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  1. More Hockey Stats
    Original post
    On Talent In General
     
    When you want to do some useful work, you need a skill to do that work. Naturally, one doesn't need a skill to tweet, but that's not a useful work to start with. But to do stuff that actually profits you a certain level of skill is absolutely necessary.
     
    In order to have the skill, you need to learn it, and then to improve it. And there are only two basic factors that define how well you learn and improve in the skill - the talent and the effort. The bigger is your talent, the bonus from the nature, whether it's thanks to inborn memory, flexibility, or a quick eye, the less effort you need to achieve the given level of skill. And the trade-off is not even linear, there are areas, mostly creative ones, such as music or painting where no amount effort, grit and determination can bring you to a certain level of skill.
     
    On the other hand, the bigger the talent, the less necessary the effort becomes, and at the extreme level of talent, also known as ... genius the person sometimes doesn't need practically any effort to improve at an incredible pace. This phenomena, already extremely rare, is mostly restricted to mind activities, bound by the necessity in constant exercise to maintain a high level of skill in a physical activity. Names of Wolfgang Amadeus Mozart in composing, Jose Raul Capablanca in chess or Robertino Loreti in music come to mind when we talk about such geniuses. Mozart was composing himself already at age five, Capablanca learned the game of chess from observation only, but won the Cuban Championship when he was twelve, and Loreti became a European super-star shortly after he was noticed singing folk tunes on the streets of Rome.
     
    Talent And Skill In Hockey
     
    Hockey is also a work that requires skill. It's a complex skill that consists of many abilities: skating, observation, agility, strength, endurance, wit an others. Since it's a team game, the team consists of players that excel at these abilities on a different level, and a "complete hockey player" would actually be someone who can skate like Mike Gartner, is observant like Wayne Gretzky, can shoot like Mike Bossy, has the strength of Eric Lindros, endurance of Nicklas Lidstrom, and, actually, can easily take a hit from Cam Neely (and hit like Neely, too) and hold his ground in a fight against Tie Domi, and such a "complete hockey player" would exist mostly in the computer games.
     
    Nevertheless, of course the hockey players have different levels of ability in these dimensions of the hockey skill, and, unfortunately, today, mostly the ability to stickhandle is exclusively classified as 'skill'. No, the hockey skill is composite, and the wonderful dekes are just one aspect of it. Naturally, the most appealing, and probably the most important dimensions (we're not talking about goaltending here, but the reader can make similar projections to that position, too) are the ones directly relating to the goal scoring, and the players who excel at them are generally valued higher.
     
    However, in the way the hockey is defined by the NHL rules and and the NHL tradition, other qualities of the skill - hitting, blocking shots, fighting are required to make the complete hockey team. In a different league, such as the USSR league was, with very limited hitting and explicitly prohibited fighting, the sportsmen would develop more into the goal-scoring oriented hockey players.
     
    Where The Talent Comes From
     
    Well, from mothers' wombs. But then, the players usually begin to learn the skill of hockey from a very young age, and by the age of the NHL draft eligibility, their talent is well-evaluated and the positions in the draft order give a good approximation of the order of the talent of the available players. There are few exceptions, and these mostly are the European players, especially the Eastern-European ones who do not take part in the draft, but continue to develop in their leagues, such as the KHL. But the rule that the biggest chunk of the hockey talent is available at the annual draft, and that the talent is sorted according to the actual draft picks pretty much holds.
     
    Therefore, the teams that feature the higher draft picks in their roster are on average definitely more talented ones than the ones with the lower picks. Are they most skillful? Not necessarily. Remember, that in the first part of this essay we stated that to develop a skill, both talent and effort are required. Some players, for whatever reason, fail to put the necessary amount of effort to achieve the skill level expected for their talent, and became disappointments, or even draft busts. Some, on the other hand, put a great effort and determination, and leap beyond such expectations. The latter ones, unfortunately, are bound by that aforementioned ceiling that sometimes lack of talent produces.
     
