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Identifying Completed Pass Types and Improving

Passing Lane Models

David Radke, Tim Brecht and Daniel Radke

David R. Cheriton School of Computer Science, University of Waterloo

Abstract. The implementation of a puck and player tracking (PPT)

system in the National Hockey League (NHL) provides signiﬁcant oppor-

tunities 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

address two fundamental limitations of our previous model for passing

lanes by modeling 1-bank indirect passes and the expected movement of

players. We implement our pass classiﬁcation and extended passing lane

models and analyze 198 games of NHL tracking data from the 2021-2022

regular season. We study the types of completed passes and introduce a

new passing metric that shows about 59% of completed 1-bank passes

have an equal or more open indirect passing lane than the direct lane.

Furthermore, we show that our expected movement addition reduces re-

ceiver location error in over 94% of completed passes.

Keywords: Hockey ·Passing ·Metrics ·Passing Lanes ·Tracking Data

1 Introduction

Ball and player tracking systems have revolutionized soccer and basketball ana-

lytics with extensive implications for scouting, coaching, player development, and

fan engagement. Recently, the National Hockey League (NHL) deployed a puck

and player tracking (PPT) system that records the location of the puck and ev-

ery player with high resolution and frequency (60 and 12 times per-second for the

puck and players respectively). Traditional methods of performance evaluation

in hockey have relied mostly on oﬀensive events like goals and shots despite these

representing only a small fraction of the actual game play. Hockey has lagged

behind other sports in advanced analytics due to technical challenges caused by

the fast pace, small puck, white-colored ice, and other hardware challenges [14,

13, 3]. However, the new tracking system broadens the scope of potential metrics,

analysis, and performance evaluations in hockey.

Most of the game play in hockey involves puck possession and passing between

teammates. Previously, we developed a model to quantify the availability of

passing lanes for completed passes, which associated smaller values with more

diﬃcult (or less open) passes [8]. While that model eﬀectively calculates the

available space between a passer and receiver, it assumes passes can only be

direct (i.e., they are not banked oﬀ of or around the boards) and it treats player

2 David Radke, Tim Brecht and Daniel Radke

locations as static with respect to the time the pass was initiated. In reality,

players often use the boards to complete passes when direct passing lanes are

small or unavailable and pass to where their intended receiver is expected to be

instead of where they are at the time the pass is initiated. In this paper, we

make the following contributions:

–We develop a model to classify completed passes in PPT data to be either

Direct, 1-bank, Rim, or Other passes. This is required to apply passing lanes

models that are appropriate for diﬀerent types of passes.

–We extend our passing lane algorithm [8] to 1) model the available passing

lanes for 1-bank indirect passes and 2) include the expected movement of all

players while the pass is made.

–We analyze passes using PPT data from 198 games from the 2021-2022

NHL regular season and devise a new metric for comparing completed 1-

bank indirect passes with the alternative direct passing lane to the same

receiver. We also examine the improvement in receiver location accuracy of

our expected player movement model.

2 Related Work

Numerous passing models have been developed for football (soccer) and bas-

ketball using tracking data. These are typically used to analyze aspects of the

game, such as pass disruptions to defensive formations [5], the expected value of

passes [2, 4], and the number of outplayed opponents by passes [11]. The focus

of that work is on the impact of passes instead of the actual diﬃculty or risk

associated with a pass, which could provide insight into decision making, skills,

and player risk proﬁles. Expected pass completion models (xPass) have gained

popularity in soccer and are used to estimate the probability of passes being

completed, or the diﬃculty of a pass, using physics [9], logistic regression [7],

Graph Neural Networks [12], and supervised machine learning [1]. While these

models can give signiﬁcant insight into a player’s decision making and passing

ability, they rely on data for incomplete passes or ball control which may be

diﬃcult to determine in hockey.

To model the availability of passing lanes without relying on data for incom-

plete passes, Steiner et al. [11] calculate the angle from the direct pass line to the

nearest opponent, where smaller angles correspond to less available passes. This

model is limited by not including opponents behind the passer or receiver and

not scaling for pass length. In response to these limitations, in previous work [8]

we deﬁned four key requirements for a passing lane model: 1) always assign a real

numbered value, 2) incorporate the area surrounding the passer and receiver, 3)

be asymmetric with respect to pass direction, and 4) scale with respect to the

pass length. Our passing lane model presented in [8] assigns a value to each pass

(in R+) that deﬁnes how open a passing lane is and simultaneously satisﬁes all

four requirements without requiring data for incomplete passes. In this paper,

we extend this passing lane model in three ways. We classifying diﬀerent types

of passes from the PPT data, calculate passing lanes for 1-bank indirect passes,

and model the expected movement of players.

