Earlier this week, Tom Tango, a prominent baseball analytics writer who has crossed over into other sports from time to time, published an article on his blog, tangotiger.com, entitled "Introducing Weighted Shot Differential (aka Tango)." The article is linked here. It is short and I highly recommend giving it a read. I wanted to give it a few days to marinate in the hockey analytics community before writing about my opinions on it.

Basically, the article states that the way in which hockey analysts have hung their hat on Corsi, a measure of shot attempts for and/or against that does not factor the type or quality of the shot, or whether it was blocked or missed the net, is seriously misguided. He argues that we have been ignoring valuable data by treating goals the same as other shot attempts. Goals should be weighted more heavily in any shot attempt differential metric (such as CF%) because they are more predictive of future scoring than any old shot attempt.

He goes further by arguing that different types of shot attempts might receive different weighted values in an analysis of a team's "Corsi" but that, for practicality's sake, we might start at valuing a goal as 1 and, through baking numbers going back several years, he determined a value of "about" 0.2 for every non-goal shot attempt. He self-titled the weighted shot differential Tango and declared it more predictive of future goals in his comments to the article.

My first thought when reading Tom Tango's article** was, "Ok, interesting idea, and yes, goals do matter more than shots...nobody denied that. But don't the goals get washed out by the sheer enormity of non-goal shot-attempt data?"

**well second thought after "the tone of this piece is myopically snarky towards years of research by smart hockey people."

Score-adjusted Corsi vs. Tango

Score-adjusted Corsi is currently our most correlative stat for predicting future goals and wins.

As of late, score-adjusted Corsi has gained traction in the analytics community, and for good reason. Score-adjusted Corsi basically takes into consideration the various game states. It is currently our most predictive stat of future goals and wins, and thus has been used more as of late than raw 5v5 corsi, and has rendered 5v5 score close Corsi (which ignores a portion of data from game states) relatively obsolete.

The basis and methods for score-adjusting possession proxy stats like Corsi (all shot attempts) and Fenwick (all unblocked shot attempts), and analyzing game states (and score effects) within raw Corsi data, date back several years. Score adjusting helps to ease the impact of score-effect. Score-effect is basically the propensity for a team leading later in a game to go into a "defensive shell," thereby allowing the opposition to run up their Corsi/Fenwick For total. Score-adjusting has notably improved predictivity to goals and wins.

Read more about score-adjusted Corsi's virtues here.

So, I went to work pulling data to do regression analysis and compare correlation of weighted shot differential to the various incarnations of Corsi and, most specifically score-adjusted Corsi.

Before I dove in, thankfully, I checked Twitter. The Neutral, Editor over with our friends at Fear the Fin, beat me to it:

Correlation between @tangotiger's new metric and score-adjusted Corsi for the 2013-14 season is nearly perfect. pic.twitter.com/9GIsCmPh4U — Fear The Fin (@fearthefin) December 1, 2014

Tango's (obviously) right goals are more important than non-goals. Unfortunately there aren't enough NHL goals scored for that to matter. — Fear The Fin (@fearthefin) December 1, 2014

So giving goals additional weight doesn't make a difference. They get drowned out and you're left with a metric identical to Corsi. — Fear The Fin (@fearthefin) December 1, 2014

This was my thinking as well. "Tango," or weighted shot attempt differential, doesn't provide enough goal data points to move the needle. The correlation between the two is ~1, which would be exactly the same. So it would be a lateral change at best, and unduly confusing at worst, to even adopt it.

Anyway, hadn't the hockey analytics community already chased the shot attempt dragon, caught it, and realized it wasn't fire breathing? When we look at things like score-adjusted team Corsi as predictive of goals/wins, then weighting shots might be of some use. But the problem is, and always has been, sampling and the unpredictable/imperfect nature of goals. Further, as described in those tweets, weighting them, whether arbitrarily or not, doesn't change the numbers at all because there are too few goals. It gets washed out.

It is well established that inserting shot quality does not help the data analysis.

And this issue, the issue of shot quality not helping to predict future goals/wins any better than all shot attempts, has been well researched and established in the hockey analytics community.

Eric Tulsky, formerly of Broad Street Hockey and SBN's Outnumbered, and now an NHL team consultant, previously wrote:

In general, shot quality factors tend to be small enough that they don't grossly alter our understanding of the game, and they tend to be swamped by noise during in-season analysis. The best possible understanding obviously requires more than a cursory glance at shot totals, but shot-based analysis has consistently proven to be a strong approach to identifying talent and predicting future outcomes.

Garret Hohl of Hockey-Graphs more recently very astutely added:

To correct for one straw man argument often used: just keep in mind [this] doesn't mean shot quality is not important on the ice [emphasis added]. What is important to strive for by the players and teams is not the same as what is important in analyzing data.

