination of behavior within social groups. How do social groups maintain cohesion? What are the costs and benefits of interacting with each other within a social group? And ants, of course, are a perfect subject for a system for that.
But basketball teams are also, because they have a cost and benefit to interacting and coordinating with each other. There’s sort of a bit of a tension between individuals being successful and the group being successful. Ultimately, though, the group success is what’s going to be the metric that you should be measuring for a basketball team. So it’s a coordinated group of individuals that have a common goal, just like an ant colony.
Steven Cherry: Let’s start with the paper’s methodology. You looked at a basketball game, or actually 16 basketball games, through the prism of graph theory.
Jennifer Fewell: Yes. We’re trying to find ways to capture this coordination, this interaction, and graph theory is a way to do that because it asks how individuals are connected to each other. So when you watch a basketball team interacting, the connections are very obvious and very easy to measure, because the ball is actually the link, right, between players, and from the inbounds through the players to an outcome. And then you have the basket, which is not only a node but also a success/failure outcome that you can measure. So a basketball team, it’s very easy to capture as a graph.
And what we basically did in the paper is use each offensive play, look at the passing of the ball across the players, and then we added up each of those plays to create what we call an “association network,” which shows you what the most frequent passes are down to the least frequent in a graph, basically what we call a “weighted graph.” And it’s also directional, because it can show who passes to whom, etc. And outcomes are interesting because they’re also a node in the graph.
Steven Cherry: So you looked at two things in particular: something you call “uphill/downhill flux” and entropy. Let’s start with uphill/downhill. What is that?
Jennifer Fewell: So basically what we did was we looked at the probability of passing from A to B to C, something like from the point guard to the power forward. And then we looked at the differential in their shooting success. And if the power forward has a higher shooting success than the point guard, then moving the ball toward the power forward obviously gives you a positive uphill/downhill. If it were the opposite—and for some teams it actually is, right? Their point guard is also their best shooter. If the point guard is distributing the ball out but not actually shooting it, they’re moving it away from higher probability of success. And we put that all together and we called it “uphill/downhill.”
Steven Cherry: Entropy, the way the term is used in information theory, can be a little confusing, so let me take a shot at this. In chemistry and physics, it’s the level of organization. So greater entropy—the famous second law of thermodynamics—is greater disorganization or chaos, the poet William Yeats’s equally famous “things fall apart.” In information theory, it’s sort of the same thing, looking at signal and noise, where noise is unpredictable or chaotic. We usually want more signal and less noise, but here entropy is good because we don’t want the other team to anticipate our next pass or shot. Did I get that right?
Jennifer Fewell: Yes. Yeah, exactly. We’re coming at it from an information theory perspective, where for low entropy you have a high probability that if A has the ball you know that ball’s going to B, right? With higher entropy, lower predictability, if A has the ball, you don’t actually know where that ball’s going next. And you can imagine from a team’s perspective that they don’t want it to be as obvious where the ball is going.
Steven Cherry: Okay. So one thing you found was that each team seemed to have a distinct style, which I guess comes as no surprise to sports fans, except that you were able to discern that just from the graphs.
Jennifer Fewell: Yes. We basically did two things: The first thing we did was compile all of the data and look at what we would call a typical NBA team, and that was our first figure in the paper. And it was really interesting, because it sort of captured what we think of as a classic NBA team, which would be one where the point guard is very central, inbound goes to the point guard, and then the point guard distributes out to different players. And if those players are not able to take a shot, they usually distribute back to the point guard. And then usually it’s something like the shooting forward or the power forward will go for a shot. The center is more likely to rebound the ball than other players. All of that was captured immediately in the graph, right?
But then you can take a look at the individual teams and ask, Well, how do they differ from this? And we got some really nice differentials that sort of were a proof of concept for the use of networks. For example, you might have a team like the Jazz or the Suns, where you have a point guard—and I should remind everybody this is 2010, so the Suns had Steve Nash as their point guard, right? And so he was a beautiful ball distributor, and you could see that ball going out to other players and coming back to him. Then you go to something like the Mavericks, and the ball goes to Dirk Nowitzki, right? That’s their main player, and that’s who’s going to shoot the ball, and that’s who they’re distributing the ball to.