Identifying Completed Pass Types and Improving Passing Lane Models 3

2.1 Background

Puck and Player Tracking Dataset Location data is collected through track-

ing technology that is inserted into the sweater of each player (back of the right

shoulder) and embedded into pucks. Location information contains x, y, and

z-coordinates to record locations in 3-dimensional space. The x and y locations

are relative to center ice (which is 0,0) and the z locations are relative to the

surface of the ice. The PPT data is recorded at 60 locations per second for the

puck and 12 locations per second for each player on the ice, resulting in a total

of about 734,400 location readings of main interest in a 60 minute game. Addi-

tional location data is obtained once a second for players that are deemed to be

oﬀ of the ice. The tracking data is accompanied by event data including shots,

goals, faceoﬀs, hits, and completed passes among others. These event labels con-

tain information about the time of the event and the identities of the players

involved.

Passing Lane Model To the best of our knowledge, the passing lane model

in [8] is the only attempt to quantify the availability of passing lanes in hockey.

The model uses the spatial locations of players in PPT data to estimate the

available space between a passer pand any receiver r. The model utilizes event

labels in the tracking data which have been identiﬁed by the data collection

company, SportsMEDIA Technology (SMT)1.

For each passing event, the passing lane model constructs a teardrop-like

passing lane shape (shown in Figure 1) between the x, y locations of a passer p

and receiver rthat simultaneously satisﬁes all four requirements listed in Sec-

tion 2. The size of this lane is determined by the locations of opposing players,

representing the space between pand rwithout opponents (i.e., the open space).

The passing lane size and shape is described by a positive real-numbered value

γ, where larger γvalues represent a wider lane and more open pass.

To determine the value of γfor a pass, we initialize γ= 0 (the direct line

from pto r,pr in Figure 1). In this paper, we relabel pr to be ⃗pr to use vector

notation. Increasing γexpands the passing lane shape until the edge of the lane

contacts the location of an opponent. For example, increasing γin Figure 1 grows

the passing lane from the blue, to the green, to the yellow shaded regions. Since

opponent 1 (o1) is contacted ﬁrst by the growing shape, the passing lane from p

to ris represented as the blue shaded region. The resulting γvalue is determined

to be the passing lane value (for eﬃciency, we implement binary search instead

of unidirectional growth). In Figure 1, γ= 0.6since it is the smallest γvalue

with respect to each opponent (i.e., o1was contacted by the growing passing lane

ﬁrst). While γhas no direct correspondence with completion percentage, values

of γcan be compared across time, locations, or players. We refer the reader to [8]

for a more detailed description about the original passing lane model.

1www.smt.com/hockey

4 David Radke, Tim Brecht and Daniel Radke

Fig. 1: Passing lane diagram from [8]. This example shows three passing lane

shapes regulated by a parameter γ. The passing lane grows until the edge con-

tacts the nearest opponent. The passing lane in this example has value γ= 0.6

and is the blue shaded region (the others are included as examples if o1or o2

did not exist). In this work, we relabel the direct passing line pr as ⃗pr.

3 Completed Pass Classiﬁcation

The PPT data includes event labels to identify instances of a completed pass;

however, there are multiple ways to pass the puck in hockey that should be

modeled diﬀerently. A passer pcan pass directly to r(a Direct pass), bank oﬀ a

ﬂat section of boards (a 1-bank pass), or rim the puck around a curved corner

of the surrounding boards (a Rim pass). We construct a model to identify these

types of completed passes from the PPT data and overcome several challenges

in the process. For example, there may exist some noise in the exact location

of the puck (potentially from puck ﬂuttering or position accuracy) or the time

labels associated with passes. We found that the trajectory of passes cannot be

assumed to compose perfectly straight lines, even for Direct passes. The puck

may also contact the boards between consecutive readings of its location (i.e.,

the puck is traveling towards the boards at time tbut traveling away from the

boards at time t+ 1). Thus, the puck location never truly contacts the boards in

the data. Our model uses a sequential ﬁltering approach to diﬀerentiate between

completed passes that are Direct, 1-bank, and Rim passes, and leave more ﬁne-

grained classiﬁcation for future work.

