Using statistics to tell a sports story

July 3, 2020 | Science
Nicholas Lupul (Bachelor of Science, Applied Statistics, '20) has loved basketball since he first started playing it in eighth grade. But in Winter 2019, he took his love for the game to a whole new level. 

Studying abroad in Lithuania made it difficult for Nicholas to watch the Toronto Raptors compete in the playoffs. "Once it became clear that they had a shot at winning their first championship in team history, I would wake up between 2 and 4 stream the games on my laptop so I could watch them live," he says. "I watched around 20 of the Raptors' 24 games this way."

When Nicholas returned to Canada, he rewatched some of the games to study them in depth. "Turning it into a stats project seemed like the perfect way to get credit for doing something I love."



MacEwan University is celebrating student research with an ongoing series of stories that look at subjects our students were investigating throughout 2019/20. Many students who were planning to present at the 2020 Student Research Day have submitted their papers, posters and presentations to the university’s research repository, RO@M.

Title of work: "Kawhi Leonard’s impact on the Toronto Raptors’ 2019 playoff run as a Markov chain"

What is a Markov chain?

"Essentially a Markov chain is a sequence of events occurring with varying probabilities depending on the application," explains Nicholas. "The catch is that the only thing that determines the next step in the chain is the previous step."

Nicholas explains Markov chains like this: Imagine stepping stones that make up multiple paths through a garden. Some lead to dead ends, some loop back to the starting point or some take a turn but return to the main path. Now imagine a child running through the garden only stepping on the stones. Their next step depends only on what step they are currently on, so if they only have two options, they will randomly choose one to continue jumping from stone to stone.

"Markov chains can be used to model and study processes in the world in all fields of study from biology to sports," says Nicholas. "They are also used extensively in computer applications."
Another example of a Markov chain, Nicholas explains, is the algorithm used to determine what pages you see when you Google something.

What is your research about?

Nicholas's goal was to prove that Kawhi Leonard, a player on the Raptors, was crucial in the team winning the championship.

"In my analysis, I assigned the events, or 'states' as they are called, to 13 different events that are common in a basketball game: making a shot, missing a shot, turning over the ball or securing a rebound, for example," he explains. "From there, I mapped out on paper all possible paths or transitions between those states. With some help from my faculty supervisor, Dr. Karen Buro, to define the original chain, I was ready to begin data collection."

Data collection was the most time-consuming part of his research — Nicholas had to scroll through play-by-play accounts of all 24 games on and record every transition by hand as a tally. Each game took anywhere between 20 to 40 minutes to record, which turned out to be over 8,000 individual tallies.

"With this data I was able to calculate observed transition probabilities between each state and enter this into the computer program R, which we use for statistical analysis," he says. "From this point everything was done on the computer using R."

While he was able to confirm many of his hypotheses in the research, Nicholas says he would have liked to have had additional time to apply more data to the analysis to get more conclusive results.

What happened after?

Upon his faculty supervisor's recommendation, Nicholas submitted his paper to the MacEwan University Student eJournal (MUSe) and was also invited to present at the Canadian Statistics Student Conference in Ottawa. Though COVID-19 cancelled his travel plans, Nicholas was able to present his work virtually — and ended up winning the Best Undergraduate Presentation Award.

"Nicholas's presentation was very well laid out and the subject well explained," says Buro. "I am very impressed by the results and how well they were communicated.

"I felt very proud of myself as this was one of the first projects I did without a partner and did every step by myself, with Dr. Buro's guidance, of course," he says. 

Connecting Markov chains and basketball

In the Applied Statistics major, faculty members encourage students in the 300- and 400-level courses to choose topics of personal interest for their projects — one of Nicholas's favourite things about his degree.

His research on Kawhi Leondard's impact on the Toronto Raptors' playoff run wasn't the first time he got to study something he was interested in — past projects featured research into an NCAA march madness basketball tournament and the tabletop game Battleship.

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