And you get some interesting differences, too. For example, in the Cavaliers, even though the ball started with the point guard, it immediately went to LeBron James, and you could actually see him as a central node. And he’s actually the distributing node. And then finally, you move to the Lakers, which is a classic Phil Jackson Lakers, and the pattern changes really kind of dramatically. The point guard becomes less central to the network, and you find that the ball is being distributed fairly evenly across all the players. Even Kobe is not actually sort of hogging the ball in the Phil Jackson Lakers; he’s distributing the ball also. And you get what we call a more “distributed network.”
That network also has another interesting feature, where if you look at any set of three players, they’re interconnected. So the shooting guard is not just connected to the point guard; he’s also connected to the power forward. And the center is not just connected to the point guard; he’s also connected to the shooting guard. And those triangles are what generate higher entropy in that graph compared to something like the Suns, where you have a central player making the decision.
Steven Cherry: And you looked at only 16 games, and we should mention that these were playoff games, but still you found one style to be generally more successful?
Jennifer Fewell: Yeah, we did. And I just want to say that basketball, one of the beauties of basketball is it’s a very complex sport, and so we can’t say that this is the strategy that works all the time. But in the 2010 playoffs, the graphs that were more successful were the graphs generally that had higher entropy. I think it was six out of eight matchups, the team that had higher entropy went on to win that round. And the two graphs that had the highest number of triangles that are connected to each other, that’s another measure called “clustering,” where you actually can say if A is connected to B and B is connected to C, is A also connected to C? Do they know each other or are they passing the ball to each other? The two teams with the highest clustering were the Lakers and the Celtics, so that was pretty nice to get that.
Steven Cherry: Because they did very well.
Jennifer Fewell: They did very well. They were the ones in the finals, so they did very well indeed.
Steven Cherry: I guess the obvious question is, Can you extend the research to things even more useful than basketball? In the paper you write, “The dynamic between within-group cooperation and conflict, and group versus individual success, is an inherent feature of both human and biological social systems.” Are there any lessons for businesses, for example?
Jennifer Fewell: Well, I would take objection to the “anything more useful than basketball.” I mean, basketball is useful in itself. It’s so beautiful. But, yes, I think it is something that we’re trying to push beyond the realm of just one specific sport or even one human social interaction. I think that these dynamics between cohesion and individual versus group success, biologically, is a central question in social theory.
I mean, one of the questions that you have in the success of any social group, from business to, I talk about “cooperative associations” of lions also, is how do you balance individual productivity with group productivity, individual success with group success. In a cooperative system, you have to have some benefit for all of the individuals in the group, but that can also cause a dynamic sort of trade-off between group success and individual success. I mean, for example, you might think of the ball hog, and there might be an analogy to that in business systems, where individuals are working for their own success but they’re actually damaging the function and cohesion of the group.
You see that in cooperative groups of social insects also. This is a big question, the interaction between cooperation and conflict, and how do you deal with conflict, because one individual is taking over resources. I think you could see this in the team network sort of interestingly in that some teams function specifically around a very successful individual, while other teams, the individuals who have the potential for success, back off from shooting, because that’s usually what individual basketball players are measured for, and distribute the ball more so that the team as a whole is more likely to win. So, yeah, I think it’s a really interesting dynamic that we were able to capture.
There’s a group that is doing network analyses on soccer teams, and they published a paper on European soccer players’ flow centrality, which sort of measures the probability that the ball will go through that individual, and compared their salaries based on flow centrality, and found that the ones that got paid more generally did control the ball more, which is interesting. So, yeah.
Ice hockey is another sport where I think you could do this. To me it seems stochastic because they’re always hitting each other, right. But apparently they control the puck more than I thought.
Steven Cherry: Your Ph.D. was in biology from the University of Colorado, and your dissertation concerned the foraging strategies of a particular species of harvester ants. It had the subtitle of “Costs, Currencies, and Constraints.” What are the costs, currencies, and constraints of harvester ants?
Jennifer Fewell: Oh, wow, that’s going back. I was interested in how individuals in a social group, ants in a colony, make decisions about what resources they bring back to the colony, so the cost, currencies, and constraints, I measured actually how much it specifically cost an ant to go out and collect a seed, what they use as decision criteria to bring seeds back, and what are the constraints on them in terms of their ability to switch strategies.
