Fig 2 - uploaded by David Radke

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# (a) Project 5 ways for p to pass to r (excluding corners). "Direct" pass if the path with least error (Euclidean distance from p i ) is ⃗ pr and/or puck is never within distance d b of the boards. (b) Calculate puck direction changes in the rink corners. "Rim" passes have more than three direction changes in a corner that are greater than threshold t θ . (c) Identify where the puck trajectory direction changes quadrants of the Unit Circle. "1-bank" passes have at most 3 of these points within distance d b of the boards for specific changes of direction.

Source publication

The implementation of a puck and player tracking (PPT) system in the National Hockey League (NHL) provides significant opportunities to utilize high-resolution spatial and temporal data for advanced hockey analytics. In this paper, we develop a technique to classify pass types in the tracking data as either Direct, 1-bank, or Rim passes. We also ad...

## Contexts in source publication

**Context 1**

... Rim Passes: The set of remaining completed passes are those not classified as Direct (i.e., indirect). Some indirect passes may be rims, where p directs the puck around a curved corner of the boards so the puck contacts the boards multiple times (Figure 2b). Our intuition to classify "Rim" passes is that the puck 1) changes direction multiple times and 2) these changes in direction are close to the corner boards. ...

**Context 2**

... intuition to classify "Rim" passes is that the puck 1) changes direction multiple times and 2) these changes in direction are close to the corner boards. To calculate general puck direction vectors (and reduce change in direction noise), we average every 10 readings for the puck locations for passes |p i | > 10 (red arrows in Figure 2b; shorter passes are not averaged). We calculate the difference in direction between adjacent vectors θ i p (in degrees), ...

**Context 3**

... we build on the intuition of detecting significant types of direction changes since a puck contacting the boards once will completely change its direction of travel. Our model draws on concepts from the quadrants of the Unit Circle in Trigonometry (Figure 2c left). To reduce the noise in the puck's trajectory we use an average of 10 consecutive readings (we do not use averages for short passes). ...

**Context 4**

... reduce the noise in the puck's trajectory we use an average of 10 consecutive readings (we do not use averages for short passes). For example, a sequence of 30 points could result in the three points p i a , p i b , and p i c shown on the right side of Figure 2c. We then calculate vectors between these points to determine the general direction of the puck (red and green vectors in Figure 2c). ...

**Context 5**

... example, a sequence of 30 points could result in the three points p i a , p i b , and p i c shown on the right side of Figure 2c. We then calculate vectors between these points to determine the general direction of the puck (red and green vectors in Figure 2c). In the right of Figure 2c, the red vector (from point p i a to p i b ) represents the puck traveling towards the boards (at 60 • ), and the green vector (from point p i b to p i c ) represents the puck traveling away from the boards after the contact (now at 120 • ). ...

**Context 6**

... then calculate vectors between these points to determine the general direction of the puck (red and green vectors in Figure 2c). In the right of Figure 2c, the red vector (from point p i a to p i b ) represents the puck traveling towards the boards (at 60 • ), and the green vector (from point p i b to p i c ) represents the puck traveling away from the boards after the contact (now at 120 • ). Note that angles are relative to 0 • which is the line perpendicular to the boards in this example. ...

**Context 7**

... plot these vectors for the puck traveling to and from the boards on the Unit Circle shown on the left of Figure 2c. For a 1-bank pass, our model identifies the three points (p i a , p i b , and p i c ) that comprise two consecutive vectors (red and green) where their directions appear in different quadrants of the Unit Circle (0 • , 90 • , 180 • , 270 • ). ...

**Context 8**

... is not possible for a puck to contact a straight segment of boards and continue in the same quadrant of the Unit Circle. Therefore, 1-bank passes are classified if three or fewer points associated with puck direction vectors that are within distance d b of the boards where the direction changes due to the boards (in the example in Figure 2c the angle of the vectors changes quadrants from Q1 to Q2). ...

**Context 9**

... consider an in-game example when both teams are at even strength (no penalties), consider a passer p. Given any potential receiver r, p has the option to make a Direct pass, or bounce the puck off either side-boards or end-boards (e.g., shown in Figure 2a). Some of these lanes will make more sense than others, since a player is unlikely to pass the puck off their defensive end-wall when in the offensive zone. ...