Please note: This article was written before Kyle Lowry was signed by the Raptors to a one year contract extension, meaning he will no longer be a free agent next summer. Clearly, Masai Ujiri was listening to our advice!

Flexing our analytics muscles means approaching and solving problems with a scientific and actionable perspective. Our process – called ‘Write the Speech’ – involves four steps:

  1. Think carefully about the desired outcome,
  2. Identify the decision we’re trying to inform,
  3. Generate hypotheses, and
  4. Do the research to confirm or deny the hypotheses.

By following these steps and starting with the end in mind to help focus research, we avoid analysis paralysis and arrive at insights that are not only interesting but also actionable.

Though we are researchers and analytics experts, we are also huge sports and Toronto Raptors fans. We love solving data problems, and as we begin the new NBA season, we decided to give ourselves a hypothetical analytics project. We imagined a problem that Masai Ujiri, the General Manager of the Toronto Raptors, might bring to us:

‘Next summer, three of our well-established veteran players – Kyle Lowry, Marc Gasol, and Serge Ibaka – will become free agents, meaning any of them could leave the Raptors to join other teams. They will all be looking for big pay days so we won’t be able to keep all three on our team. There are lots of statistics we can use to compare players, but the value of these three players is intangible. It goes beyond scoring baskets and other traditional stats. We’re worried that traditional numbers might not capture their true value. Specifically, we want to understand how well these players help our team get the ball more often (possessions), and thus give us more chances to score baskets. Especially in Lowry’s case, we believe this might set him apart. Could you tell us which of these three players gets our team the most possessions on the court?’

We began by reframing the problem in terms of our ‘Write the Speech’ process. 

Think carefully about the desired outcome

The desired outcome is for Ujiri to identify and sign the veteran player who would help the Raptors get the most possessions, and thus the most chances to score baskets, win games, and ultimately win more championships.

Identify the decision we’re trying to inform

Ujiri wants to know which of the three players would help the Raptors get the most possessions with the basketball to help inform his decision of which player to sign.

How would we provide him with this information? Data on possessions is not readily available so we would have to find another metric that could act as a proxy. Since 87% of possessions end with a shot attempt at the basket (regardless of whether or not the shot goes in), we thought that shot attempts would make an effective proxy for number of possessions. To determine which player gave the Raptors the most possessions relative to their opponent, we calculated the number of Raptors’ shot attempts and compared it to the number of opponent shot attempts while each Raptors player was on the court. We will refer to this statistic as ‘shots plus-minus’ since after Raptors’ shot attempts are compared with opponent shot attempts, each player will end up with either more Raptors’ shots than the opponent (a ‘plus’) or fewer Raptors’ shots than the opponent (a ‘minus’).

Generate hypotheses

All three players – Lowry, Gasol, and Ibaka – play all-around games (i.e., both offensive and defensive) to help the Raptors maximize their number of possessions with the basketball. That said, perhaps more than any other player in Raptors history, Lowry has made his reputation not just on scoring, assists, and other traditional stats, but on diving after loose balls and ‘taking charges’ to get his team extra possessions. He has used his hustle and heart to establish himself as one of the all-time Raptors greats, but sports statisticians sometimes struggle to quantify his greatness. Because Lowry’s focus on possessions is potentially his greatest asset, we hypothesized that he would outperform Gasol and Ibaka in terms of their shots plus-minus scores. If confirmed, this result would point to Lowry as the player Ujiri should prioritize over Gasol and Ibaka.

Do the research to confirm or deny the hypothesis

Here are the steps we followed to conduct our analysis:

  1. First, we found the right data to answer our question – i.e. freely available play-by-play data for the 2018-19 season, available at This dataset comprises every play from every game allowing us to test our hypothesis about Lowry’s effectiveness in getting his team more shots at the basket than the opponent.
  2. Since we were specifically interested in comparing Toronto Raptors players, we looked only at games played by the Raptors.
  3. For each of the Raptors’ players, we computed (1) the number of Raptors’ shots at the basket, and (2) the number of opponents’ shots at the basket while that player was on the court.
  4. To calculate the shots plus-minus metric, we subtracted the Raptors’ shots from the opponents’ shots for each player.

Here’s what we found.

Lowry had the highest shots plus-minus score last season out of any Raptors’ players in the starting lineup for at least 30 (out of 82 total) games. Compared to Gasol, the Raptors had 8 more shots at the basket while Lowry was on the court. And compared to Ibaka, the Raptors had 116 more shots at the basket with Lowry playing. Even compared to Leonard, the reigning NBA Finals most valuable player and the Raptors’ overall best player from last season, the Raptors had 115 more shots at the basket with Lowry playing.

Image source:,

These results suggest that, among the Raptors’ best players from last season and fellow veteran-free-agents-to-be, Lowry appears to make a unique impact on the game by focusing on possession of the ball the most which leads to relatively more Raptors’ shots at the basket. This same quality, reflected in Lowry’s diving after loose balls and taking charges is likely what has carried the undersized yet highly competitive point guard into the ranks of the all-time greatest players in Raptors’ history. And this is why the Raptors should prioritize signing Lowry over Marc Gasol and Serge Ibaka next off-season.

This is a prime example of how to tackle an analytics problem to get an actionable result. Think about the desired outcome of identifying the Raptors veteran who will give the team the most possessions. Identify the decision to see which player gives the Raptors the most shots at the basket relative to their opponent. Generate the hypothesis that Kyle Lowry will score highest on the shots plus-minus metric compared to Gasol and Ibaka. Confirm or deny the hypotheses to land on an actionable recommendation of prioritizing Lowry as the free agent to sign who will give the Raptors the most possessions compared to their opponent.