Let Pbe the set of all passes in a game, Pi∈ P be a single pass, and pi

be the set of x, y puck locations for Pi(origin at center ice). Our classiﬁcation

algorithm identiﬁes: 1) Direct (Pd), 2) Rim (Pr), and 3) 1-bank (P1) passes in

that order, each time reducing the set of possible passes to consider (starting at

P). The remaining unclassiﬁed passes compose a fourth class, Other, which we

discuss in detail later. Since two consecutive readings close to the boards may

represent actual contact with the boards (a challenge described above), all three

phases use a value db, a distance from the boards, to construct a buﬀer that is

used to determine puck readings that are suﬃciently close to the boards.

Identifying Completed Pass Types and Improving Passing Lane Models 5

1) Direct Passes: We identify completed Direct passes using two charac-

teristics: 1) they may never be close to the boards and 2) have relative straight

trajectories when compared with the possible indirect passes to the receiver. Our

algorithm has two phases. First, if no points in piare within distance dbof the

boards, Piis classiﬁed as to be Direct. Since Direct passes may also happen

close to the boards, if any points in piare within distance dbof the boards,

we proceed to the second phase. If not identiﬁed as a Direct pass in the ﬁrst

phase, we determine the ﬁve possible paths for pto pass to r, ignoring corners

(i.e., the direct path ⃗pr, and oﬀ of both side-boards and both end-boards). Fig-

ure 2a shows this procedure in an example box (not-to-scale). The purple dots

represent pi, which has some change in direction near the receiver (i.e., likely

contacting the receiver’s stick before being considered received). To mimic actual

puck behavior, we remove any of the ﬁve passing paths that contact the net or

a rounded corner since the puck would not follow the projected trajectory fol-

lowing contact. We estimate the error from Pito each projected path using the

total Euclidean distance from each of the points pito each of the ﬁve possible

paths. If ⃗pr has the least error, the pass is considered Direct.

(a) Direct (b) Rim (c) 1-bank

Fig. 2: (a) Project 5 ways for pto pass to r(excluding corners). “Direct” pass if

the path with least error (Euclidean distance from pi) is ⃗pr and/or puck is never

within distance dbof 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 tθ. (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 dbof the boards for speciﬁc changes of direction.

2) Rim Passes: The set of remaining completed passes are those not classi-

ﬁed as Direct (i.e., indirect). Some indirect passes may be rims, where pdirects

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. To calculate general puck direction vectors (and reduce

change in direction noise), we average every 10 readings for the puck locations

for passes |pi|>10 (red arrows in Figure 2b; shorter passes are not averaged).

We calculate the diﬀerence in direction between adjacent vectors θi

p(in degrees),

6 David Radke, Tim Brecht and Daniel Radke

and deﬁne a threshold tθto determine if a direction change is suﬃciently large.

Since direction changes can have several causes (e.g., deﬂection from a stick,

player, or referee) we only consider those direction changes that occur within db

of the corner boards. In our implementation, a Rim pass is determined to have

greater than three direction changes greater than tθ= 4◦within distance dbof

the corner boards. We choose three points since 1-bank passes should contain

at-most three points with speciﬁc direction changes (explained next).

3) 1-bank Passes: From the remaining completed passes, we determine the

set of 1-bank passes, where the puck only contacts a straight segment of the

boards once. Since we are only detecting a single change in direction, the model

for Rim passes is unable to be adapted since a change in the puck’s direction

of travel could happen for any number of reasons (i.e., deﬂections from sticks,

inaccuracies in device readings, or inaccuracies with time labels associated with

the pass). Therefore, 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). For example, a sequence of 30 points could result in the three

points pi

a,pi

b, and pi

cshown 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 pi

ato pi

b) represents the puck traveling towards the boards (at 60◦), and

the green vector (from point pi

bto pi

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.

We 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 (pi

a,pi

b, and pi

c) that comprise two consecutive vectors (red and

green) where their directions appear in diﬀerent quadrants of the Unit Circle

(0◦,90◦,180◦,270◦). It 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 dbof 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).

4 Passing Lanes for 1-bank Passes

The original passing lane model only considers the direct line from pto r, which

only represents Direct passes. For example, the model would consider the passing

lane from pto rin Figure 3a extremely small (red arrow) because there is an

opponent odirectly on the path from pto r. However, a 1-bank pass can avoid

the opponent oand is more open than the Direct pass. Our goal in this section

is to model such passing lanes.