And it was very interesting, because ants, like basketball players, can’t make infinite decisions when they’re out there in the field, right? They have limitations on what they can do. We all do. And so if you don’t factor those into your consideration of the system, then you’re not going to have an accurate representation of what’s going on. Ants are very directional based. They can’t switch directions very easily. They memorize a path very well, but they don’t go in other directions very well. So that was one of the constraints on them.
Steven Cherry: I guess the lesson here, or at least one of the lessons here, is that networks are all around us. My undergraduate major was mathematics, so on behalf of all sports lovers, mathematicians, and especially sports-loving mathematicians, thanks for your research and for telling us about it today.
Jennifer Fewell: Well, thank you. I love talking about basketball, so it was a lot of fun.
Steven Cherry: We’ve been speaking with Jennifer Fewell about network theory, as applied to the basketball court, business, and the biological colony.
For IEEE Spectrum’s “Techwise Conversations,” I’m Steven Cherry.
This interview was recorded 7 March 2013.
Audio engineer: Francesco Ferorelli
Read more “Techwise Conversations” or follow us on Twitter.
NOTE: Transcripts are created for the convenience of our readers and listeners and may not perfectly match their associated interviews and narratives. The authoritative record of IEEE Spectrum’s audio programming is the audio version.
Have you ever looked at a diagram of a network, with its circles and lines connecting them? The circles are called “nodes,” and the lines are called “links,” or “edges.”
Have you ever looked at the diagram from a playbook in a sport like basketball? They share some similarities. If you draw circles for the players and then draw a line for every time the ball is passed from one to the other over the course of a complete play, you get something that looks quite a bit like a network diagram.
 |
| Figure 1. Weighted graph of ball transitions across all teams and all games. Edge width is proportional to probability of transition between nodes. Red edges represent transition probabilities summing to the 60th percentile. doi:10.1371/journal.pone.0047445.g001 |
That insight, or something like it, seems to have been the inspiration for a clever and fun mathematical research paper. “Basketball Teams as Strategic Networks” is its name, and it was published by the open-access online journal PLOS ONE back in November.
Network theory has been around since the 1700s, but with the rise of the Internet, it’s become tremendously important. It can explain the winner-take-most popularity of our largest websites, how information spreads through a cocktail party, and the strong and weak social ties through which most of us will get our next job. Maybe it was inevitable someone would use it to see which style of basketball play—get-the-ball-to-the-point-guard, or a more distributed passing game—is more successful.
My guest today is the lead author of “Basketball Teams as Strategic Networks,” Jennifer Fewell. She’s a professor at Arizona State University, where, among other things, she studies ant colonies as self-organizing networks. She joins us by phone.
Jennifer, welcome to the podcast.
Jennifer Fewell: Thank you.
Steven Cherry: Jennifer, I was guessing about the genesis of the research. How did you detour from insects to basketball teams, or is that not a detour at all?
Jennifer Fewell: It’s not actually that much of a detour. I joked to a friend of mine that I think sometimes of basketball players as premarked ants because, you know, they have their names on their backs and they’re running around interacting with each other. I’m interested in the coordination of behavior within social groups. How do social groups maintain cohesion? What are the costs and benefits of interacting with each other within a social group? And ants, of course, are a perfect subject for a system for that.
But basketball teams are also, because they have a cost and benefit to interacting and coordinating with each other. There’s sort of a bit of a tension between individuals being successful and the group being successful. Ultimately, though, the group success is what’s going to be the metric that you should be measuring for a basketball team. So it’s a coordinated group of individuals that have a common goal, just like an ant colony.
Steven Cherry: Let’s start with the paper’s methodology. You looked at a basketball game, or actually 16 basketball games, through the prism of graph theory.
Jennifer Fewell: Yes. We’re trying to find ways to capture this coordination, this interaction, and graph theory is a way to do that because it asks how individuals are connected to each other. So when you watch a basketball team interacting, the connections are very obvious and very easy to measure, because the ball is actually the link, right, between players, and from the inbounds through the players to an outcome. And then you have the basket, which is not only a node but also a success/failure outcome that you can measure. So a basketball team, it’s very easy to capture as a graph.
And what we basically did in the paper is use each offensive play, look at the passing of the ball across the players, and then we added up each of those plays to create what we call an “association network,” which shows you what the most frequent passes are down to the least frequent in a graph, basically what we call a “weighted graph.” And it’s also directional, because it can show who passes to whom, etc. And outcomes are interesting because they’re also a node in the graph.
