Stochastic Tracking II: Next Gen Solutions and Player Performance

In our previous post on Stochastic Tracking, we took a look at motivating a Hierarchical Bayesian process in filtering tracking data and producing more robust estimators for the velocity. During the discussion, we limited the data sampled to be of two-dimensions only and had to assume that acceleration was constant between sampled points. Due to these limitations, we fail to capture other important information about player motion: verticality and explosiveness. To illustrate, we may ask the question from a player capability perspective: “How well does [player X] explode off the dribble to blow-by a defender?” Or we may ask the question from a player performance perspective: “In an effort to understand fatigue over the course of a sequence of days, how much load is being placed on a player?”

To capture data to answer these questions, we resort to “Next Generation” tracking methodologies; which are commonly equated to items such as wearable devices. In an effort to motivate Next Gen devices, let’s consider the aforementioned player performance problem.

Player Training: Internals and Externals

One of the goals for monitoring the load of a player is to help inform a coaching staff about the availability of a player. May it be at the micro-scale: say within the course of a game; or at the macro-scale: say over the course of several days. Early models propose that player performance increases with proper training, decreases when training is not applied, and plateaus if consistently applied.

Screen Shot 2018-09-26 at 7.45.21 AM.png

Basic Performance – Training relationship identified in Calvert et. al (1976).

To this end, no training is ever the same for two different players. One player’s body may be at a different stage of growth, a different type of build, and/or a different type of medical background. In order to understand the differences in training regimens, we must next need to define a “training model.” The most relatable model is strength and conditioning. But to simply say that training is only these two components would not only be dismissive, it would be a disservice to understanding basic player performance modeling. Instead, we start at S&C and ask how we define strength and conditioning.

Screen Shot 2018-09-26 at 7.49.18 AM.png

Using Calvert’s (1976) model, they propose a cardiovascular, strength, skill, and psychological component-based methodology. For the cardiovascular component, we measure endurance components such as oxygen intake, blood circulation, and blood lactate. We call these measurements the internal measurements of the system. For the strength component, we measure power output, speed, acceleration, and other various seemingly-odd measurements such as angular velocity, balance, and distributional force. We call these measurements the external measurements.

The skill measurement is the most well-known component in basketball. This component measures “competency” at completing tasks. One of the most basic measurements is shooting free throws after a sequence of sprints. Any basketball player from age five on up is most likely familiar with this practice-ending habit. At the professional level, more robust skill activities are performed; but the idea is still the same.

The psychological measurement is the most-publicized and least-understood of these four components. If you’ve ever seen a Gatorade commercial, you’ve seen marketing for this component. Here, we attempt to measure the “drive” of a player and attempt to understand the motivation for completing a task in the face of adversity; such as body fatigue. However, measuring this component is excessively difficult as it requires understanding the mental tenacity of a player.

Just on these four components, we see that only one component (skill) has been thoroughly addressed, while two others (cardiovascular and strength) are currently in the midst of a technological breakthrough, and the fourth (psychological) is still in its infancy. For internal measurements, we attempt to use monitors such as oxygen intake masks and heart rate monitors; but these are hidden state devices and we are still attempting to make head-way in better understanding how to measure internals of a player. For external measurements, we have the benefit of next generation devices; one of the best (at the moment) is the accelerometer.

Next Generation: Wearables

Over the previous handful of years, wearable devices have been mentioned as being an up-and-coming innovation in player tracking. Companies like Kinexon Sports, based out of Munich, Germany, have popped up to provide technology and dashboard-based insight into the external measurements of player motion. To be a complete system, it too provides a tracking methodology akin to Second Spectrum, but instead relies on a wearable radio frequency (RF) device instead of a camera-based device.

Since we introduced Kinexon as the example, let’s stick with their product as the exemplar. Despite the RF technology present in the wearable, it’s not so much the RF technology that creates the Next Gen solution. It’s the internal measurement unit (IMU) package they employ. Not to be confused with internal measurements from before, an IMU is an engineering concept for measuring the body in motion using a measurement device on the system. In this case, Kinexon deploys an accelerometer, a magnetometer, and a gyroscope.

Let’s focus on what these components actually do. Please note, this is not going into the specifics of what Kinexon does, but rather focuses on what the types of components can do. If you’re interested in the actual system, I refer you to click on their name above!


An accelerometer is a device that was invented within rocket science decades ago with the purpose of measuring acceleration of a rocket. A goal was to understand required accelerations to achieve proper trajectories for rockets to stay on a desired course. More importantly, the devices could measure rocket apogee and orientation. Today, accelerometers are used in cell phones as they help us with simple things like turning the screen on when we orient the phone towards our face.

Warning Techno-Babble: Decades ago, accelerometers were big and bulky; but today they are small. Small enough to fit inside a cell phone as a microchip. Acceleration is typically measured through the use of semi-conductance. An electrode sits inside a small “container” and is supported by a cantilever. The cantilever is wired to a circuit to process the electrode motion. Within the container, two other electrodes line the walls of the container, producing a couple of capacitors. As we move the container, the electrode shakes. The amount of capacitance that changes between the walls identifies the motion. More importantly, the chance in electric charge identifies not only the direction of motion, but the amount of motion as well. Hence we have acceleration in magnitude and direction!

