The data used here is for the complete 2011-12 and 2013 seasons.  In total there are n= 476614 plays that were recorded, 399171 of those were at even strength(5v5 or 4v4).  All of the estimated values here are based upon an average per play performance for these two seasons.  We estimate that home ice over this period was worth about 0.31 goals per game.  This estimate comes from the effect on each play extrapolated to approximately 244 events recorded per game.  This is consistent with other estimates from recent seasons.  As we have noted previously (here), a  ZS at even strength is worth about five times what home ice is worth to a given play.  Another way to think of an even strength ZS is that moving from starting a shift in the neutral zone to starting in the offensive zone is equivalent to replacing an average player on a given line with a top 10 player (e.g. a Johnathon Toews or a Daniel Sedin).   

The score effect term in our models is only present if the score differential is more than two goals.  As other hockey analytics folks have noted, teams that are ahead tend to play differently.  Empirically, we find that this is true and that the effect grows as the score differential grows.  

The Top 10 Players in these ratings are: E. Staal (5.55 wins over average) , D Sedin (5.38) , S. Weber (4.92) A. Kopitar (4.81) , C Kunitz (4.74) , J Eberle (4.74) , E. Karlsson ( 4.73), J Toews (4.49), L Couture (4.16) , D Doughty (3.99). P. Datyzuk finishes just below D. Doughty and his THoR rounds to the same number of wins 3.99.  For the even strength only ratings the top ten was the following: A. Kopitar, E. Staal, E. Karlsson, P. Bergeron, J. Toews, L. Couture, H. Sedin, C Kunitz , D. Hamhuis and R. Getzlaf.  

The number of wins over an average player at their position for which they are responsible in an 82 game season.   These values account for the amount of time that players played.  Thus, E. Staal is the top because he is near the top in per play value but because he plays so much he is the most valuable player in these rankings.  On a per events on the ice, D Sedin is better than E Staal but E Staal contributes more total because he was on the ice for more action over the past two years.  Defensemen do better in the THoR ratings this time around as we have adjusted players by average impact at their respective positions.  Note that this means that THoR finds than average forwards have a greater impact than average defensemen on generating goal differential.  Note that to get wins over replacement you can add approximately half a win to each player, e.g. S. Weber would be worth about 5.42 wins over a replacement D.  

Sidney Crosby is not in our top 10 or top 20 for this period.  The story there is that Crosby has not been in enough games.  We are ranking players based upon their total contributions over the past two seasons.  It’s not that Crosby has not been good (or dominant as he was for significant portions of the 2013 season) when he has played,  but rather the model penalizes Crosby and others for not playing.  Ridge regression, the statistical method we are using, weights toward zero, or shrinks, our estimated values this especially impacts those with fewer games played.  We do this to deal with the flucutations in player ratings due to small sample sizes and multicollinearity which here means consistently playing with the same teammates..  

At the team level of the teams still in the hunt for the 2013 Stanley Cup,  Boston has 3, Chicago has 5 (with P Kane sitting at 105), Detroit has 3 (with J Franzen at 102), LA has 6, the Rangers have 1, Ottawa has 2, Pittsburgh has 5 (not including Crosby), and San Jose has 5.   

I appreciate the work of both but I prefer to think of what is gained by an individual  zone start.  Bruce McCurdy is on the right track, in my opinion, with this as quoted by Dellow in his first post.   For the discussion below I’m using data from 2011-12 and 2013 regular seasons through April 14, 2013.  I’m using 5v5 and 4v4 data and I’m looking at all non-stoppage events in the RTSS files.  That’s n=381,333 events in total.  Our outcome metric is the NP20 which is the net expected value of a goal in the 20 seconds after the event from the Total Hockey Ratings (THoR) paper.  We’re using an updated (since that paper) THoR model which includes a rink effects and score effects.   Latest results can be found on the THoR page. Estimates given below are from running the THoR even strength model.

There are some benefits to the THoR model and one of them is that we get an estimate of the impact of an ZS per play on expected goal differential, at least as measured by NP20.  That estimate for the effect of a ZS on subsequent outcomes in the most recent THoR is about 0.0055, meaning that for every additional play that started in the Offensive Zone, the expected goal differential gained is 0.0055.  As Gaelan noted in the comments of the first of Dellow’s posts, this is just the sort of thing that multiple regression should be used for.  

The value 0.0055 seems small to me as a first pass.   However, for a player like Henrik Sedin or Jordan Staal who were on the ice for over 7000 plays during this period, the impact can be significant.  Comparing the value of a ZS to the impact of home ice on a given play (0.0011), we see that a ZS is worth about five times as much as home ice.  Now this is at even strength and the home ice effect appears in every play and balances out generally as teams play as many home games as away games.  That ZS is worth 5 times home ice appears to be consistent across years that we have studied.

