Eric Fehr, Matt Hendricks, Brooks Laich celebrate goal

Photo credit: Rob Carr

Not all goals are created equal. A team scoring first has almost twice the win percentage of a team that trails first, while scoring an empty net goal almost always means the game was out of reach. But what about all the goals scored in between? Of all those goals that a player scores, how many contribute to victories and how vitally do they contribute?

There is a direct relationship between how many goals a club scores and allows to its won-lost record, often called the Pythagorean expectation. The formula is pretty simple: win% = GF^2/GF^2+GA^2 where GF = goals for, GA = goals against, and ^ means “raised to the power of”, in this case, 2.

For example, last year Washington scored 318 goals and allowed 233, for a Pythagorean win expectation of 318^2/(318^2+233^2) = .651 or 53 games out of 82. They won 54 games last year.

Using this we can weight the value of each goal scored this year to how much it increased the Capitals chance of winning. A goal scored in a 0-0 game has more of an impact on the outcome than the fifth goal in a 7-0 blowout. Scoring in one-goal games will always be at a premium. Washington has already matched their total of 1-goal games (41) from last year, making those goals even more meaningful. I will say there are obvious limitations, such as ignoring assists to give a better picture of who is contributing overall to wins and I am looking into adding this metric — as well as other improvements — to future iterations.

In the table below, goals are the skater’s current goal total this season through game 75. Total Win% Added is the cumulative sum of how much all his goals increased the teams chances of winning and W% added per goal is the average increase that player’s goal contributes to the team’s chances of winning.

Player Goals Win% Added W% added Per goal
Alex Ovechkin 29 4.53 15.6%
Alexander Semin 25 2.65 10.6%
Mike Knuble 20 2.84 14.2%
Nicklas Backstrom 18 4.36 24.2%
Brooks Laich 16 2.94 18.4%
Marcus Johansson 12 3.13 26.1%
Eric Fehr 10 1.82 18.2%
Jason Chimera 8 1.21 15.1%
Matt Hendricks 8 1.33 16.6%
Mike Green 8 1.56 19.5%
Mathieu Perreault 7 1.64 23.5%
John Carlson 6 1.15 19.1%
Matt Bradley 4 0.50 12.5%
Boyd Gordon 3 0.79 26.2%
John Erskine 3 0.56 18.7%
Jason Arnott 2 0.10 5.1%
Jay Beagle 2 0.11 5.7%
Karl Alzner 2 0.79 39.3%
Tom Poti 2 0.24 11.9%
Andrew Gordon 1 0.50 50.0%
Dennis Wideman 1 0.00 0.0%
Jeff Schultz 1 0.50 50.0%
Scott Hannan 1 0.50 50.0%
Tyler Sloan 1 0.11 11.4%

Let’s start with the three skaters who have eight goals so far on the season: Jason Chimera, Matt Hendricks and Mike Green. On average, a goal scored by Chimera adds a 15.1% chance at a win, while Hendricks’ tallies add 16.6%. Then there’s Mike Green, who’s robust 19.5% shows us why his nickname is “Game Over.”

When Alex Semin scores a goal the Caps are 23-0, but a look at the table shows that he increases the chances of a Caps’ win by about 10% with each one — far less than some of the others atop the leaderboard. Here’s why: almost half his goals have no significant impact on winning. Ten have come when the Caps already have the lead, six when the score is tied and the rest when the Caps trail.

The most intriguing values, at least to me, are those of the centers. Across the board they seem to be higher than the other skaters prompting me to take a look at last year’s values as well. Backstrom’s average contribution is significantly higher this year (24.2%) than last year (14.9%) despite having almost twice as many goals, while Boyd Gordon is relatively even, seeing 26% this year vs. last year’s 30% average contribution. Which brings us to the rookies, Mathieu Perreault and Marcus Johansson, both of whom seem to score goals when it counts.

So what does this all mean? Perhaps this is a different way of looking at who has been “most valuable.” Perhaps Semin’s goals are just windrow dressing and have less impact on the game than we think. Perhaps we are one step closer to defining what “clutch” play truly is — or if it even exists.

Perhaps I just have too much time on my hands.

  • Peter

    Well done!

  • http://www.calacirian.org sonja

    I love this post … love it love it love it.

  • 28ISGREAT

    Interesting. But when I see these sorts of quantitive analysis I always wonder how they can be improved on further – you identified assists and the reduced value of pile on goals – but what about the relative timing of a goal?

    While a win is a win is a win, couldn’t it be argued that a GWG scored late in the 3rd is more potent (i.e. lethal) a goal than a GWG scored early in the first (e.g. a late go-ahead goal means less time/opportunity for an opposing team to even it up), and is therefore arguably more valuable a goal? And what about GWG scored short handed? It would seem those could be “valued” differently based on the effects they may have on certain intangibles of a game?

