In hockey, the PDO is considered to measure luck. Could you please explain me why ?

From my understanding, the PDO is computed as "goals for / shoots on post for + saves against / shoots on post against". That is: your team is good at shooting (the guys score often) and you have a good goalie (he saves a lot). I don't see any luck here (that's also written in https://jfresh.substack.com/p/percentage-luck-in-hockey-explained : [..] there are elements of PDO that aren’t caused by luck, like shooting talent and goaltending).

When you sum the PDO of the two teams, you obtain 200%. That is: the two teams will share theses 200%. As the teams plays in the same league, there are more or less equally good, so it is expected each team get about 100%. We can find Gaussian distributions centered on 100% on the web (e.g. https://medium.com/hockey-stats/advanced-hockey-stats-101-pdo-part-3-of-4-d3f319f2e1f1 ). A wide Gaussian could indicate big differences between teams in the league, while narrow Gaussian could indicate tight differences between teams in the league. When low performing teams play against high performing teams, they learn and over years, they become better, making the Gaussian to be narrower (explaining why the PDO traditionally regress to the 100% mean, e.g. in https://jfresh.substack.com/p/percentage-luck-in-hockey-explained ). But again, I don't see any luck here.

Is "puck luck" an kind of "default reason" to explain phenomenons that we are not able to explain (like all the natural events that were considered as divine manifestations in ancient times, but are now scientifically explained) ? From my point of view, the defenders are under considered in the PDO (and in other metrics as well): they hinder the attackers so that the attackers shots are less dangerous, thus indirectly the defenders protect the goalie. The goalie save rate is higher because the shots are easier to stop, but the defenders impact is not measured (I agree it would be difficult to measure the "inconvenience" produced by the defenders). Also note that the opponent defenders have impact on our attacker goal ratio, so that the defender role has impact on the two components of the PDO.

I'm sure luck exists in hockey (we could get good bounces or bad bounces), but definitively, I don't understand how the PDO reflect it.

Note: I could not find an answer in https://www.reddit.com/r/canucks/comments/196pfxp/help_me_understand_why_pdo_is_considered_luck_in/ or https://www.reddit.com/r/hockey/comments/1ac81yv/the_whole_concept_of_pdo_as_a_measure_of_luck_is/

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This article goes into the specifics: https://cnsmaryland.org/2017/02/03/how-an-advanced-hockey-stat-measures-luck-in-the-nhl/

In short, PDO is normalized throughout the league to 100 and anything in between 98-102 is considered sustainable. The "luck" aspect comes from being above or below the 98-102 threshold as an indicator of good luck or bad luck. I'm not sure it "measures" luck as much as it "indicates" luck.

This is very similar to Pythagorean Winning Percentage in baseball that measures expected win-loss record by runs scored and allowed: https://www.mlb.com/glossary/advanced-stats/pythagorean-winning-percentage

Both metrics indicate luck by taking for/against statistics and compares it to actual results. The word indicate is emphasized as these statistics do not measure luck in itself but it indicates luck by taking measurable statistics against actual results.

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    So if I rephrase, "out of the 98-102 normal range, it indicates luck". But then, what proves it's luck and not something else ? Also I don't understand your comparison between Pythagorean Winning Percentage (PWP) and PDO. PWP is a prediction formula, but the PDO is a metric in itself and is not compared to the actual results. So saying it's very similar is strange. Feb 5 at 20:27

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