Identifying Completed Pass Types and Improving Passing Lane Models 7

(a) 1-bank Passing Lane (b) Expected Movement

Fig. 3: (a) We calculate passing lanes for 1-bank passes by reﬂecting receiver r

and opponent oabout the boards. (b) We ﬁt the passing lane to the expected

movement of rand ousing their locations, velocities, and expected pass distance.

Using the theory of geometric reﬂections, a 1-bank pass oﬀ the boards is

geometrically equivalent to a Direct pass through the boards to a reﬂected rep-

resentation of r(ˆr). This assumes the angle of incidence is equal to the angle of

reﬂection which we acknowledge may not be completely accurate due to puck

spin, ﬂuttering, board imperfections, and variables such as drag and energy loss.

However, our model is an approximation of the available passing lane instead

of modeling the exact trajectory of the pass. We reﬂect all players besides the

passer about the boards so that the 1-bank pass can be modeled as a Direct

pass (in Figure 3a, green dotted line can be modeled as the orange dotted line

extension). In the example in Figure 3a, we keep pat it’s location and reﬂect

rand oto locations ˆrand ˆorespectively. Using ˆras the location of r, we cal-

culate the passing lane with respect to the nearest opponent (also considering

their reﬂections). We acknowledge that 1-bank passes should be considered more

diﬃcult than Direct passes. This is accounted for in our model, as γscales with

the pass length and a 1-bank pass would be longer than the Direct pass.

To consider an in-game example when both teams are at even strength (no

penalties), consider a passer p. Given any potential receiver r,phas 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. Since γdecreases as the length increases, excessively long 1-bank

passes will receive very low γvalues. We calculate γfor all ﬁve passing options

from pto rwith respect to all opponents. The largest γvalue is the most open

passing option for pto pass the puck to r. We expect a similar reﬂection-based

methodology may work for Rim passes, but leave this for future work.

5 Expected Player Movement

To compute γ, the passing lane algorithm in [8] uses the locations of players

taken at the time the pass is initiated. The asymmetry of the passing lane shape

8 David Radke, Tim Brecht and Daniel Radke

accounts for opponents closer to rhaving more time to react to a pass (i.e., skate

towards the pass and/or move their stick in an attempt to intercept or disrupt

the pass). Furthermore, receiver rwill most often not be stationary and receive

the pass at a diﬀerent location than where they were when the pass was initiated.

We expand the previous passing lane model to include the expected location of

all players when computing the passing lane. In Section 6, we demonstrate how

our new model improves the expected location of the actual pass reception. Our

method calculates 1) the approximate distance of a pass Pi(dPi), 2) the expected

speed of the pass (s⃗pr ), 3) the duration of the pass (tPi), and 4) the expected

locations of receiver rand opponents o(r′and o′). Visualized in Figure 3b, we

ﬁt the passing lane from pto r′with respect to o′.

The approximate pass distance (dPi) is calculated using the Euclidean dis-

tance from pto where the pass is estimated to be received (r′), deﬁned later.

Given the approximate pass distance, we train a linear regression model on pre-

vious passes πto produce the expected speed of a pass with distance dPi, so

that π(dPi)→s⃗pr produces a positive real number. We calculate the duration

of a pass as tPi=dPi

s⃗pr and use r’s velocity vector (which includes direction) at

the time of the pass vrto determine their expected location, r′=r+tPivr.

This assumes rwill continue in the current trajectory for tPitime.

Since opponents only have until the puck passes their location to disrupt the

pass, we only project o’s movement for time to, the time until the puck passes

their location along the pass trajectory ⃗pr. For this computation, consider the

example in Figure 3b where ois located between pand r. Taking the dot product

of owith respect to pand the direct passing line ⃗pr determines the perpendicular

location of oonto ⃗pr (the red dashed line in Figure 3b). The expected time for the

puck to reach this intersection is calculated to be to. If ois behind p,to= 0, and

if ois behind r,to=tPi. We solve o′=o+toor, where oris the velocity vector

for oat the time the pass is made. Given the locations of p,r′and o′, we calculate

the passing lane using the algorithm from [8], shown as the blue shaded region

in Figure 3b. In this example we only show one rand ofor simplicity; however,

we can calculate passing lanes for any rwith respect to all opponents. This

allows us to determine the receiver with the largest passing lane (i.e., the most

open player). The tracking data does not include information on stick location,

although this could be included if collected or estimated in future work.