Steven Cherry: So you looked at two things in particular: something you call “uphill/downhill flux” and entropy. Let’s start with uphill/downhill. What is that?
Jennifer Fewell: So basically what we did was we looked at the probability of passing from A to B to C, something like from the point guard to the power forward. And then we looked at the differential in their shooting success. And if the power forward has a higher shooting success than the point guard, then moving the ball toward the power forward obviously gives you a positive uphill/downhill. If it were the opposite—and for some teams it actually is, right? Their point guard is also their best shooter. If the point guard is distributing the ball out but not actually shooting it, they’re moving it away from higher probability of success. And we put that all together and we called it “uphill/downhill.”
 |
| Figure 2. Mean flow centrality by position (+/− S.D.). Dark bars represent flow centrality calculated across all player possessions in a sequence, and light bars represent flow centrality calculated across the last 3 player possessions in successful sequences. doi:10.1371/journal.pone.0047445.g002 |
Steven Cherry: Entropy, the way the term is used in information theory, can be a little confusing, so let me take a shot at this. In chemistry and physics, it’s the level of organization. So greater entropy—the famous second law of thermodynamics—is greater disorganization or chaos, the poet William Yeats’s equally famous “things fall apart.” In information theory, it’s sort of the same thing, looking at signal and noise, where noise is unpredictable or chaotic. We usually want more signal and less noise, but here entropy is good because we don’t want the other team to anticipate our next pass or shot. Did I get that right?
Jennifer Fewell: Yes. Yeah, exactly. We’re coming at it from an information theory perspective, where for low entropy you have a high probability that if A has the ball you know that ball’s going to B, right? With higher entropy, lower predictability, if A has the ball, you don’t actually know where that ball’s going next. And you can imagine from a team’s perspective that they don’t want it to be as obvious where the ball is going.
Steven Cherry: Okay. So one thing you found was that each team seemed to have a distinct style, which I guess comes as no surprise to sports fans, except that you were able to discern that just from the graphs.
Jennifer Fewell: Yes. We basically did two things: The first thing we did was compile all of the data and look at what we would call a typical NBA team, and that was our first figure in the paper. And it was really interesting, because it sort of captured what we think of as a classic NBA team, which would be one where the point guard is very central, inbound goes to the point guard, and then the point guard distributes out to different players. And if those players are not able to take a shot, they usually distribute back to the point guard. And then usually it’s something like the shooting forward or the power forward will go for a shot. The center is more likely to rebound the ball than other players. All of that was captured immediately in the graph, right?
But then you can take a look at the individual teams and ask, Well, how do they differ from this? And we got some really nice differentials that sort of were a proof of concept for the use of networks. For example, you might have a team like the Jazz or the Suns, where you have a point guard—and I should remind everybody this is 2010, so the Suns had Steve Nash as their point guard, right? And so he was a beautiful ball distributor, and you could see that ball going out to other players and coming back to him. Then you go to something like the Mavericks, and the ball goes to Dirk Nowitzki, right? That’s their main player, and that’s who’s going to shoot the ball, and that’s who they’re distributing the ball to.
And you get some interesting differences, too. For example, in the Cavaliers, even though the ball started with the point guard, it immediately went to LeBron James, and you could actually see him as a central node. And he’s actually the distributing node. And then finally, you move to the Lakers, which is a classic Phil Jackson Lakers, and the pattern changes really kind of dramatically. The point guard becomes less central to the network, and you find that the ball is being distributed fairly evenly across all the players. Even Kobe is not actually sort of hogging the ball in the Phil Jackson Lakers; he’s distributing the ball also. And you get what we call a more “distributed network.”
That network also has another interesting feature, where if you look at any set of three players, they’re interconnected. So the shooting guard is not just connected to the point guard; he’s also connected to the power forward. And the center is not just connected to the point guard; he’s also connected to the shooting guard. And those triangles are what generate higher entropy in that graph compared to something like the Suns, where you have a central player making the decision.
Steven Cherry: And you looked at only 16 games, and we should mention that these were playoff games, but still you found one style to be generally more successful?