    A team whose top draft picks underperform on a regular basis must recognize it has a culture problem. When time after time, players, who are supposed to be easy learners and advance rapidly, stall or degenerate it means that the organization, and, pardon the pun, it's farm, has a soil problem, that even the best seeds planted in it fail to yield the desired fruit.
     
  2. More Hockey Stats
    Original post.
     
    The practice of chess tournaments provides two traditional metrics that are used to rank participants beyond their mere scoring. Their names are the Buchholz coefficient and the Sonneborn-Berger coefficient (often called just Berger). They are frequently used as tie-breakers in chess events, however I arrived to completely different application for them for the National Hockey League seasons.

    1. The Buchholz coefficient

    The Buchholz coefficient is simply the sum of the points of your opponents.
     
    B = Σn=1N Pn   So, if you played five games, and your opponents currently have 5, 3, 8, 6 and 6 points, your Buchholz value will be 28. Please note, that the current number of points is always used, not the number of points at the moment of meeting. The outcome of the game does not matter (for that one see the Sonneborn-Berger).

    At first, the usefulness of such a criteria would prompt a raise of the eyebrow. However, it's not used in round-robin all-play-all tournaments as a final tie-break, because, naturally, the coefficient would be the same for all tied parties. It's used in a special format of chess events called the Swiss Tournament, not very popular outside of the realm of board games for purely logistic reason. But then, consider, first, an NFL season. The list of opponents every team plays there over the 16-game season may be quite different. And, whoever would end up with a larger Buchholz coefficient, clearly would've had stronger opposition on the way.

    Now let's go back to hockey. First of all, at the end of the season, although everyone has played everyone, they did so a different number of times. Thus, the sum of opponents' points at the end of the season could be different between teams - including within the same division, if they had a different schedule. So, this could still be a very valid tiebreak. Secondly, the season is so long (82 games, unlike a chess Swiss which is rarely longer than 11 rounds), and that gives us a lot of midway points in time, when the all-play-all has not been completed yet! Here the Buchholz coefficient can clearly show, who has had the stronger opposition up until a certain moment.

    Then, if we look at the remainder of the schedule for each team, and for every game we add the opponent's points we get an excellent remaining schedule strength estimator.

    Wait... there's a caveat.

    Unlike in a chess tournament, where every round occurs for everyone at the same time, and barring very rare circumstances, every participant played an equal amount of games at any point of the tournament, there may be a significant difference in the number of games played by different teams, so summing the opponents up will not work very well. And these opponents also played a different number of games, so their total amount of points is not a very good indicator.

    Fortunately, it's not a big deal. Instead of totals, let's operate with per-game numbers. So the NHL Buchholz Coefficient for a team after N games becomes:
     
    B = (Σn=1N PPGn)/N.    Same applies for the remaining schedule strength, where the per-game numbers of the remaining opposition are summed an averaged.

    So, if the team played three games against opponents who currently are:
    A) 6 points in 4 games, B) 3 points in 3 games, C) 2 point in 5 games, then the team's Buchholz value would be (6/4 + 3/3 + 2/5) / 3 = 2.9/3 ~ 0.967pts.

    Here are the current (Mar 12th 2017) Buchholz coefficients and remaining schedule strengths for the entire 30 times (and note how the Blues stand out with plenty of matchups vs Colorado and Arizona remaining).

