### NHL faceoff skill adjusted for strength of opposition

Last season, Yanic Perreault led the NHL in faceoff winning percentage with 62.2% (559-340). But might that be because of the quality of opposition he faced? Maybe Perreault took more faceoffs against inferior opponents, and that inflated his numbers.

Meanwhile, Sidney Crosby was one of the worst in the league, winning faceoffs at only a 45.5% rate. Was he really that bad, or were his numbers lowered because he faced a lot of skilled opposition front-line centers?

In this study, Javageek tries to figure that out. He assumed that each player in the league has an intrinsic faceoff winning percentage. Then, he assumed that when a player faces another, his chance of winning is determined by pythagorean projection (The log5 method (explained here) might have been a better choice, but I don't think it matters a whole lot).

He then took 121 faceoff men, and looked at their records against each other. That's 7,260 possible faceoff pairs. Javageek figured out (confession: I didn't really read the algebra) that the question could be answered by solving 121 equations in 121 unknowns. He did that, and came up with an adjusted faceoff percentage for each player, corrected for the quality of opposition.

Bottom line: the adjustment doesn't matter much. Javageek didn't give any metrics comparing actual vs. theoretical, but a look at the two charts shows that in most cases, they're almost the same. Find any player in the left (theoretical) column, and he can be found not too far away in the right (actual) column. Yanic Perreault still leads, with an adjusted 63.8%, and Sidney Crosby drops to 43.8%.

It's important to note that these are still not ~~unbiased~~ the most appropriate esimators of the players' actual faceoff skills – you still have to regress to the mean to get an estimate of their true talent. You'd probably want to use this technique to do that.

One thing that bothers me a bit about the results is that the top players become less extreme after the adjustment, but the bottom players become *more* extreme. You'd expect both halves of the data to be less extreme -- closer to the mean -- after you've adjusted out some of the luck. We don't see that with the bottom players, and I'm not sure what to make of that.

## 5 Comments:

A technical nitpick: the resulting estimates are in fact "unbiased" estimates. Unbiasedness is a property of a statistic, i.e. the formula that converts a sample into a number, and not the resulting number.

For example, if we take a collection of coins and toss them each 100 times and count the proportion of heads for each coin, that proportion is an unbiased estimator of the true probability the coin will land heads. If we have two coins, one which lands heads 53 times and the other 47 times, then .53 and .47 are the unbiased estimates of the true probability for the coins. This is true even if both coins are, in reality, fair coins.

Unbiasedness simply means that there's no systematic error in one direction or another from the "true" probability.

I'm not arguing that we shouldn't regress to means -- we should -- but the reason isn't because the estimators are biased.

Right, that's true. Thanks.

But if the statistic under consideration isn't the proportion of faceoffs won for Yanic Perreault, but the proportion of faceoffs won for the player *who's first in the league*, isn't that estimate now biased? That is, *the first order statistic* (ie, highest) of the observed proportions of the 121 players is a biased estimator of the proportion of the actual probability for the associated player.

Trying to wiggle out on a technicality. Did it work? :)

Regardless, I will change "unbiased" to "accurate".

Yes, that version's correct, and more precise in some sense, since it captures the essential point: the variance in observed performance is greater than the variance in actual talent.

(Now if only we could get that through the heads of 95% of the people who play sports simulations...)

There's actually a pretty big problem with this, as I have recently discovered that the face-off percentage on the power play = 55%.

So if you take a lot of short handed face-offs you'll be lower and power play face-offs you'll be higher.

I recalculated the theoretical value using only even strength face-offs and got this table: Vermette got a higher rating than Perreault

看房子,買房子,建商自售,自售,台北新成屋,台北豪宅,新成屋,豪宅,美髮儀器,美髮,儀器,髮型,EMBA,MBA,學位,EMBA,專業認證,認證課程,博士學位,DBA,PHD,在職進修,碩士學位,推廣教育,DBA,進修課程,碩士學位,網路廣告,關鍵字廣告,關鍵字,課程介紹,學分班,文憑,牛樟芝,段木,牛樟菇,日式料理, 台北居酒屋,日本料理,結婚,婚宴場地,推車飲茶,港式點心,尾牙春酒,台北住宿,國內訂房,台北HOTEL,台北婚宴,飯店優惠,台北結婚,場地,住宿,訂房,HOTEL,飯店,造型系列,學位,SEO,婚宴,捷運,學區,美髮,儀器,髮型,看房子,買房子,建商自售,自售,房子,捷運,學區,台北新成屋,台北豪宅,新成屋,豪宅,學位,碩士學位,進修,在職進修, 課程,教育,學位,證照,mba,文憑,學分班,台北住宿,國內訂房,台北HOTEL,台北婚宴,飯店優惠,住宿,訂房,HOTEL,飯店,婚宴,台北住宿,國內訂房,台北HOTEL,台北婚宴,飯店優惠,住宿,訂房,HOTEL,飯店,婚宴,台北住宿,國內訂房,台北HOTEL,台北婚宴,飯店優惠,住宿,訂房,HOTEL,飯店,婚宴,結婚,婚宴場地,推車飲茶,港式點心,尾牙春酒,台北結婚,場地,結婚,場地,推車飲茶,港式點心,尾牙春酒,台北結婚,婚宴場地,結婚,婚宴場地,推車飲茶,港式點心,尾牙春酒,台北結婚,場地,居酒屋,燒烤,美髮,儀器,髮型,美髮,儀器,髮型,美髮,儀器,髮型,美髮,儀器,髮型,小套房,小套房,進修,在職進修,留學,證照,MBA,EMBA,留學,MBA,EMBA,留學,進修,在職進修,牛樟芝,段木,牛樟菇,關鍵字排名,網路行銷,PMP,在職專班,研究所在職專班,碩士在職專班,PMP,證照,在職專班,研究所在職專班,碩士在職專班,SEO,廣告,關鍵字,關鍵字排名,網路行銷,網頁設計,網站設計,網站排名,搜尋引擎,網路廣告,SEO,廣告,關鍵字,關鍵字排名,網路行銷,網頁設計,網站設計,網站排名,搜尋引擎,網路廣告,SEO,廣告,關鍵字,關鍵字排名,網路行銷,網頁設計,網站設計,網站排名,搜尋引擎,網路廣告,SEO,廣告,關鍵字,關鍵字排名,網路行銷,網頁設計,網站設計,網站排名,搜尋引擎,網路廣告,EMBA,MBA,PMP,在職進修,專案管理,出國留學,EMBA,MBA,PMP,在職進修,專案管理,出國留學,EMBA,MBA,PMP,在職進修,專案管理,出國留學,婚宴,婚宴,婚宴,婚宴,漢高資訊,漢高資訊,比利時,比利時聯合商學院,宜蘭民宿,台東民宿,澎湖民宿,墾丁民宿,花蓮民宿,SEO,找工作,汽車旅館,阿里山,日月潭,阿里山民宿,東森購物,momo購物台,pc home購物,購物漢高資訊,漢高資訊,在職進修,漢高資訊,在職進修,住宿,住宿,整形,造型,室內設計,室內設計,漢高資訊,在職進修,漢高資訊,在職進修,住宿,美容,室內設計,在職進修,羅志祥,周杰倫,五月天,住宿,住宿,整形,整形,室內設計,室內設計,比利時聯合商學院,在職進修,比利時聯合商學院,在職進修,漢高資訊,找工作,找工作,找工作,找工作,找工作,蔡依林,林志玲

Post a Comment

<< Home