6 Analysis

We implement our pass classiﬁcation algorithms and passing lane extensions to

analyze completed passes using a combination of the raw tracking data and la-

beled event data. Our dataset is from 198 games played in November of the

2021-2022 NHL regular season. We utilize the pass event labels in the dataset

to determine when a pass was made; however, this dataset does not contain la-

bels for passes that were not completed. Additionally, the automated labeling

of events is a diﬃcult problem; thus, the dataset may be missing some com-

pleted passes and/or include labels for events that are not actually completed

Identifying Completed Pass Types and Improving Passing Lane Models 9

passes. This dataset is still considered unoﬃcial by the NHL, and may diﬀer from

other datasets that contain complete and/or incomplete passes (e.g., a hand la-

beled dataset). In this paper, we utilize the event labels provided in the dataset

while including techniques to handle some, but not all, inaccuracies. We ana-

lyze features of our classiﬁcation algorithm, 1-bank passing lanes, and expected

movement extensions in isolation to identify interesting passing behavior and

hypothesize about the potential performance of our models in the absence of

ground truth data.

6.1 Pass Classiﬁcation and Statistics

We ﬁrst analyze general features of the completed passes in our dataset and

how our classiﬁcation model diﬀerentiates them. We observed db= 2.5feet

(ft) captures multiple adjacent puck readings for Rim and 1-bank passes that

are close to the boards in most cases. Table 1 shows the results of our pass

classiﬁcation algorithm on the set of all completed passes. Since our tracking

dataset only includes completed passes, the information may be biased towards

successful events and not necessarily reﬂect the game as a whole (i.e., what

was attempted and failed). As shown in Table 1, our model identiﬁes 84.4% of

the passes labeled complete in this dataset to be Direct, 10.2% to be 1-bank,

2.6% to be Rim, and 2.8% to be Other. Forwards as a whole tend to complete

slightly more passes (49.5%) than defence (47.2%); however, when considering

there are typically two defence and three forwards on the ice, a defensive player

on average completes 43% more passes than a forward. We consider the relatively

small percentage of unclassiﬁed completed passes (Other) to be acceptable, but

is something we plan to examine in future work. After manually inspecting a

signiﬁcant number of these unclassiﬁed passes, we believe that most are either

mislabeled as passes or consist of edge-cases that are diﬃcult to identify (e.g.,

inaccurate timestamps resulting in odd changes in trajectory by a player).

Type Direct 1-Bank Rim Other Total

Forward % 41.9 4.8 1.2 1.5 49.5

Defence % 39.7 5.1 1.2 1.1 47.2

Goalie % 2.8 0.3 0.2 0.1 3.4

Avg/Game % 84.4 10.2 2.6 2.8 100.0

Table 1: Completed pass categorizations. Note that this data is based on events

labeled as completed passes. Actual values may diﬀer if labels are incorrect,

missing and/or if incomplete passes are included.

Figure 4 compares the paths of completed 1-bank passes made by defence

(left) and forwards (right). Darker green represents more 1-bank passes in that

region. We see that most of the completed 1-bank passes initiated by defence are

10 David Radke, Tim Brecht and Daniel Radke

behind their own net or oﬀ the defensive half-walls. In contrast, the majority of

completed 1-bank passes from forwards are made behind the oﬀensive net or oﬀ

the oﬀensive half-walls (likely passing back to defence).

Fig. 4: Heatmap of completed 1-bank passes; defence (left), forwards (right).

Figures 5a and 5b show Cumulative Distribution Functions (CDF) for pass

distance (puck travel distance) and pass speed for completed passes, calculated

by comparing the total puck travel distance with the duration of the pass. For

example, half (0.5) of all completed passes had a distance of about 38 ft or

less, shown in Figure 5a. Interestingly, while the distances for completed indi-

rect passes (1-bank and Rim passes) are typically longer than completed Direct

passes, we observe almost no distinct diﬀerence between these classes for pass

speed (Figure 5b). Thus, we hypothesize that players pass the puck harder to-

wards the boards for indirect passes than they would for a Direct pass, to account

for the expected energy loss from the boards. The distributions of this data may

be diﬀerent when considering all pass attempts.

0.00

0.25

0.50

0.75

1.00

0 20 40 60 80 100 120 140 160 180

CDF(Fraction)

Distance(ft)

All

Direct

1-Bank

Rim

Other

(a) Pass puck travel distances.