    +-----------------------+-----------+-------+-------+
    | Team Name             | PPG       | Buch  | RStr  |
    +-----------------------+-----------+-------+-------+
    | Washington Capitals   | 1.4179105 | 1.119 | 1.133 |
    | Pittsburgh Penguins   | 1.4029851 | 1.117 | 1.127 |
    | Minnesota Wild        | 1.3939394 | 1.090 | 1.070 |
    | Columbus Blue Jackets | 1.3731343 | 1.125 | 1.132 |
    | Chicago Blackhawks    | 1.3283582 | 1.088 | 1.096 |
    | San Jose Sharks       | 1.2985075 | 1.106 | 1.106 |
    | New York Rangers      | 1.2941176 | 1.120 | 1.184 |
    | Ottawa Senators       | 1.2537313 | 1.105 | 1.169 |
    | Montreal Canadiens    | 1.2352941 | 1.122 | 1.097 |
    | Edmonton Oilers       | 1.1791044 | 1.121 | 1.040 |
    | Anaheim Ducks         | 1.1764706 | 1.102 | 1.150 |
    | Calgary Flames        | 1.1764706 | 1.099 | 1.140 |
    | Boston Bruins         | 1.1470588 | 1.115 | 1.151 |
    | Toronto Maple Leafs   | 1.1343284 | 1.114 | 1.150 |
    | Nashville Predators   | 1.1323529 | 1.105 | 1.116 |
    | St. Louis Blues       | 1.1194030 | 1.144 | 0.943 |
    | New York Islanders    | 1.1194030 | 1.142 | 1.103 |
    | Tampa Bay Lightning   | 1.0895522 | 1.121 | 1.134 |
    | Los Angeles Kings     | 1.0746269 | 1.118 | 1.104 |
    | Philadelphia Flyers   | 1.0447761 | 1.122 | 1.179 |
    | Florida Panthers      | 1.0298507 | 1.118 | 1.175 |
    | Carolina Hurricanes   | 1.0000000 | 1.138 | 1.136 |
    | Buffalo Sabres        | 0.9855072 | 1.127 | 1.158 |
    | Winnipeg Jets         | 0.9565217 | 1.110 | 1.143 |
    | Vancouver Canucks     | 0.9558824 | 1.115 | 1.152 |
    | Dallas Stars          | 0.9552239 | 1.119 | 1.100 |
    | Detroit Red Wings     | 0.9545455 | 1.151 | 1.059 |
    | New Jersey Devils     | 0.9117647 | 1.148 | 1.132 |
    | Arizona Coyotes       | 0.8358209 | 1.133 | 1.098 |
    | Colorado Avalanche    | 0.6119403 | 1.128 | 1.164 |
    +-----------------------+-----------+-------+-------+
      In the next installment we're going to talk about the application of the Sonneborn-Berger coefficient to the NHL regular season.
  3. More Hockey Stats
    Original post.
     
    There was nothing wrong with ties. The 2-1-0 point system works fine in various sports around the world. It's just ... not fitting into the mind of a North American sports fan. "Who won?" - "It was a tie." - "Who won on a tiebreak?" Basketball and baseball do not have ties, and American Football has them at a rate of 1-2 times per whole season. So more than ten years ago NHL went with the flow and abolished ties, introducing the shootout, and with a twist, where the team making it past the regulation would still get the point, and a 2-2-1-0 point system came to life.
    Since then the argument rages, whether the ties should come back, or whether the consolation point should be taken away, or whether the much more energetic 3-2-1-0 point system, adopted across the ocean and by the IIHF should make its way into the NHL as well. The feeling that there is something unhealthy when a team loses and still gets something, while the winner is not penalized is nagging.
     
    The argument from the NHL leadership claims the system creates denser standings and thus more interest and drama throughout the season is a valid one. However, this system, as we show below, creates a wrong incentive.
     
    The standings in the NHL are defined by a points total, and the seeding in the playoffs are first and foremost the divisional standings. The relative standings across conferences have a rather minor effect of the potential home advantage in the Stanley Cup Finals, the same standings within the same conference but across divisions have an impact on the seedings in the whole playoffs, but also to a limited effect. Therefore, at least with the exception of intradivisional games, but possibly including these games too (especially against the competition that has fallen out of the playoff picture), the only thing that matters are the points accrued by the team itself, and not the points the opposition gathers. Let's wield the statistic that says that 25% of the games go to the overtime and the
     