When analyzing the data, shot attempt differential simply evens out the craziness of sh% in smaller sample sizes a lot quicker and handles the unpredictible (often lucky/random) nature of scoring chances and goal-scoring plays better. It thus makes sense to look at total shot differential as opposed to goal differential. Tom Tango and several of his analytically inclined readers who commented on his article may not have been aware of this of course. But the presumptuous and dismissive nature of his article certainly rubbed some folks, who had spent time and effort to uncover that, the wrong way.

Further, the weighting doesn't make sense to me. Tango argues .2 for a non-goal based on the data and regressions he ran but it is neither here nor there. However, the data year to year comes out random at best. Also, Corsi sh% hovers around 4%. So, if you really want to "weight" goal data so greatly that it stands out, you would want to make it 25 times more valuable than other types of shots, at least. IE 1 for a goal, .04 for a non-goal, right? The bottom line, to me, is that this approach doesn't make sense. For all of us who have watched the sport for any length of time, we generally know that goals are not all the same, shot attempts are not all the same, and the data gleaned from goals is often no greater than non-goal shots. Sometimes pucks just...you know...go in. Sometimes they just don't, even though the shot type, distance, plane, trajectory, speed, etc are the same or similar. Arbitrarily weighting every goal 25 times greater, or even 5 times greater, than every non-goal just wouldn't make sense because of the luck and unpredictability of goals. And adjusting to different types of goals would be subjective at best, arbitrary and misleading at worst.

Corsi is a proxy for possession. Possession is 9/10ths of the law (or something).

From a utility standpoint, Tango's purpose does not entirely coincide with Corsi's purpose. I think this is the point where baseball analytics and hockey analytics diverge. Corsi has traditionally been utilized as a proxy stat for puck possession. Because we do not have real-time possession data in hockey, but want to know who has the puck, we presume that the team who has more shot attempts (typically at even strength so as not to skew the numbers with special teams), has generally "won" the possession battle. Weighting shots does not do anything for this usage of Corsi.

In his comments to his article Tango argues that "if you score a goal, you likely possessed the puck longer than with a non-goal shot." That is a pretty large leap for reasons I really should not have to detail. While Tango goes on to argue that using Corsi as a proxy for possession is an assumption at best, years of research have correlated the stat to real-time possession within ~.9, which is very very close correlation. It is a necessary assumption, and one that we have come to accept, and have to accept, as being worthwhile for the purpose of analyzing the performance of players and teams. Otherwise, we simply don't have anything.

If we are trying to measure possession with Corsi, then weighting would actually muddy the water with luck-based variables, randomness, and variables that are not possession-dependent. This would include a goalie's sv% and shooter's sh%. There simply is no purpose to the weighting under a possession-focused analysis using shot differential based stats.

Public Consumption Practicality

Purely for practicality's sake, making unnecessary lateral changes to the lexicon right now, when so many are just starting to adopt stats like Corsi and Fenwick, hardly makes sense. The bubbling up of analytics in the mainstream belies the fact that research behind the scenes has been going on for many years. But the general hockey watching public is only just getting comfortable with these named stats with actually fairly simply concepts behind them. And this is worth considering.

The goal (punny) in every type of statistic that the hockey community adopts should be drawing greater correlations and predictivity to success (goals, goals saved, goal differential, wins) by analyzing data drawn from the repeatable abilities or events occurring on the ice. There are a number of exceptional thinkers that run the gamut from "math-centric" to "hockey knowledge centric" (technical terms, I know) who can contribute to doing so. Sometimes we will run tests, or theorize, and it won't net any return. And that is OK. Tom Tango's thought process does make sense. We should not be tossing aside data, and weighting is a valuable consideration. But if the net return doesn't move the needle, why adopt it? Why argue that a team should adopt it? It doesn't provide any edge. It is thus tough to justify using it.

This is a message for everyone in the hockey analytics community:

Theorize away. But run the tests, see if there is an actual and reliable improvement, think about the value of the statistical analysis and how it can be used to impact repeatable hockey skills on the ice, and then relate it in a straight-forward and non-controversial manner. Work inclusively, not exclusively. The exclusivity, and snark, is undermining to progress, and simply reflects poorly on a community that is trying to come out of the shadows, not remain lurking within them. As a newcomer to the community, but not a newcomer to the sport or analyzing it, I find this to be the #1 barrier to entry for folks with a genuine interest in learning more and adding to the discussion. And I myself have been guilty of it as well.

Until we have the means for compiling data that some other sports have in place, such as SportVU and real-time tracking technology, we are stuck with proxies and imperfect data we have. No one stat is the be-all-end-all. We all acknowledge that. But that fact doesn't mean that years of research and analysis should be cast aside every time a seemingly (but not really) novel thought comes along. Nor does it mean that we should be jumping out of our shoes every time we think we might have improved something.

One day, probably not too far in the future, all of this Corsi and Fenwick chatter will either evolve with technology or be cast aside in favor of new analytical measures. But not today.

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