    And what’s the difference between using the Pythagorean expectation model and just looking at GWG metrics? Particularly if you’re looking at individual player values.

  • Darla

    “Who’s” = who is or who has. If neither of those replacements makes sense in your sentence, use whose.

  • http://www.russianmachineneverbreaks.com Ian

    Really impressive post, Neil. Though stats like “The Capitals are 23-0 when Alex Semin scores” sound awesome and legit, I’m glad you tried to dispel it’s importance. And just FYI, this was probably my favorite line above:

    The formula is pretty simple: win% = GF^2/GF^2+GA^2 where GF = goals for, GA = goals against, and ^ means “raised to the power of”, in this case, 2.

  • Neil – RMNB

    @28isgreat “what about the relative timing of a goal?”

    Good question and yes when the goal is scored ( time/period) would weigh more heavily, but then we are moving to a Poisson model — which is FAR more complex. Also, Poisson models provide a little more accuracy, but we are talking barely a few percentage points.

    “And what’s the difference between using the Pythagorean expectation model and just looking at GWG metrics?”

    GWG is binary: did he score the winning goal or not. My method looks at how much the goal increased the team’s chances of winning regardless of when it came. If someone scores two goals when the game is close or tied, than he has prob done more for his team than if he just scored the goal that put them ahead for good.

  • Yuk

    I think the presented stat analysis is an example of bad one and not to ‘love’ or ‘praise’. Several factors are completely missed. It partially mentioned by “28..”. For example, when Caps leading by one the second leading goal in the third period, even empty netter, could be the most defeating and deflating for opponents. Games and second goals against Habs are example.
    The stat flaws is visible in Semin’s explanation and example. It is clearly stated that when Semin score the Caps is 23:0! Then by some strange logic, it is stated that “..almost half his goals have no significant impact on winning. Ten have come when the Caps already have the lead, six when the score is tied and the rest when the Caps trail.” This conclusion is totally upside down. It means that, at-least, 15 goals (or 60% of all his goals) Semin scored when Caps were down or tied but then they won, remember 23:0!) probably exactly because Semin score. Simply saying, if Caps trailing or tied and Semin score it is almost guaranty the Caps eventually will win. What is more, it also means that it would be irrelevant how many goals opponents score when he is on the ice in games when he score!?!? And this is not counting his deflating, secondary goals, like in the last games against Habs. The same flaws probably can be find in other players stats, it’s just Semin’s stat is pure one (23:0!).

  • JW90

    Well we already knew Marcus was a beast

  • 28ISGREAT

    Thanks Neil! Both for the great post & response, and for ruining my ability to toss out the “when Semin scores the Caps win” stat.

  • http://twitter.com/ngreenberg Neil – RMNB

    @Yuk

    “the second leading goal in the third period, even empty netter, could be the most defeating and deflating for opponents”

    It very well could be the most defeating and deflating MENTALLY, but aren’t we already measuring that by giving the team that scores the goal more of a chance to win in terms of probability?

    “The stat flaws is visible in Semin’s explanation and example.”

    Let’s use an extreme example and say I score a goal every time my team is up 5-0. We win all those games. Is it because I scored?

    Also, please reconsider loving and praising me. I’ve had a bad day.

  • Tim

    Great article. Some of the players with the highest W% added/G are not who I would expect. One thing I can’t figure out – how is Beagle’s so low when both his goals have been GWGs? I’m sure there’s something in the article that answers that, but I’m not seeing where it is.

    Just for comparison, where would Bradley last season have ranked on this, with his 5 GWGs out of 10 goals?

  • yuk

    Neil, i don’t know whether we talking about different topics or statistics.. What can be less simple, then understand the statistics with Semin. When he score (15 goals according to your stat when Caps behind or tied , not when he adding another goal to the victory) Caps coming out always victorious (you saying 23:0).. Will you consider this as contribution to Caps victory or meaningless? If Caps has something like 15:8 when Semin score I even not bother to discuss. But to my opinion 23:0 also wrong from you, you should check it, Because as I remember Semin has 3 hat-tricks, not counting doubles. Which mean that at-least 6 goals are not counting to additional Caps victories, and it should be,, at-most, 25-6=19 Caps victories and 0 losses.
    In other extreme, what your stat saying is that you should put on ice beagles, perraults, gordons and the Caps will have 82:0 seasons. In reality, what your stat is saying is that this approach is completely meaningless to individual players and spark only empty discussions.
    As example of really good individual statistical approach is from todays PuckDuddy. about goalkeepers and rebound control and goals. This gives a lot of info about tactical approach to how to play hot goalies of Bruins, Flyers, during playoffs. In fact, in the same site, in Caps-Habs review they citate Habs player who said that “Habs was in the game until Semin scored the second goal “. Nothing to add.