    So what are the point expectations in a 2-2-1-0 system? Let's compare a few situations when teams A and B play.
    Team A has 75% chance of winning the game (that's a huge, possibly maximum imaginable favorite odds) Team A has 67% chance of winning. Team A has 60% chance of winning. Team A has 50% chance of winning.
    Let's wield the statistic that says that 25% of all games go to the overtime and the shootout occurs in 40% of these games. Let's also assume that the 3-vs-3 overtime is more random and reduces by half the advantage of the better team (i.e. 75-25 becomes 62.5-37.5), and that the shootout is completely random, so the chances of winning it are 50/50. Then, the probabilities of the outcome become:
     
              Chance PwReg    PwOT      PwSO    xPoints
    Team A    75%    0.5625   0.09375   0.05    1.51875
    Team B    25%    0.1875   0.05625   0.05    0.73125
    Team A    67%    0.5025   0.08775   0.05    1.39275
    Team B    33%    0.2475   0.06225   0.05    0.85725
    Team A    60%    0.45     0.0825    0.05    1.2825
    Team B    40%    0.3      0.0675    0.05    0.9675
    Team A    50%    0.375    0.075     0.05    1.125
    Team B    50%    0.375    0.075     0.05    1.125
     
    Now let's consider than the stronger team A plays intentionally for overtime and manages to force it in 75% of the cases.
     
              Chance PwReg    PwOT      PwSO    xPoints
    Team A    75%    0.1875   0.28125   0.15    1.55625
    Team B    25%    0.0625   0.16875   0.15    1.19375
    Team A    67%    0.1675   0.26325   0.15    1.49825
    Team B    33%    0.0825   0.18675   0.15    1.25175
    Team A    60%    0.15     0.2475    0.15    1.4475
    Team B    40%    0.1      0.2025    0.15    1.3025
    Team A    50%    0.125    0.225     0.15    1.375
    Team B    50%    0.125    0.225     0.15    1.375
     
    In ALL cases it's worth for both teams to steer the game into OT. For the even odds case, the expectation gain is a whopping 0.25 points! Even in the case of super, uber favorite, it's still worth for that team to head to overtime, as it projects a gain of 0.04 points. And the gains for the underdogs are so big that there is no reason for the underdog to disturb the force of the overtime, so they will happily comply! Meaning: we'll see more fun overtime, we'll see more dumb shootouts, but more importantly the 60 minutes of hockey will lose a lot of their significance. The only quantitative incentive to finish the game in regulation becomes denying extra points for your opponents - hardly a significant matter in what, fifty out of the eighty-two season games!
    Now, let's repeat these calculations with 3-2-1-0 point system and combine them into another table:
     
                           2-2-1-0                       3-2-1-0
              Chance Exp25%OT  Exp75%OT   Δexp     Exp25%OT  Exp75%OT   Δexp
    Team A    75%    1.51875   1.55625   +0.0375   2.08125   1.74375   -0.3375
    Team B    25%    0.73125   1.19375   +0.4625   0.91875   1.25625   +0.3375
    Team A    67%    1.39275   1.49825   +0.1055   1.89525   1.66575   -0.2295
    Team B    33%    0.85725   1.25175   +0.3945   1.10475   1.33425   +0.2295
    Team A    60%    1.2825    1.4475    +0.165    1.7325    1.5975    -0.135
    Team B    40%    0.9675    1.3025    +0.335    1.2675    1.4025    +0.135
    Team A    50%    1.125     1.375     +0.25     1.5       1.5        0
    Team B    50%    1.125     1.375     +0.25     1.5       1.5        0
     
    Now there is no incentive for the stronger team to push for overtime, and even the gain for the weaker team decreased. 3-2-1-0 definitely encourages a regulation decision!
    Reasons where brought up against the 3-2-1-0 system. One states that the spread over the standings will be too thin, and more teams will be eliminated from the playoff race early. This argument has had no statistical support, and the element of drama when a team pulls a goalie in a tied score trying to force a 3-0 point win may actually more than make up for it. Another argument refers to soccer studies that claim the 3-1-0 point system there encourages teams to sit on their early leads trying to stifle the game, which decreases the attractiveness of the game. This argument is more valid, although it's notably harder to preserve a lead in hockey than in soccer. But beyond that this argument prompts for another, a truly revolutionary suggestion...
     
