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# Shot Differential

"Shot differential is the only thing that matters"

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

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

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