0.00

0.25

0.50

0.75

1.00

0 20 40 60 80 100 120 140

0 14 27 41 55 68 82 95

CDF(Fraction)

Feet/sec

MPH

All

Direct

1-Bank

Rim

Other

(b) Pass speeds.

Fig. 5: (a) CDF of pass length (distance traveled) for each type of completed

pass. (b) Speed of completed passes for each type (distance traveled divided by

total duration of the pass).

Figure 6a shows a CDF for the extra distance the puck traveled for each type

of pass. We calculate this as dpuck

dp,r , where dpuck is the actual distance the puck

traveled and dp,r is the Euclidean distance from pto r(i.e., the shortest path for

Identifying Completed Pass Types and Improving Passing Lane Models 11

the puck). In theory, Direct passes should have the least extra distance traveled

compared to dp,r and Rim passes must travel corners which accumulates more

distance. Figure 6a shows that Direct passes generally do travel the least extra

distance, followed by 1-bank, and Rim passes.

0.00

0.25

0.50

0.75

1.00

1 1.2 1.4 1.6 1.8 2

CDF(Fraction)

PuckPathDistance/Shortest

Direct

1-Bank

Rim

Other

(a) CDF Extra Distance Traveled (zoom).

0.00

0.25

0.50

0.75

1.00

0 50 100 150 200 250 300

CDF(Fraction)

PuckPathDistance/Shortest

Direct

1-Bank

Rim

Other

(b) CDF Extra Distance Traveled.

Fig. 6: (a) CDF comparing the distance the puck traveled to the shortest possible

distance (Euclidean distance from pto r) for completed passes. (b) Zoomed out

CDF to show the long tail, likely due to event labeling or classiﬁcation errors.

We do note that the actual path of most Direct passes is longer than the

shortest possible path (dp,r ). These passes are those with values on the x-axis

greater than 1. Extreme examples of this can be also seen by the long tail in

Figure 6b (an un-zoomed version of Figure 6a). We believe this is due to pucks

being deﬂected by sticks or bodies (but the pass should still be considered Di-

rect). Furthermore, inaccuracies in the timestamps of pass events also lead to

add additional distances.2Motivated by these challenges, our ﬁrst classiﬁcation

phase considers such passes Direct if the puck is not within distance dbfrom

the boards during the pass. We hypothesize that the Direct, 1-bank, and Rim

ordering for extra distance in Figure 6a provides some insight into the accuracy

of our classiﬁcation algorithm despite these artifacts.

6.2 Passing Lanes for Indirect vs Direct Passes

We now analyze our addition to the passing lane model for calculating 1-bank

passing lanes. Without any ground truth for how open a passing lane is, our goal

is to analyze how our passing lane model captures 1-bank passing behavior by

comparing Direct and indirect passing lanes for completed 1-bank passes. For

this analysis, we only consider the set of completed 1-bank passes for the reason

that a more open indirect passing lane does not always indicate a better play

and depends on the context of the game. For example, a player will likely opt

2By manually inspecting a signiﬁcant number of these cases, we observed the times-

tamp at the end of the pass may occur after the pass was received and the receiver

changed directions.

12 David Radke, Tim Brecht and Daniel Radke

for a Direct pass on a 2-on-1 oﬀensive rush instead of a 1-bank pass, even if the

1-bank is technically more open.

For each completed 1-bank pass, we calculate the value of the indirect 1-bank

passing lane γias well as the direct passing lane γdfor pto pass to receiver r

and deﬁne a new metric, γ-ratio =γd

γi. If the γ-ratio < 1, the indirect passing

lane was more open than the direct lane, otherwise the Direct pass was actually

more open. Figure 7a shows a CDF of the γ-ratio for completed 1-bank passes

separated by player position for forwards and defence. We observe that about

59% of 1-bank passes were completed when the 1-bank passing lane was equal to

or more open than the direct passing lane size (the γ-ratio ≤1). There is little

diﬀerence between the behavior of forwards and defence when the γ-ratio < 1;

however, when the γ-ratio > 1, defence tend to make more 1-bank passes when

both lanes are similar (i.e., the γ-ratio closer to 1).