  • http://twitter.com/ngreenberg Neil – RMNB

    @Yuk I feel like we are BFFs. I hope you do too. Seriously. I feel like me and you could truly embody the Sheen Way of Winning. Like Starsky and Hutch, only with hockey and probably a much less cool car.

    It is true: when Semin scores Caps win. But last time I checked there were other players on the team.

    Also, not sure how ice beagles with his +5% win added per goal would make the Caps 82-0 but I will ask the Monte Carlo Machine. It’s kinda smart and deserves love and praise.

    As for PD: I did see the rebound post and believe it or not I have one of my own coming out which you can also not love or praise.

  • adam

    I like to promise things and then take months+ to deliver on them, but I’m working on a more complete model (Poisson-based) that will account for more than goals, e.g. penalties, just plain shots, etc (and I hope it’ll be done in the next two weeks), as well as more specific time/skater-situational stats. I look forward to sharing it with you (look for it at BtN, probably), because I thrive on stuff like this.

  • yuk

    Neil, remove Beagle I just put his name as an AHLer w/o looking and because I remember his goal when he make 180o degree revolution before scoring and Caps won at the end., In science,, when you feel uneasy about interpretation/results, you start checking original data, That’s why semin’s, the easiest one, and that’s why you have usually three unseen, unfortunately, reviewers before managing to publish data.

    Forget rebounds, it’s already impressively done (to watch and analyse all 700 goal after all-star game thats something!) i can suggest another topic: how many goals playoff-bound teams score because of tip-in and deflection. The reason is I think Caps is probably rank the last, comparing to Pens (remember Crosbys goal against Caps), Flyers or Bruins.. The last goal i can remember by Caps was by Ovi against Toronto couple month ago. And I think Fehr is the only player who purposefully trying to score by tipin or deflection. This stats will show what Caps tactically missing comparing to others, who probably score 25-40% of all goals by this method.

  • MM

    Nice work. Good read. Well written.
    I think that goals scored when you have the lead are also important, more so than what you’re assuming. If you score when the game is tied, or when your team is already ahead by a goal, you reduce the chances that the opposing team can score enough to make a come back; you’re also taking away their motivation by putting them even farther behind; there’s also the adage “taking the crowd out of the game” but I don’t know how to quantify that (cough-nudge-wink).
    In short, I think scoring with the lead is pretty important. It might not be the game winning goal, but it does something to secure a victory.

  • Bob29

    Another item left out of your analysis especially on Semin is the timing of his goals he got in his four hat tricks.
    - Against Atlanta he got goals all the Caps goals in regulation and Flash scored the OT winner.
    - In a 6-3 over TB, he had the 3, 4, and EN goals with the 4th being the GWG plus 2 assists
    - In their 6-0 shutout of TB he had the 3d 4th and 5th goals which by their timing were clearly deflating for TB
    - His last hat trick against Anaheim, his first 2 goals tied the game and his 3d goal was the GWG.

  • D

    Isn’t it interesting that the only people calling this statistic useless are obviously Semin fans…

  • http://amusingfool.blogspot.com/ AMusingFool

    This was very interesting analysis. It would be interesting to expand it to a W%-weighted +/-, although I don’t know if the data are available.

    Another thing that would be cool (although the data definitely are NOT available) would be to weight things even further by where the play is taking place. That is, by the current analysis, in OT, the W% is always 50/50, until someone scores. And that goal always increases W% by 50%. But should it really be considered 50/50 if one team is in the offensive zone? How about if they keep it in the O-zone for half a minute? I know, I know, it would take a while to figure out how to factor that in, even if the data were available… This post just got me thinking about it.

  • Neil – RMNB

    Perhaps I should repost this disclaimer?
    “I will say there are obvious limitations, such as ignoring assists to give a better picture of who is contributing overall to wins and I am looking into adding this metric — as well as other improvements — to future iterations.”

    @Bob29

    “- In a 6-3 over TB, he had the 3, 4, and EN goals with the 4th being the GWG plus 2 assists
    - In their 6-0 shutout of TB he had the 3d 4th and 5th goals which by their timing were clearly deflating for TB
    - His last hat trick against Anaheim, his first 2 goals tied the game and his 3d goal was the GWG.”

    My metric takes ALL OF THIS into account. All of it. Every last drop and he STILL comes out weak.

    “In their 6-0 shutout of TB he had the 3d 4th and 5th goals which by their timing were clearly deflating for TB”

    Can you point to a link (or anything) that has evidence of this “deflation?”

  • http://amusingfool.blogspot.com/ AMusingFool

    Sorry, I didn’t mean that to come across as criticism. It was meant more in the spirit of “here’s what I think would be cool improvements for those future iterations”.

  • http://amusingfool.blogspot.com/ AMusingFool

    (Assuming availability of data, of course :)

  • WB

    Semin is now 23-0-1 when he scores.