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Shot Differential

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"Shot differential is the only thing that matters"

Dennis Wierzbicki-USA TODAY Sports

If you take more shots than your opponent you generally win the game.

Simulations

Assume one team takes 15 shots. The other team takes 16, 17, 18, etc. up to a shot differential of +15. Both goalies have a save percentage of 0.911. Whether any shot gets saved is determined by a random number generator. I ran 10,000 simulations at each level. I counted only non-tied game results.

For 15 shots you get

Shot Differential

Win Percentage

1

0.5233405289

2

0.556311716

3

0.5835902936

4

0.614465739

5

0.6321065822

6

0.6524776815

7

0.6632440863

8

0.6952975659

9

0.7200203252

10

0.7320137038

11

0.7567197611

12

0.7690888971

13

0.7737423313

14

0.7883309073

15

0.7974714028

For 20 shots

Shot Differential

Win Percentage

1

0.5213454075

2

0.5445607763

3

0.5663187373

4

0.5785092698

5

0.6063359838

6

0.6279510163

7

0.6521467798

8

0.6732477789

9

0.6773435568

10

0.699275807

11

0.7169376365

12

0.7279100689

13

0.7434630678

14

0.7597333016

15

0.7780038296

25 shots

Shot Differential

Win Percentage

1

0.5340353516

2

0.5493150685

3

0.5593367158

4

0.5763025003

5

0.5904904157

6

0.6224514861

7

0.637056759

8

0.6538789429

9

0.6647272727

10

0.6788530466

11

0.7068634509

12

0.7112177564

13

0.7245323484

14

0.7345059615

15

0.7529866479

And finally 30 shots

Shot Differential

Win Percentage

1

0.5197657394

2

0.5469908815

3

0.5598838616

4

0.5797224927

5

0.5955988456

6

0.598688206

7

0.6244863428

8

0.6450495641

9

0.6618781907

10

0.6647612242

11

0.681412772

12

0.7050206734

13

0.7073142051

14

0.733044395

15

0.7312179188

Graphically, it looks like

Shotdiff_medium

Where Group A is 15 shots against, B is 20, C is 25, and D is 30.

NHL data

I took the data from 2007-08 to present, and looked at all games that were won in regulation or overtime (no shootout). While the team with more shots generally wins, the effect is not nearly as strong as the simulations. Overall, the team with more shots on goal won 54.9% of the games.

Shot Differential

Win Percentage

1

0.502722323

2

0.7531584062

3

0.4664107486

4

0.5191489362

5

0.479253112

6

0.5022421525

7

0.5210643016

8

0.4700460829

9

0.4881266491

10

0.5736677116

11

0.5282392027

12

0.496350365

13

0.4931506849

14

0.5431472081

16-19

0.5435244161

20-29

0.5835294118

30-51

0.8101265823

Graph1_medium

Two thing explain the difference. Bad games by goalies and score effect. The model has the goalie at a save percentage of 0.911 every shot, every game. That isn't true in real games. Score effects happen when the team with the lead "takes their foot off the pedal". They sit back and tend to allow more shots (although these are typically of lower quality).

First Period Shot Differential

I can eliminate some of the score effect by looking only at the first period. If we compare who has more shots in the first period with who has the lead at the end of the first period, it looks a lot more like the simulation data. Overall, the team with more shots on goal in the first period led after the first period in 63.3% of the untied games.

Shot Differential

Win Percentage

1

0.5265957447

2

0.5525568182

3

0.5877862595

4

0.6140651801

5

0.6733067729

6

0.6774193548

7

0.7092651757

8

0.689516129

9

0.7725118483

10

0.75

11

0.7924528302

12

0.8356164384

13

0.7551020408

14

0.756097561

15

1

16-24

0.8076923077

Graph2_medium