Note that in Figure 7a the x-axis is centered around 1 and is limited to a

maximum of 2, since if γdis much larger than γi, the γ-ratio grows instead of

trending to zero. For an in-game scenario, Figure 8 (left) in Section 7 shows how

our model captures the 1-bank passing lane from Player #86 (who has possession

of the puck) up to Player #3, whereas our previous model [8] does not. For this

pass, the γ-ratio =0.23

0.46 = 0.5and completing this pass increases the subsequent

passing lane to Player #28 from γ= 0.3to 0.98 (right side of the ﬁgure).

0.00

0.25

0.50

0.75

1.00

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Directlane>IndirectlaneIndirectlane>Directlane

CDF(Fraction)

Ratio

Directlane/Indirectlane(Forwards)

Directlane/Indirectlane(Defence)

Directlane/Indirectlane(All)

(a) The γ-ratio by position.

0.00

0.25

0.50

0.75

1.00

-2 -1 0 1 2 3 4 5 6

CDF(Fraction)

Feet

ErrorReductions

(b) Expected movement improvement.

Fig. 7: (a) CDF of the γ-ratio to show the fraction of completed 1-bank passes

where the 1-bank passing lane was more open (< 1) or direct lane was actually

more open (> 1). (b) Location of rerror improvements with expected movement.

6.3 Player Movement

Our motivation for including expected player movement when model passing

lanes is to better ﬁt the shape of the passing lane to the location of the receiver

when they receive the pass (and opponents to where they would be when the

puck passes their location). For the set of all completed passes, we have the

labeled location of the receiver at the time when the pass is considered received

(r∗

t). Therefore, we calculate the diﬀerence between r∗

tand their location when

Identifying Completed Pass Types and Improving Passing Lane Models 13

modeled with expected movement (r′

t) and without expected movement (rt). We

calculate the two location errors as the Euclidean distance between 1) r’s true

location and their projected location with expected movement (r∗

tand r′

t), and 2)

r’s true location and their location without expected movement (r∗

tand rt). The

diﬀerence of these two errors provides insight into whether or not the expected

movement model better estimates the location of rwhen they receive the pass

(i.e., there less error). Figure 7b shows a CDF for the diﬀerence between these

two errors, where positive values correspond with expected movement reducing

the location error by the distance along the x-axis (more accurate location of

r). We ﬁnd that expected movement reduces the error of r’s location for over

94% of passes, in one case up to 5.3 ft, and increases error in a small fraction of

passes by a small amount (at most up to 2.0 ft).

7 Potential Applications

The inﬂux of data in professional sports has given broadcasters and fans the

ability to absorb more information about an event, such as shot speed, shift

length, or face-oﬀ win probabilities; this information is typically presented by

overlaying graphics or augmented reality (AR) on the live video broadcast. Our

passing lane model can also be used in this context to display the most available

passing option for one or more teammates, or the γof a successful pass. Further-

more, our model could provide more ﬁne-grained metrics that may be useful in

fantasy sports or gambling applications. This can increase fan engagement and

enjoyment by drawing attention to player formations and passing options.

When reviewing video of games, our passing lane model would give players

and coaches quantitative data for the availability of passing lanes to devise new

plays or assess performance. For example, the “up-and-over” is a common pow-

erplay sequence to shift the defence to a new side of the ice and open passing

lanes to certain players, shown in Figure 8. Using our models, coaches would be

able to adjust the location of oﬀensive or defensive players to ﬁnd positioning to

increase passing lane sizes, or to reduce the size of an opponent’s passing lanes.

While GMs are tasked with constructing rosters and assessing players, watch-

ing every game or shift of a player is often infeasible and current metrics (such

as goals and points) provide only a coarse view of player performance skewed

towards oﬀense. Our passing lane model could quantify passing behavior in a

game or across a season (for assessing consistency). If augmented with incom-

plete passes, our model could determine how often players force passes when a

more open alternative is available and provide insights into the passing skills of

players (e.g., whether players manage to complete passes with smaller lanes).

8 Discussion

The high fraction of the γ-ratio ≤1 (59%) shows that NHL players in our dataset

typically complete 1-bank passes when the indirect lane is larger or equal to

14 David Radke, Tim Brecht and Daniel Radke

Fig. 8: Powerplay scenario for the Orange team, showing the best passing lanes

to each player at times tand t+i. At time t(left ﬁgure), Player #86 has the

puck. Our new passing lane model identiﬁes the 1-bank lane to Player #3 as

being the most open (twice as large as the direct lane). Player #86 chooses this

lane for their pass (purple line). At time t+i(right ﬁgure), after Player #3

receives the pass, the cross-ice lane to #28 increases from 0.3 to 0.98 (a factor

of 2.3). Completing this pass is known as an “up-and-over” on the powerplay.

the direct lane deﬁned by our model. Reducing the location error for rin the

majority of completed passes (94%) shows that expected movement better aligns

with where NHL players pass the puck than when it is not included. However,

our analysis has several limitations that are important subjects of future work.