Accelerometers give us fantastic measurements. They may be slightly messy, but from our previous stochastic tracking article we know we can filter the results and obtain quite reasonable estimates! Want to know which direction a player is actually moving? Look at the accelerometer data. At this point, we can revisit the stochastic model and remove the assumption that acceleration is constant between two points and now state I know the acceleration.

Despite now having acceleration in hand, we still don’t know certain aspects of the player motion: which way the player is facing or how fast a player is moving. The gyroscope helps us understand that.


The gyroscope is another important piece of wearable technology that actually has existed for nearly 200 years. The purpose of the gyroscope is to identify three-dimensional angular velocity. That is, understand when orientation is changing. One of the most common applications of the gyroscope is in Steadycam technology.

Warning Techno-Babble: Much like the accelerometer, the gyroscope of old are large devices. However, today’s gyroscopes can be modeled as a micro-electro-mechanical (MEM) system using silicon. In these small chips, a ring is typically suspended through an etching process, supported by a spoke system to help old the ring in place and measure its vibrations during movement. The vibrations then travel through the wired system where it is processed into vectors of motion. The result of this technology provides us with angular velocity and changes in orientation.

To illustrate its use, consider the simple running drill of sprinting to half court and turning to face and opponent; back-peddling the rest of the way. The accelerometer will identify the sudden drop in speed as you break into your turn, even providing the negative acceleration direction. The gyroscope will identify the actual speed and direction of speed throughout the process.

What neither the accelerometer nor the gyroscope tell us are, what direction is the player facing? To answer this, we use the magnetometer.


Magnetometers are effectively compasses. They identify directionality of an object. These devices are part of the MEMs technological package mentioned above and simply point to magnetic north. Thus, when fashioned to a player’s shorts at the logo along the waistline, the resulting vector is the direction at which the player is facing!

If we combine these three IMU components, we have the orientation of a player, which way they are moving, whether they are rotating, and how rapidly the changing their motion. Therefore, we are able to build a comprehensive model of player motion.

The only component we are missing is their actual location. Note: this is where the RF component of Kinexon comes in handy (and self-sustainable) and the camera-component of Second Spectrum helps.

By the way, with current technological capabilities, these devices are tiny and light-weight. Think roughly the weight of a AAA-battery and the size of a match-box.

Putting It All Together

So if we run with an IMU-based external measurement device and a position locating sensor, we are able to measure effectively all of our core mechanical motion. Set’s perform a simple exercise.

Suppose a player is located at (87.0, 30.0, 3.3). Consider the value 3.3 as the height of the wearable. Then as the player jumps for a rebound, we see the acceleration vector have a fairly large magnitude downward, decreasing at the position at which the player explodes upward, and then large magnitude vectors upward towards the basket. Similarly, we will obtain slight motion in the forward-backward directions and the left-right directions as the player squats (body motion may move backwards if the player is a poor jumper) and tilts for the ball (towards the basket).

Screen Shot 2018-09-26 at 9.35.56 AM.png

Of course, this is a simplified view of the acceleration. The data that comes out are x-,y-, and z-directed values relative to acceleration (or capacitance). Note that there is a sixth vector there, it’s just the value (0,0,0) as the player has come to rest before exploding upward.

The angular velocity plot is similar, but the vectors will be in much different directions, as they define the change in angular direction. Instead of plotting these vectors, instead focus on the acceleration plot and note what is striking. Got it? The vectors all come from the origin. This means, we do not know the players location. Therefore, we simply add these vectors to the position estimate to obtain the “Donnie Darko effect.” That is, a vector protruding from the player at each path between their initial point of the jump (87.0, 30.0, 3.3) and their position at some point after explosion (86.4, 28.7, 6.2).

The result is a diagram like such:

Screen Shot 2018-09-26 at 9.50.56 AM.png

IMU measurements superimposed on a player. We include the orientation (Green), angular velocity (blue), and acceleration (red). [Illustration Only]

Piecing all four components together, we obtain the player motion. In the illustrative image above, we obtain the orientation of the player (green vector) showing that he is facing the baseline during a rebound. Similarly, we obtain the angular velocity of the player (blue line), which is point upward and away from the basket, indicating the player is rotating backwards, upwards, and away from the basket. Finally, we obtain the acceleration of the player (red line), which is point downward and towards the corner of the key, which indicates the player is starting to be initiated in contact and coming near his apex in his jump.

All of this tracking cannot be obtained clearly from simple tracking points.

So Where Does Stochasticity Come In?

All this description has been about measuring the externals of a player, with very little mathematical modeling at the stochastic level. The reason why? Data is severely limited and enhanced modeling is in its infancy when it comes to player motion.

At the moment, we are able to improve the parameters of the stochastic model outlined in the previous article. However, that’s only a small piece of the puzzle. Instead, we’d like to measure load and fatigue; and study their effects on player performance. And to that end, we need to get working.


One thought on “Stochastic Tracking II: Next Gen Solutions and Player Performance

  1. Pingback: Stochastic Tracking II: Next Gen Solutions and Player Performance — Squared Statistics: Understanding Basketball Analytics – Advance Pro Basketball

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