To put these numbers in context, we inflate them to give us a games worth.  Home Ice at Even strength is on average during this period about 210 plays per game and that works out to a goal differential favoring the home team of 0.23 (210*0.0011) per game.   ZS’s appear in about 68 plays per game or about 0.37 (68*0.0055) goals per game for the team starting in their offensive zone.  This does not show up blantantly in a game but it does have an impact over the course of a season.  Unlike home ice, ZS’s don’t even out over the course of a season. Unfortunately using the current ZS% we don’t get a sense for the differential in the number of ZS’s for a given player so it is hard to assess this with an example.  Hypothetically, someone who has approximately 200 more ZS’s in a given season should yield an extra goal differential. 

Another way to think of ZS is that the value of Zone Start per play is the same as that for the top players in the league.  So moving the start of your shift from the Neutral Zone to the Offensive Zone (or similarly from the Defensive Zone to the Neutral Zone) is like taking replacing an average player with a top player in the league.  Think replacing a Jay McClement with Jonathan Toews for a shift or replacing Trevor Daley with Shea Weber. 

However you think about it, ZS’s are an important factor in analyzing player value.  Models like THoR, those of Brian MacDonald and others can assess that effect and can isolate the impact of one factor among many.  

One more thought from watching some games recently is that it seems that some teams, especially Boston — being in the northeast US, I get to see plenty of them — instead of dumping and chasing behind the net, shoot at the goalie and charge toward the goalie.  They end up with a ZS from the goalie holding the puck.

Kudos to Dellow and Johnson for starting this conversation.  

The data used here is all Even Strength (5v5 and 4v4) data for the complete 2011-12 season and the 2013 season through games played through Sunday, April 14th, 2012.  

The top players for total contribution are Kopitar( +4.68), E. Staal (+4.28), Toews (+3.73), Bergeron (+3.73) and Couture (+3.61).  THoR is measured in wins over an average player in an 82-game season.  Thus, we are saying here that Kopitar is worth more than 4 and a half wins to his team.  Note that a replacement player is approximately 0.3 goals below an average player in THoR.  The top D is reigning Norris Trophy winner Erik Karlsson(+3.16).  Sidney Crosby is penalized in both the total contribution and average contribution of THoR by the amount of time that he has during both seasons.  Rounding out the top 10 are H. Sedin, Kunitz, the aforementioned Karlsson, Tavares and Getzlaf.  Not a bad group.

The THoRStandard which is average contribution per play on the ice is topped by Steen (+4.87), Hornqvist (+4.60), Kennedy (+4.54), Toews (+4.52) and Clarkson (+4.44).  It was this ordering that caused a ruckus with the original THoR but the model despite the changes listed above and the swapping out of the 2010-11 season for the 2013 season still thinks that good things happen when Steen and Kennedy are on the ice relative to what would be expected.  (At least we’re getting consistent results.)

One criticism of THoR from Scott Cullen at TSN can be found here and it is the fact that THoR ignores scoring rate, the rate of shots by a given player that are goals.  He validly points out that shots from Steven Stamkos are more likely to go in than shots by Tyler Kennedy.  True.  However, we know that shooting rates fluctuate a good deal over short periods like over a season.  Further, we are not just counting shots by Stamkos and Kennedy in their value but the shots both taken by their teammates and opponents when they are on the ice.  We’ll continue to assess this further and potentially tweak THoR.  But when we tested this idea in the past it lead to much greater fluctuation in estimated player value.  

Total Hockey Ratings Paper

Here is the abstract of that paper:

Hockey is a fluid sport with players frequently coming on and off the ice without the stoppage of play.  It is also a relatively low scoring sport compared to other sports such as basketball.  Both of these features make evaluation of players difficult.  Recently, there have been some attempts to get at the value of National Hockey League (NHL) players including Macdonald [1], Ferrari [2], and Awad [3].  Here we present a new comprehensive rating that accounts for other players on the ice will a give player as well as the impact of where a shift starts, often called zone starts, and of every non-shooting events such as turnovers and hits that occur when a player is on the ice.  The impact of each play is determined by the probability that it leads to a goal for a player’s team (or their opponent) in the subsequent 20 seconds.  The primary outcome of this work is a reliable methodology that can quantify the impact of players in creating and preventing goals for both forwards and defenseman.  We present results based on all events from the 2010-11 and 2011-12 NHL regular seasons. 

 The full paper is available here.

