
a standard pitch dimension (105m x 68m) based
on the venue information associated with each
match, addressing variations in actual pitch sizes.
These normalized coordinates are then scaled to
fit a 104×68 grid representation for efficient pro-
cessing in NumPy and TensorFlow. Velocities are
smoothed using a Savitzky-Golay filter to reduce
noise.
• Direction Standardization and Cleaning: We
standardize the data by ensuring all attacks pro-
ceed uniformly from left to right. Additionally,
we remove instances of players recorded outside
the pitch boundaries to improve data integrity.
• Real Playing Time Calculation: To accurately as-
sess pass value, we calculate the actual playing
time, excluding periods when the ball is out of
play. This ensures that our evaluation window of
15 seconds following each pass reflects only the
active duration of the game, providing a more pre-
cise assessment of in-game actions.
• Data Alignment: To ensure synchronicity, we
align the event data with the tracking data. This
ensures that each pass event is accurately reflected
in the tracking data, enabling precise spatial and
temporal analysis. The tracking data includes ball
height (z-axis). Positional data from optical track-
ing systems inherently contains noise (with typi-
cal errors around 7–8 cm (Linke et al., 2020)); our
1 m grid resolution is robust to such deviations in
the (x, y) positions.
For the pass likelihood, pass success, and pass value
models, we use the features described in Fern
´
andez
et al. (2021) and additionally incorporate the z-value
(height) of the ball.
3.3 Model Architecture
We select a U-Net–type architecture (Ronneberger
et al., 2015) due to its proven effectiveness in image
segmentation tasks, which share similarities with pre-
dicting dense, spatially-aware surfaces like pass EPV
across the pitch. The U-Net’s encoder-decoder struc-
ture with skip connections allows the model to cap-
ture both fine-grained local details (e.g., player prox-
imity) and broader global context (e.g., overall team
formation), which are both crucial for accurate EPV
estimation.
Our pass OJN-EPV model takes a multi-channel
grid representation of the game state over the pitch
with dimensions (104×68) and produces a single out-
put grid of the same size. Each cell corresponds to
the predicted quantity at that location (e.g., pass suc-
cess probability, pass likelihood, or pass value). The
model comprises encoder and decoder blocks with
max pooling, replication padding, attention gates, and
concatenation layers. A diagram is provided in Fig-
ure 1.
Each encoder block applies two repetitions of:
replication padding, a convolution with a 5×5 kernel,
batch normalization, and a LeakyReLU activation (al-
pha = 0.1). The number of filters per block is 16,
32, and 64 in the contracting path, then 32 and 16 in
the expanding path to mirror the U-shape. Decoder
blocks consist of upsampling, replication padding, a
5×5 convolution with the corresponding number of
filters, batch normalization, and LeakyReLU (alpha
= 0.1).
Downsampling is performed by max pooling after
the first two encoder blocks; pooling is omitted after
the third to preserve spatial resolution. The most con-
tracted feature maps are 26×17.
In the decoder, feature maps are upsampled. At-
tention gates modulate the high-resolution encoder
features using a gating signal from the decoder before
concatenation. The concatenated features are then
processed by the decoder convolutional blocks, com-
bining local detail with global context.
The final layer uses a sigmoid activation for the
pass success model and softmax over the 104 × 68
grid for the pass likelihood model. For pass value,
we employ a softmax per grid cell with three classes
indicating outcomes within 15 seconds: goal for the
passing team, no goal, or goal for the opponent.
3.4 Model Training and Evaluation
We split the matches into training, validation, and test
sets using an 80-10-10 split for Eredivisie matches
and a 60-20-20 split for 2022 FIFA Men’s World Cup
matches. Due to the smaller size of the 2022 FIFA
Men’s World Cup dataset, we assign a higher per-
centage of samples to the validation and test sets to
enhance their statistical relevance. Table 1 shows
the distribution of successful and unsuccessful passes
across both datasets.
We first train on the larger Eredivisie dataset
and subsequently fine-tune on the 2022 FIFA Men’s
World Cup data. The training employs a cyclic learn-
ing rate, which fluctuates between a base learning rate
of 1× 10
−6
and a maximum learning rate of 1 × 10
−4
following a triangular policy with a full cycle lasting 8
epochs (Smith, 2017). This method helps to avoid lo-
cal minima. Subsequently, we fine-tune the model us-
ing data from the 2022 FIFA Men’s World Cup, where
the maximum learning rate is decreased to 1 ×10
−5
.
A batch size of 128 is used for all OJN-EPV mod-
els. Training stops when the validation loss does not
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