  In team-based invasion sports such as soccer and basketball, analytics is
important for teams to understand their performance and for audiences to
understand matches better. The present work focuses on performing visual
analytics to evaluate the value of any kind of event occurring in a sports
match with a continuous parameter space. Here, the continuous parameter space
involves the time, location, score, and other parameters. Because the
spatiotemporal data used in such analytics is a low-level representation and
has a very large size, however, traditional analytics may need to discretize
the continuous parameter space (e.g., subdivide the playing area) or use a
local feature to limit the analysis to specific events (e.g., only shots).
These approaches make evaluation impossible for any kind of event with a
continuous parameter space. To solve this problem, we consider a whole match as
a Markov chain of significant events, so that event values can be estimated
with a continuous parameter space by solving the Markov chain with a machine
learning model. The significant events are first extracted by considering the
time-varying distribution of players to represent the whole match. Then, the
extracted events are redefined as different states with the continuous
parameter space and built as a Markov chain so that a Markov reward process can
be applied. Finally, the Markov reward process is solved by a customized
fitted-value iteration algorithm so that the event values with the continuous
parameter space can be predicted by a regression model. As a result, the event
values can be visually inspected over the whole playing field under arbitrary
given conditions. Experimental results with real soccer data show the
effectiveness of the proposed system.