First, Bruce McCurdy of the Edmonton Journal wanted to know about whether there was a difference if the shootout went longer than 4 shots rather than the 6 shots that we considered in the original. Going first wins 62 of 132 shootouts that were four or less (46.9%). Going first wins 501 of 1006 shootouts whose length was 5 or more (49.8%). That difference is not statistically significant or practically significant for that matter.

The second and more difficult query to address came from Mike McKenna who is a goalie for the Peoria Rivermen, the AHL affiliate of the St. Louis Blues. He’s also a St. Lawrence University graduate in economics.  Mike wanted to know if there was an effect of scoring first. This was a harder task and took some time for me to get my head around. Clearly scoring first provides an advantage in and of itself since you are scoring and that provides a benefit. The question ultimately rests on whether scoring first improves your chances relative to what we would expect by chance alone.  From the data 921 of 1138 or 80.9% of shootouts have been won by the team that scores first.  

To answer that question requires some work.  There has been some analysis of scoring first in the NHL.  JLikens at Objective NHL  wrote on scoring first in the NHL during regulation and overtime based upon Alan Ryder’s work.  There is some really nice analysis there.  There was also a recent article in the Journal of Quantitative Analysis in Sports (JQAS), Responses to Scoring or Conceding the First Goal in the NHL by Marshall Jones that looked at the impact of scoring first in an NHL game.  Note that I’m not a fan of this JQAS article despite the fact that I’m an Associate Editor for JQAS.

To assess scoring first I wrote some R code to simulate what the probability would be for winning given you score first in the shootout assuming that goals come randomly (from a iid Bernoulli distribution).  I simulated 1 million shootouts using this model.  If we assume that scoring first has no impact, based upon the simulations 80.5% of shootouts were won by the team scoring first.  This value easily fits within a confidence interval for the probability of winning if you score first based upon the data (78.5%, 83.2%).   

Again so much of what we know about the shootout can be described with one word: randomness.

NB: From a strickly statistical perspective I should have run a  two sample test of proportions but given the small amount of variability in a 1,000,000 simulations it didn’t seem necessary.  

Our focus this time around is to look at whether or not a team goes first matters.  As most readers of this post will know, the home team has the choice of going first or second in the shootout.  We looked at all 1138 NHL shootouts that have been recorded and added data on which team went first.  (Many thanks to my student Zach Nelson for doing some data entry on this.)  

More often than not, 67% of the time, the home team chooses to go second.    And as far as winning is concerned, it does not matter whether a team goes first or second.  Going second you win about 50.5% (575 /1138) of the time.  That is more but not statistically significantly more than half of the time.

We also found that away teams win slightly more faceoffs than home teams.  That difference was statistically significant but it can’t be helped, so that is nice to know but not very practical knowledge.

Here are more of the gory details: Going First 

 More Statistical Analysis of Hockey articles can be found here: Hockey Analyses

1. It takes approximately 76 more faceoff wins than losses to gain a goal differential in the NHL.  We had previously found a similar number.  What we have added to our analysis is the number of wins that it takes .  Thus, not all NHL faceoff wins are equal.  A win on the power play or a win outside the neutral zone is more value than a win at even strength or a win in the neutral zone.

2. We also looked at rating individual players on their ability to win faceoffs accounting for faceoff prowess of the opponent, location on the ice (offensive, defensive or neutral zone), the teams strength (even, power play, shorthanded) and whether or not a player was playing at home.  Adjusting for these factors we found player ratings that are highly correlated (p>0.95, with their raw faceoff win percentage.  This suggests that raw faceoff percentage is nearly as good at rating players as statistically adjusted faceoff percentage.

 More details on this can be found in our short paper on the topic.  That paper is here: Faceoff Analysis.

Additional work done by our group on hockey can be found at here:  Other Statistical Hockey Articles.

For that analysis we looked at a variety of season level metrics for all of the US Division I hockey programs over the last 10 years.  Most of those metrics focused on the things that teams do: win percentage, power play percentage, goal against average, etc.  We played with a variety of regression type models but at the end of the day the two factors that we were important for predicting a given years percent capacity were the team (i.e. Michigan or RPI or North Dakota)  and their winning percentage. 

One more thing that was quite intriguing to us was that we found that a teams winning percentage was equally affected by goals for and goals against.  That is, scoring another goal was just as important as preventing another goal in terms of predicting season level win percentage.  

Here’s a link to the article: Just Win, Ehh!

It is clear that the probability at each location increases from Even Strength to the Power Play.  That’s not a surprise.  The maps do allow you to get a sense of where the high probability areas are for each type of shot. 

Here they are: Shot Probability Maps.