  4. More Hockey Stats
    Despite all the delays we move on to League's Yearly Tendencies.

    PART III

    This view shows stacked bars of various event counts per season in the NHL.All the stats are presented per game, since the amount of games played varied every season. 

    For the first time we encounter the stat selection menu, on top of the graphs. On this page it features the following options:
     
    Category of the stats Stage of the games (Regular or Playoff)
    Available stats are: 
    Shots Goals (available since 1987, from Boxscore reports) Shots on Goal (available since 1987, from Boxscore reports) Misses (available since 2005, from PBP reports) Blocks (avaliable since 2005, from PBP reports) Icings (available since 2002, from PBP reports) Margin of victory (available since 1987, from Boxscore reports) Penalties Minor Major Fighting Misconduct Match Penalty Goals per Game The stats are available for regular season, playoffs and both stages combined.

    The PBP reports from the NHL dating before 2005 are wildly inconsistent, thus we didn't use them for MISSES and BLOCKS.

    We are using the wonderful d3js library for producing these graphs.

    WE NEED YOUR HELP!
    If you are an experienced Webmaster, especially with Javascript and CSS we would greatly appreciate the potential tidy-up and enrichment you could provide to these graphs. Your work will be credited for future reference! Write to us, or get in touch with us on Twitter. Thanks!

    Possible future additions:
    PowerPlay success Minor penalty breakdown Aggregations and overlays Mouse graph manipulations Your ideas are welcome!
  5. More Hockey Stats
    Original post.
    2. The Sonneborn-Berger coefficient.

    This stranger beast is a metric extensively used for tie-breaks in chess-round robins and as an auxiliary tie-break tool to the Buchholz coefficient in non-round robins. Let's start with the definition.
     
    SB = Σn=1N f(Rn,Pn)   where Rn is the result against the n-th opponent, and Pn is the opponent's points score.
    The function  f(Rn, Pn) is defined as:

    f(Win, Pn)  = Pn
    f(Tie, Pn)  = Pn/2
    f(Loss, Pn) = 0

    The result value evaluates whether the participant performed better against stronger and weaker opposition. Actually, I do have a problem with this criteria as a tie-breaker, in my opinion ALL points are created equal, and it doesn't matter if they came from a contender or a bottom feeder. However, this metric does answer the notorious statements like "This team only shows up for big games" and "This team is only good against garbage opposition."

    So, first of all, for the NHL application, we will modify the function f(Rn, Pn) to:

    f(Win, Pn) = Pn
    f(OW, Pn)  = 2*Pn/3
    f(OL, Pn)  = Pn/3
    f(L, Pn)   = 0

    to account for the overtime point.

    Then, we can calculate the minimal possible SBmin value for a team with the given schedule so far this season, by assigning Wins to be against the weakest teams played, and the OW/OL against the weakest remainder until the sum of W, OW and OL points add up to the number of points the team currently has.

    Similarly we shall calculate the maximal possible SBmax value by assigning Wins to be against the strongest teams played, and the OW/OL against the strongest of the remainder, assuming OT wins are about 1/4 of the whole.

    Then the closer the actual SB is to the SBmin or SBmax we may be able to say whether the team is successful more against the bottom feeders, the top guns, or whether it achieves its points from the whole spectrum available.

    Here is the table describing how this season's teams have their SB positioned between SBminand SBmax.
     