Jennifer Fewell: Yeah, we did. And I just want to say that basketball, one of the beauties of basketball is it’s a very complex sport, and so we can’t say that this is the strategy that works all the time. But in the 2010 playoffs, the graphs that were more successful were the graphs generally that had higher entropy. I think it was six out of eight matchups, the team that had higher entropy went on to win that round. And the two graphs that had the highest number of triangles that are connected to each other, that’s another measure called “clustering,” where you actually can say if A is connected to B and B is connected to C, is A also connected to C? Do they know each other or are they passing the ball to each other? The two teams with the highest clustering were the Lakers and the Celtics, so that was pretty nice to get that.
Steven Cherry: Because they did very well.
Jennifer Fewell: They did very well. They were the ones in the finals, so they did very well indeed.
Steven Cherry: I guess the obvious question is, Can you extend the research to things even more useful than basketball? In the paper you write, “The dynamic between within-group cooperation and conflict, and group versus individual success, is an inherent feature of both human and biological social systems.” Are there any lessons for businesses, for example?
Jennifer Fewell: Well, I would take objection to the “anything more useful than basketball.” I mean, basketball is useful in itself. It’s so beautiful. But, yes, I think it is something that we’re trying to push beyond the realm of just one specific sport or even one human social interaction. I think that these dynamics between cohesion and individual versus group success, biologically, is a central question in social theory.
I mean, one of the questions that you have in the success of any social group, from business to, I talk about “cooperative associations” of lions also, is how do you balance individual productivity with group productivity, individual success with group success. In a cooperative system, you have to have some benefit for all of the individuals in the group, but that can also cause a dynamic sort of trade-off between group success and individual success. I mean, for example, you might think of the ball hog, and there might be an analogy to that in business systems, where individuals are working for their own success but they’re actually damaging the function and cohesion of the group.
You see that in cooperative groups of social insects also. This is a big question, the interaction between cooperation and conflict, and how do you deal with conflict, because one individual is taking over resources. I think you could see this in the team network sort of interestingly in that some teams function specifically around a very successful individual, while other teams, the individuals who have the potential for success, back off from shooting, because that’s usually what individual basketball players are measured for, and distribute the ball more so that the team as a whole is more likely to win. So, yeah, I think it’s a really interesting dynamic that we were able to capture.
There’s a group that is doing network analyses on soccer teams, and they published a paper on European soccer players’ flow centrality, which sort of measures the probability that the ball will go through that individual, and compared their salaries based on flow centrality, and found that the ones that got paid more generally did control the ball more, which is interesting. So, yeah.
Ice hockey is another sport where I think you could do this. To me it seems stochastic because they’re always hitting each other, right. But apparently they control the puck more than I thought.
Steven Cherry: Your Ph.D. was in biology from the University of Colorado, and your dissertation concerned the foraging strategies of a particular species of harvester ants. It had the subtitle of “Costs, Currencies, and Constraints.” What are the costs, currencies, and constraints of harvester ants?
Jennifer Fewell: Oh, wow, that’s going back. I was interested in how individuals in a social group, ants in a colony, make decisions about what resources they bring back to the colony, so the cost, currencies, and constraints, I measured actually how much it specifically cost an ant to go out and collect a seed, what they use as decision criteria to bring seeds back, and what are the constraints on them in terms of their ability to switch strategies.
And it was very interesting, because ants, like basketball players, can’t make infinite decisions when they’re out there in the field, right? They have limitations on what they can do. We all do. And so if you don’t factor those into your consideration of the system, then you’re not going to have an accurate representation of what’s going on. Ants are very directional based. They can’t switch directions very easily. They memorize a path very well, but they don’t go in other directions very well. So that was one of the constraints on them.
Steven Cherry: I guess the lesson here, or at least one of the lessons here, is that networks are all around us. My undergraduate major was mathematics, so on behalf of all sports lovers, mathematicians, and especially sports-loving mathematicians, thanks for your research and for telling us about it today.
Jennifer Fewell: Well, thank you. I love talking about basketball, so it was a lot of fun.
Steven Cherry: We’ve been speaking with Jennifer Fewell about network theory, as applied to the basketball court, business, and the biological colony.
For IEEE Spectrum’s “Techwise Conversations,” I’m Steven Cherry.
This interview was recorded 7 March 2013.
Audio engineer: Francesco Ferorelli
Read more “Techwise Conversations” or follow us on Twitter.
NOTE: Transcripts are created for the convenience of our readers and listeners and may not perfectly match their associated interviews and narratives. The authoritative record of IEEE Spectrum’s audio programming is the audio version.
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