Reference library: Variance and regression

Updated: November 14, 2012 at 4:50 pm by Eric T.

This article is part of the NHL Numbers reference library, which seeks to collect articles from around the web that have contributed to our understanding of the game.

This page is devoted to articles that look at the role of variance and regression in hockey. This will include looking at how much variance a given statistic has and whether it reflects a true talent, how actual performances compare to random chance models, etc.

We need your help to keep the library complete and up to date — contact me on Twitter (@BSH_EricT) or via email (bsh.erict -at- gmail) with suggestions of articles you think we should consider adding.

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Title – Individual Stats
Author Date Site Description
Shooting percentage vs shot rate: Sidney Crosby edition Jonathan Willis 11/18/2009 Backhand Shelf Variance of individual sh%, points, and shooting percentage
Points v. Scoring
mc79hockey 11/27/2009 Battle of Alberta Calculating IPP, showing that it regresses heavily
Fooled by randomness: Goaltender save percentage Hawerchuk 4/20/2010 Arctic Ice Hockey Probability that an average goalie has a high sv% over given # of shots
Goaltender talent Hawerchuk 9/16/2010 Arctic Ice Hockey How much of differences between goalies come from luck or skill?
Why future performance, not consistency, matters Neil Greenberg 2/2/2011 Russian Machine Never Breaks Alex Semin is no streakier than a random sim
Does hockey math work? Derek Zona 5/26/2011 Copper & Blue A look back at how some predictions based on regression fared
Sample size war: Goals part I (forwards) SnarkSD 6/17/2011 Arctic Ice Hockey Method for establishing how confident we should be in a stat after n games
On-ice shooting percentage as a player talent Hawerchuk 10/10/2011 Arctic Ice Hockey Even multi-year on-ice sh% totals regress heavily
SSW: With so much luck, when are stats useful? SnarkSD 10/29/2011 Arctic Ice Hockey How many games it takes to have confidence in various boxcars
The impact of luck on prospects Derek Zona 11/19/2011 Copper & Blue How a random streak can propel or crush a prospect’s career
Is there streakiness in even-strength shooting percentage? Hawerchuk 11/30/2011 Arctic Ice Hockey Individual sh% closely matches sim, but with noticeably fatter tails
The myth of the hot goalie: Consistent goaltenders vs. inconsistent goaltenders Eric T. 5/11/2012 NHL Numbers Goalie streakiness very closely matches a random chance model
Expectation vs. reality: A look at an inaccurate label Patrick Marleau has carried his entire career SnarkSD 7/10/2012 Fear the Fin Marleau is no streakier than Pavelski or Poisson


Title – Team performance
Author Date Site Description
Wish I believed like they do, pt. 1 Tyler Dellow 10/30/2008 mc79hockey Past PP sh% does not predict future PP sh%
Possession is everything Vic Ferrari 5/4/2009 Irreverent Oiler Fans Scoring chance totals drift toward highly repeatable Corsi in long run
Real effects and team shooting percentage at even strength Vic Ferrari 6/8/2009 Irreverent Oiler Fans Repeatability for EV shot rate, sh%, and sv%
The ‘shot quality’ fantasy Vic Ferrari 7/24/2009 Irreverent Oiler Fans Goalie year-over-year change almost exactly matches random model
How much do shot totals and shooting percentage vary over a season? Jonathan Willis 10/15/2009 Backhand Shelf Variance of team sh%, sv%, and shot totals over 5-game segments
The repeatability of special teams performance JLikens 4/27/2010 Objective NHL Repeatability for PP and PK shot rate, sh%/sv%, and penalty drawing
Luck in the NHL standings Hawerchuk 11/22/2010 Arctic Ice Hockey Simple coinflip model suggests 38% of spread in team points is from luck
Even strength outshooting and team quality JLikens 1/26/2011 Objective NHL EV tied shot differential accounts for 65% of non-luck goal differential
How to tell the difference between a worn-out penny and a punk student Eric T. 2/23/2011 Broad Street Hockey The role of variance, and why people underestimate it
The luck involved in scoring ThrashersRecaps 4/6/2011 Arctic Ice Hockey Counting how many goals came on plays a viewer might call lucky
What drives power-play success? Hawerchuk 4/9/2011 Arctic Ice Hockey Magnitude of regression for PP%, shot rate, and sh%
Team even strength shooting talent JLikens 5/29/2011 Objective NHL Estimated distribution of team shooting talent matches simple regression
How often does the best team win? JLikens 6/25/2011 Objective NHL Simulations suggest best team in league wins Cup 22% of time
On luck, skill and sample size in shooting percentage JaredL 8/19/2011 Driving Play Odds that a poor-shooting team outshoots a good-shooting team
Shot distance allowed as a team talent Hawerchuk 10/24/2011 Arctic Ice Hockey Differences between teams in location of shots against are very small
Luck vs shot quality in shooting percentage Hawerchuk 10/25/2011 Arctic Ice Hockey Shot location is a persistent talent, but sh% is still driven by luck