    Team Points SBmin SBopt SB SBmax Pittsburgh Penguins 1.40 44.28 46.48 46.24 53.06 Washington Capitals 1.40 44.70 46.74 47.77 52.89 Minnesota Wild 1.37 42.25 44.36 46.63 50.66 Columbus Blue Jackets 1.37 43.10 45.36 46.44 52.15 Chicago Blackhawks 1.34 41.61 43.90 43.79 50.80 San Jose Sharks 1.31 40.68 42.97 44.16 49.84 New York Rangers 1.30 41.25 43.67 45.55 50.92 Ottawa Senators 1.25 37.84 40.07 41.79 46.78 Montreal Canadiens 1.25 39.37 41.74 41.05 48.87 Anaheim Ducks 1.19 36.86 39.43 40.12 47.15 Calgary Flames 1.18 35.97 38.49 38.20 46.05 Edmonton Oilers 1.16 35.86 38.32 37.43 45.70 Boston Bruins 1.15 34.73 37.23 37.74 44.72 Nashville Predators 1.13 33.28 36.14 38.04 44.72 Toronto Maple Leafs 1.13 34.64 36.99 35.66 44.02 St. Louis Blues 1.12 34.69 37.14 38.52 44.50 New York Islanders 1.12 34.36 36.94 37.94 44.71 Tampa Bay Lightning 1.09 32.62 34.98 35.41 42.06 Los Angeles Kings 1.07 32.10 34.66 33.56 42.34 Philadelphia Flyers 1.04 31.26 33.56 32.01 40.48 Florida Panthers 1.03 30.89 33.12 30.95 39.82 Carolina Hurricanes 1.00 29.43 31.78 32.41 38.85 Buffalo Sabres 0.99 30.09 32.49 33.43 39.68 Winnipeg Jets 0.96 27.55 30.35 31.48 38.75 Vancouver Canucks 0.96 28.48 30.91 29.02 38.21 Dallas Stars 0.94 28.05 30.62 31.16 38.34 Detroit Red Wings 0.94 29.12 31.12 30.02 37.13 New Jersey Devils 0.91 27.78 30.15 28.63 37.27 Arizona Coyotes 0.84 25.13 27.24 25.86 33.56 Colorado Avalanche 0.61 17.90 19.74 19.98 25.25
    Once again, we use Point Per Game values because the teams and their opponents have a different number of games played at most of the moments within a season.

    We would dare to make one more step forward and claim that the team that performs closer to SBmax seem to have a coach problem (notable differences highlighted in green in the table above). The roster is there to compete against the best, but the points aren't trickling in at a pace good enough against the fodder. Similarly, if the SB value is closer to SBmin is more likely to have a GM problem (notable differences highlighted in blue in the table above), that its roster is not good enough to compete, but the coach is able to squeeze close to the maximum out of it. However, it is natural to win more games against the weaker teams, so we set the balance point at SBopt = (SBmax + 3*SBmin) / 4;

    Wrapping up the talk about the Buchholz and the Sonneborn-Berger coefficients we would like to state that these values have an almost entirely descriptive value and without any predictive capability, with a small exception of the Buchholz-based remaining schedule strength metric. And even then, it's sort of a 'descriptive prediction'.

    Please see more Buchholz and Berger-Sonneborn data on the website!
  6. More Hockey Stats
    Original post.
     
    In the previous post we mentioned the Goodhart's Law and how it threatens any evaluation of an object. We said that it traps the Corsi/Fenwick approach because it substitutes the complex function of evaluation of a hockey player by a remarkably simple stat - shots.   Goodhart's law is not alone. In any research it is preceded by the two pillars: Popper's law of falsifiability and the Occam's razor. A theory willing to bear any scientific value must comply with both, i.e. to produce hypotheses that can be overthrown by experiment or observation (and then relegated to the trashcan), and to avoid introduction of new parameters beyond the already existing ones. Add Granger causality into the mix and we see that the four Brits presented the hockey analytics society with pretty tough questions that the society - at least the public one - seems to be trying to avoid.   The avoidance will not help. Any evaluation system will not be able to claim credibility unless it complies with the four postulates above, and within that compliance issues measurable projections.   To be continued...
  7. More Hockey Stats
    Original post.
     
    So after remembering the Botwinnik's quote, and after publishing the stats how the teams actually play after different breaks, a new idea came to me - check whether the teams on streaks are affected positively or negatively by breaks.

