Clutch Matches Are In The Middle: Optimizing OPR with Weighted Least Squares

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In this paper, we present an improvement to Offensive Power Rating (OPR), a popular linear regression model for assessing team performance at a given event. One key assumption of linear regression is the independence of the errors, but in the FIRST® Robotics Competition (FRC) context, this assumption is not exactly true. Using data from all district events between 2009 and 2024, we model the unweighted errors as a function of tournament progression and generate weightings to improve the regression fit through Weighted Least Squares (WLS). The best weightings show that the most representative matches for a team’s overall performance are midway through the tournament. That is, the real clutch matches are in the middle.Read More

Rocket League: esports

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Rocket League is an online game where players control cars in a soccer field with the aim of scoring as many goals as possible within 5 minutes. In this work, existing sports analytics methodology developed for soccer are applied onto Rocket League in order to gain better insights into player skill. The dataset includes instantaneous snapshots of 2 versus 2 player Rocket League games that includes location data of all 4 players, car features, ball position, and whether or not a particular shot resulted in a goal. An expected goals (xG) model using player location data to predict goals for a given shot attempt was created. Using this xG model, we explored three topics. Is outperformance a random process, or is it attributable to a player’s ability to position and utilize ball features? Even though Rocket League does not assign specific positions as soccer does, do players adopt a strictly offensive or strictly defensive position? What were the playstyles of the players in the Rocket League Championship Series games? We found that outperformance is largely due to luck or randomness. Additionally, players rarely adopt a strictly offensive or strictly defensive position, and offensive and defensive ability do not correlate. This supports the idea that most play styles involve moving around a field and being a dynamic player. As our case study shows, we can use xG as a helpful statistic in uncovering a deeper level of analysis.Read More