What follows is a post from my old hockey analysis site puckerings.com (later hockeythink.com). It is reproduced here for posterity; bear in mind this writing is over a decade old and I may not even agree with it myself anymore. This post was originally published on October 18, 2002.
Theory: Shots and Save Percentage
Copyright Iain Fyffe, 2002
In my investigation into the validity of Goaltender Perseverence,
I looked into the relationship between the number of shots a goaltender
faces per game and his save percentage. I found that, as the number of
shots per game increases, save percentage does not decrease, on
average, as the fundamental assumption of Perseverence argues. In fact,
there is some evidence of a positive relationship; that is, as shots
increase, save percentage increases.
This evidence was met
with an "it doesn't make sense" reaction from those I presented it to.
Well, common sense is often dead wrong. To explain this phenomenon, I
present the following theory.
For simplicity, I will
discuss only two types of shots: easy and tough (referring to the
goaltender's perspective). There are in actuality many varying degrees
of toughness of shots, but these two will suffice for our purposes.
Easy shots are largely
discretionary. They are shots that result from situations where a player
could choose to shoot, or choose another play. They are of lower
quality than tough shots, because they are usually taken from a greater
distance than tough shots, or less favourable circumstances.
Since easy shots are
discretionary, there must be a reason that teams do not simply shoot
every time, in order to maximize their goals scored. The reason could be
twofold: you give up the opportunity to make a pass, which could result
in a higher-quality shot, and the shot is more likely to produce a
turnover, allowing a possible scoring chance for the opposition.
Therefore, it is not always wise to take the shot rather than another
Save percentages on tough
shots are low, and save percentages on easy shots are high. And since
easy shots are primarily responsible for variation in shots faced by a
goaltender (since the number of tough shots faced is relatively
consistent), save percentage will increase as shots faced increases.
For example, let's say
that the average tough shots faced per game is 5, and the save
percentage on such shots is .800. This is the same for every goaltender.
Any difference in shots faced is due to easy shots, which we'll say
have a save percentage of .900.
A goaltender facing 25
shots will therefore face 20 easy shots (25 less 5). Goals against on
tough shots is 1.0 (5 less .800 times 5), on easy shots 2.0 (20 less
.900 times 20). 3 goals against on 25 shots is an .880 save percentage.
A goaltender facing 35
shots will have the same 1.0 goals against on tough shots, but will have
3.0 on easy shots (30 less .900 times 30). 4 goals against on 35 shots
is an .886 save percentage. The goaltender facing more shots on average
has a higher save percentage.
That is my theory of how
save percentage can increase as shots increase. Unfortunately, this
theory cannot be tested using information that is currently available.
The NHL does track certain shot data (type, location) for shots that
produce a goal, but not for shots that do not produce a goal. If this
information were recorded for all shots, it could be used to test this