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Identifying Completed Pass Types and Improving Passing Lane Models


Abstract and Figures

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 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 receiver location error in over 94% of completed passes.
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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
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.
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= 4within 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
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
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 (spr ), 3) the duration of the pass (tPi), and 4) the expected
locations of receiver rand opponents o(rand o). Visualized in Figure 3b, we
fit the passing lane from pto rwith 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)spr produces a positive real number. We calculate the duration
of a pass as tPi=dPi
spr 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,rand 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 20 40 60 80 100 120 140 160 180
(a) Pass puck travel distances.
0 20 40 60 80 100 120 140
0 14 27 41 55 68 82 95
(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.
1 1.2 1.4 1.6 1.8 2
(a) CDF Extra Distance Traveled (zoom).
0 50 100 150 200 250 300
(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 1.25 1.50 1.75 2.00
(a) The γ-ratio by position.
-2 -1 0 1 2 3 4 5 6
(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
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.
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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Measuring football players' on-the-ball contributions from passes during games
  • L Bransen
  • J Van Haaren
Bransen, L., Van Haaren, J.: Measuring football players' on-the-ball contributions from passes during games. In: International Workshop on Machine Learning and Data Mining for Sports Analytics. pp. 3-15. Springer (2018)