    For the sake of the analysis, I assumed the following:
    A break is a period of three days at least between games. A streak is a sequence of at least three wins in a row, or at least seven points in four games. So we check for the last thirty years (as far as NHL.com would let us in) if the streaking team was able to keep the streak alive, or whether the streak was broken:
     
    SEASON ALIVE BROKEN 1987/1988 5 11 1988/1989 12 7 1989/1990 8 14 1990/1991 13 11 1991/1992 17 13 1992/1993 20 16 1993/1994 19 20 1994/1995 2 7 1995/1996 15 11 1996/1997 15 11 1997/1998 12 20 1998/1999 12 9 1999/2000 18 12 2000/2001 21 11 2001/2002 17 6 2002/2003 13 10 2003/2004 12 14 2005/2006 31 15 2006/2007 16 16 2007/2008 23 24 2008/2009 15 20 2009/2010 14 17 2010/2011 19 11 2011/2012 22 11 2012/2013 6 3 2013/2014 15 15 2014/2015 16 16 2015/2016 16 14 2016/2017 8 11 TOTAL 432 376
    Actually, it looks like the streaks weren't affected by the break either way. 53.4% of the times the streak continued, 46.6% of the time it went dead. There is a very large discrepancy between the seasons, although I'd attribute it to lesser parity between the teams overall in these years. For the last 5 years, the probability for the streak to stay alive has been 50.8% (61 cases of extended streaks out of 120).

    Now, what would change, if we define a break a little bit longer, by a single day:
     
    SEASON ALIVE BROKEN 1987/1988 2 2 1988/1989 4 1 1989/1990 3 1 1990/1991 4 4 1991/1992 7 8 1992/1993 8 2 1993/1994 7 7 1994/1995 1 1 1995/1996 6 7 1996/1997 6 2 1997/1998 5 5 1998/1999 6 2 1999/2000 9 3 2000/2001 7 4 2001/2002 6 4 2002/2003 5 1 2003/2004 3 6 2005/2006 16 4 2006/2007 8 5 2007/2008 10 6 2008/2009 8 8 2009/2010 6 6 2010/2011 9 3 2011/2012 8 4 2012/2013 2 1 2013/2014 3 9 2014/2015 5 9 2015/2016 7 6 2016/2017 3 8 TOTAL 174 129   The changes are rather interesting. Now, overall, the chances of streak to continue are up to 57.4%, and only in 42.6% of the cases it came to a stop. But in the last five years - since the last lockout - and with the schedule changes so that there are at least two games between every team (increasing travel), the ratio drops from 50.8% to the humble 37.7% (20 out of 53!)

    Extending the breaks to five days provides too little data to draw any conclusions.

    So I am inclined to agree with Dr. Botwinnik, that extended breaks of more than three days throw teams off their pace and should be reduced to minimum. Three days are borderline alright.
  8. More Hockey Stats
    Original post.
     
    Frequently, the importance of carrying momentum over an intermission can be heard being talked about. I thought it were possible to measure this harmony with algebra, so I tried to do that. I choose to analyze a very specific question:

    If the regulation of a game ends in a tie, other than 0-0, how frequently would the team that tied the game with the last regulation goal win in overtime. 

    We would define the team that tied the game as the one having the momentum. We would define the other team as the one trying to show resilience. For answering the question, we analyzed the outcome of games of seasons 2007/08-2016/17 (including the ongoing playoffs). We discard the games that end in a shootout, because their outcome depend truly more on the skill of the shooting players/goaltenders rather than the whatever momentum might've been accrued.

    The results of the analysis are displayed in the table below, per season, per the time frame during which the last tying goal was scored: in the last two, five, or ten minutes, in the last period, or in one of the first two. The numbers show the percentage of wins by the team having the momentum and the number of games falling into that specific segment. Also we display a separate column and a separate row for playoffs game, although a finer granularity is not really possible because of the sample size (as of 5/1/17).
     