First, since our dataset only contains completed passes, our analysis may not

accurately reﬂect the full behavior of all attempted passes. Another potential

application of our model may be to identify incomplete passes based on the

movement of the puck; however, this is beyond the scope of this paper.

Second, more accurate time labels for the start and end of passes would

improve the precision and scope of future passing models. More accurate time

labels would also improve the ability to calculate the speed of passes which has

implications on the pass speed model we use for expected movement.

Third, future datasets could allow for more concrete evaluations such as cal-

culating classiﬁcation accuracy and lead to the development of new models. A

ground truth dataset of pass types could be used to evaluate the accuracy of our

classiﬁcation model and allow our system to learn classiﬁcation thresholds di-

rectly from data instead of observing and deﬁning values. Furthermore, a dataset

of incomplete passes could help analyze correlations between game context, γ

values, and pass completion probabilities.

Identifying Completed Pass Types and Improving Passing Lane Models 15

Fourth, extensions to the current passing lane model could explore a series of

diﬀerent directions. Rim passing lanes are a natural extension of this work. We

could further improve the passing lane model to include more advanced meth-

ods of expected movement, such as predicting a player’s movement with machine

learning (i.e, ghosting) [6], physics-based approaches used in soccer [10], or con-

sidering handedness, reach, and stick length. When modeling the expected speed

of a pass, a future iteration may consider personalized pass proﬁles by observ-

ing previous passes only by a speciﬁc player, their location, position, orientation

(augmented from a visual dataset since this is not in the PPT data), or type of

pass (i.e., Direct, 1-bank, or Rim). Another potential pass classiﬁcation could be

drop passes, which have signiﬁcantly diﬀerent dynamics (player movement and

puck speed) than most Direct passes. Furthermore, future work can leverage

the zcoordinate of the puck to analyze who makes saucer passes and where, a

common pass in hockey that elevates the puck oﬀ the ice.

Finally, we would also like to conduct a sensitivity analysis to determine if

our classiﬁcations are sensitive to db,tθ, and other variables.

9 Conclusions

The new PPT system implemented by the NHL has opened the door for a

broader scope of hockey analytics to better model higher resolution events of

the game. In this paper, we present an algorithm to classify diﬀerent types of

passes from PPT data and extend the passing lane model in [8] to include 1-

bank indirect passes and the expected movement of players. Our model estimates

that 1-bank passes comprise about 10.2% of all completed passes in our dataset

and make up the majority of non-Direct passes completed. We present gamma-

ratio, a metric to model the relationship between direct and indirect passing

lanes available to a passer. Our model calculates the indirect passing lane to be

equal or more available than the direct lane for approximately 59% of completed

indirect passes. Furthermore, we show that including the expected movement

of players reduces the error in modeling the location of the receiver when they

receive the puck for over 94% of completed passes. As PPT systems continue to

expand and improve, the impact of algorithms to leverage this type of data will

only increase.

Acknowledgments

This research is partially funded by the Natural Sciences and Engineering Re-

search Council of Canada (NSERC), an Ontario Graduate Scholarship, a Cheri-

ton Scholarship, and the University of Waterloo President’s Graduate Schol-

arship. We thank Brant Berglund, Christopher Baker, Keith Horstman, Neil

Pierson, and Russell Levine from the National Hockey League Technology, Stats

and Information Team for their participation in fruitful discussions and their

insights related to this work. In particular we would like to thank Christopher

for his timely and insightful comments on drafts of the paper. We thank Jonah

16 David Radke, Tim Brecht and Daniel Radke

Eisen, Neel Dayal and Oguzhan Cetin from Rogers Communications and Colin

Russell and Aaron Pereira from the University of Waterloo, for their help in

getting this project oﬀ the ground. We especially thank Neel Dayal for his ef-

forts in creating the relationship with the NHL, providing us with access to the

dataset and the talented group at the NHL. We also thank Alexi Orchard for

her feedback and useful discussions on drafts of this work.

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