Friday 17 October 2014

Puckerings archive: Shots and Save Percentage (18 Oct 2002)

What follows is a post from my old hockey analysis site (later 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 play.
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 theory.

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