Above and Beyond Ultimate Player Stats

"Spatial Statistics to Evaluate Player Contribution in Ultimate" was presented by Jeremy Weiss and Sean Childers (Ultiworld Statistics editors) at the 8th annual MIT's Sloan Sports Analytics Conference (Feb 28-March 1).

The paper is a statistician's dream! Using Ultimate stats application, Ultiapps, they impressively tracked 17,883 plays over 3099 possessions and 1579 points in 68 Ultimate games. Their analysis measures player contribution in the form of throws, completions, assists, scores, plus defense (blocks). Also, a sense of "best practices" for Ultimate offenses was determined, like it's better to dump-&-reset than to huck.

Two mentions are of additional interest:
1) reducing the Ultimate field for women's teams
2) postponing Ultimate games during poor weather conditions (i.e. high winds)

From the paper: "The Hail Mary strategy, know in ultimate as Huck and D, is seen in all divisions of ultimate and particularly in poor weather conditions, but is less fun for players and unappealing to spectators. Figure 5 lends support to proponents in the ultimate community of shrinking the women's playing field and of postponing games in poor...conditions."

Screen grab from the paper.

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Paper Overview
Existing statistical ultimate (Frisbee) analyses rely on summary statistics, such as completion percentage and scoring rate, to assess player strengths and weaknesses. However, these statistics are limited in their ability to evaluate a player's contribution to winning points; that is, two players of different value may look identical statistically. To better determine player contribution, we develop a spatially-aware measure.

Methods
We collected data at elite tournaments using the using the UltiApps iPad application that tracks thrower and receiver locations and point outcomes. Using the location-based data, we produce team-specific and aggregate scoring probability graphs using logistic regression, LOESS, and k-nearest neighbors models. Overlaying each play on the graph determines an attributable contribution, i.e. the change in scoring probability, which is assigned to each involved player. Averaging over all points yields a player's Expected Contribution.

Results
Our measure reliably distinguishes the best throwers, receivers, and defenders in both men's and women's divisions. The Expected Contribution measure combines these factors to produce an assessment of players that accounts for their strengths and weaknesses in each phase of the game. As a secondary outcome, the scoring probability graphs can be also be used to compare the effectiveness of strategies, such as punts versus possession and risk-seeking (high variance throws) versus risk-averse.

Read the full paper.