A Model Based Approach to Injuries Jeremy F. Sylvain1, Dr. Michael E. Schuckers2, & Dr. Nathan Currier3

Background: ● In 2016-17, the correlation between percent cap hit of injured players per game and points per game is -0.31 (nhlinjuryviz.blogspot.com) ● In 2016-17 3 most injured teams VAN, WPG, and BUF, all failed to make the playoffs* ● The 3 least injured teams WSH, CGY, and STL all made the playoffs and WSH and STL both moved on to the second round* *mangameslost.com

Introduction: ● Injured teams struggle to be successful ● Injuries to players often impacts the decisions that managers and coaches have to make ● Important to try and capture injuries in a model for teams to understand what their needs are going forward

Prior WOrk: ● 2 Model approach* - Probability Model - Severity Model ● Collision statistics rooted in how many games played* - Seasonal production ● Injuries occurring in prior seasons were not taken into consideration* *(Sylvain & Schuckers, 2017)

Goals: ● Create a model to capture injuries that occur during a regular season ● Base these models on factors that occur in game play - Events while the player is on the ice ● Use these models to create predict man games lost for individual players as well as teams

Data:

Data: ● Data From mangameslost.com and hockey-reference.com ● Data collected from 2009-10 season to 2016-2017 season to allow us to collect stable estimates Variable Definition INJ Games a player lost due to injury GP Games played by a player TOI-GM Average time on ice played per game in all situations HGT Hits a player gives divided by time on ice BPT Shots a player blocks divided by time on ice HTT Hits a player taken divided by time on ice AGE Age of player as if January 1st, of each season in years AGE2 Age of a player squared in years inD Indicator determining the position of the player

Data: ● Further for each season model, we use the prior 3 season’s INJ in the model ● To be included in the study you must have had a combination of 20 INJ and GP, as we feel at that point a player has seen a rigorous amount of a season ● Below is an example of a player: Alexander Edler: Variable GP INJ TOI.GM HTT BPT AGE AGE2 inD 2016 2015 2014 Edler 68.00 14.00 19.70 6.70 5.07 30.72 943.75 1.00 30.00 8.00 16.00

Data: ● All game situations (ES, PP, PK) aggerated ● Forwards and defensemen (goalies not included) 2012-13 2013-14 2014-15 2015-16 2016-17 Number of Players 602 694 685 676 687 Proportion of Players with INJ≥1 55.1% 69.0% 67.7% 68.3% 65.4% Proportion of Players with INJ≥10 22.1% 34.3% 32.0% 33.4% 31.9% Mean games missed 5.7 9.2 9.1 9.4 8.4 Median games missed 1 5 4 3

Injury Prone or Unlucky?

Injury Prone: ● “Injury prone” is a term that is thrown around frequently ● Never really been evaluated (to our knowledge) ●Evaluate players susceptibility to injuries across multiple years

Method: ● Break seasons into three year cohorts ● Identify players who were injured more than 10 games in each of the three years within the cohort of interest ● Calculate the average seasonal injury rate by averaging the seasonal injury rate ● Compare the expected number of players missing more than 10 games to the actual number of players

Injury Prone: ● Statistically significant difference between the expected number of players who missed more than 10 games in each cohort season and the actual numbers ● Gives reason to use prior seasons INJ going forward in our models. Cohort Players Playing in All Seasons Avg Injury Rate Expected INJ≥10 Actual INJ≥10 P-Value 10.11.12 461 0.311 13.900 15 0.324 11.12.13 429 0.290 11.240 18 0.027 12.13.14 426 0.299 11.387 0.031 13.14.15 416 0.295 10.680 0.017 14.15.16 470 0.331 17.000 36 0.000 15.16.17 446 0.325 15.310 31 14.15.16.17 379 0.328 4.440 14

Analysis: ● HTT and BPT are collision factors that occur in a game ● HIT and BLK are divided by TOI.GM to account for production while a player is on the ice not on a game by game basis ● To account for susceptibility due to aging, we use quadratic model for aging. ● To account for prior injuries and to model injury prone players we include the prior 3 season injuries

Model

INJt ~ TOI.GM + HTT + BPT + AGE + AGE2 + inD + INJt-1 + INJt-2 +INJt-3 Models: ● Different from prior studies we used one model instead of a probability and severity models ● Model uses a quasiPoisson (overdispersion) distribution Model: INJt ~ TOI.GM + HTT + BPT + AGE + AGE2 + inD + INJt-1 + INJt-2 +INJt-3 *Where “t” represents the year of interest

Results: ● “-” Represents a significant coefficient that is negative ● “+” Represents a significant coefficient that is positive Season TOI.GM HTT BPT AGE AGE2 inD INJt-1 INJt-2 INJt-3 2016-17   - + 2015-16 2014-15 2013-14 2012-13

Results: ● Position makes a difference ● Getting hit and blocking shots are significant but not as expected - Would expect the coefficients to be positive ● Prior seasons make a difference ● TOI. GM doesn’t effect the severity of an injury.

Application: ● Fit the 2015-16 model to the 2016-17 data ● Ran this simulation for 1,000 repetitions to create distribution of team INJ ● Compared the predicted INJ for each team to the actual INJ for each team from last season. ● Red line in following graphs represents the Total number of injuries for the 2016-17 season for each team

Application:

Application:

Issues: ● Questions arise for modeling injuries for rookies (they have not played in three seasons) ● Concussion protocol does potentially factors into this (2012) ● Does special teams make a difference ● LTIR players who clearly are not coming back to the league

Going Forward: ● When the injury occurred? ● Where the injury occurred? ● Does the off season training have an impact? ● Is there a difference between short term and long term injuries? ● PREDICTING INJURIES IS HARD.

Thank you j.sylvain01@gmail.com @ImaSlyGuy01