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

2. Background:
● In , the correlation between percent cap hit of injured players per game and points per game is (nhlinjuryviz.blogspot.com) ● In 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

3. 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

4. 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)

5. 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

6. Data:

7. Data:
● Data From mangameslost.com and hockey-reference.com ● Data collected from season to 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

8. 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

9. Data:
● All game situations (ES, PP, PK) aggerated ● Forwards and defensemen (goalies not included)
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

10. Injury Prone or Unlucky?

11. 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

12. 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

13. 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
461
0.311
13.900 15
0.324
429
0.290
11.240 18
0.027
426
0.299
11.387
0.031
416
0.295
10.680
0.017
470
0.331
17.000 36
0.000
446
0.325
15.310 31
379
0.328
4.440 14

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

15. Model

16. 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

17. 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 - +

18. 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.

19. 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 season for each team

20. Application:

21. Application:

22. 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

23. 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.

24. Thank you
@ImaSlyGuy01