    Season   2        5        10       20       1st/2nd  total     totalPO 2007     54.2/24  57.9/19  52.9/34  53.8/13  52.6/38  53.9/128  31.2/16 2008     43.5/23  48.1/27  45.2/31  53.8/13  40.0/40  44.8/134  25.0/16 2009     42.9/28  56.5/23  72.7/22  64.7/17  53.7/41  56.5/131  58.8/17 2010     48.6/37  54.2/24  47.1/34  40.7/27  56.8/44  50.0/166  59.1/22 2011     50.0/24  45.8/24  43.5/23  72.0/25  47.7/44  51.4/140  37.5/24 2012     62.5/16  33.3/15  50.0/22  50.0/14  57.9/19  51.2/86   53.8/26 2013     58.1/43  43.5/23  34.6/26  45.5/22  44.1/34  46.6/148  70.8/24 2014     51.7/29  65.2/23  55.3/38  46.7/15  60.5/43  56.8/148  57.9/19 2015     60.0/40  46.7/30  44.4/36  45.8/24  39.6/48  47.2/178  52.6/19 2016     43.6/39  50.0/28  60.5/38  48.1/27  61.8/68  54.5/200  63.2/19 totalPO  61.4/44  46.7/30  55.8/43  68.4/19  40.9/66  52.0/202  52.0/202 total    51.5/303 50.4/236 50.7/304 51.8/197 51.8/419 51.3/1459 52.0/202   We see that there is no specific "momentum" nor "resilience" capability overall, there is practically no indication on how the OT would end based on which team scored the last GTG. The only two moderate exceptions with decent sample sizes are the second and the sixth columns of the penultimate row. The GTG-scoring team is 27-17 (61.4%) in case it scored the tying goal in the last two minutes, however if the GTG was scored before the last period, as it happened in 66 games, the momentum would obviously not carry over two or more intermissions, and the tying team is 27-39 (40.9%) in these games.   Here is how it looks on a graph: We can see all lines wobbling slightly above the 50 mark. Insufficiently above. Even if we observe the extra 1.3% chance overall (2.0% in playoffs) - wouldn't it be more related to the home/away advantage? I haven't looked at this aspect yet. Maybe another time.  
  9. More Hockey Stats
    Original Post
     
    Hello, hockeyforums.net, from Mr. Van Winkle...

    This prolonged silence was caused by a lot of factors, led, naturally, by REAL LIFE™. But I also made a fundamental mistake in the infrastructure setup, and so I had to roll out a hastily patched setup when the season was starting; I then went back and worked on this infrastructure fix, the work which continued over three months and is now complete! Unfortunately, all this work will not be visible to the visitor, with possible exception of a slightly faster page loading - all the changes belong to the back end.

    But now, once again, with REAL LIFE™ limitations I am able to work on improving the website look, speed and features. I am being somewhat torn apart since I also need to hone the models I'm using, but I decided the models can wait with half of the hockey season gone by now. In addition I'll try to put an extra effort to promote the site and made it more visible on the Web.

    One of the things I was not able to complete is to release my code as the open source. This has also been put into a bottom drawer. However, I still welcome cooperation very much and will gladly share the code with people who would want to contribute to the project. The areas I could really use some help are:
    JavaScript/HTML/CSS MongoDB query and database optimization SEO optimization So if you feel like helping - drop me a mail.

    Also I will begin a series "Website - A Page A Day", where I plan to describe each and every statistical page on the site because I have a feeling I haven't been clear enough with the explanations until now; moreover it will help me discover errors and inconsistencies that probably crawled through.
  10. More Hockey Stats
    I read about this idea on HFBoards and finally got to implement it.
     
    Faceoff stats and Elo ratings.
     
    The available views are:
    * career/specific season
    * per zone/per stick first
     
    Here's a sample table: By stick first on the ice, 2016 season.
    FW - First Stick Wins, FL - First Stick Losses, FP - First Stick Win %
    LW - Last Stick Wins, LL - Last Stick Losses, LP - Last Stick Win %
    TW - Total Faceoff Wins, TL - Total Faceoff Losses, TP - Total Faceoff W %
    FR - Faceoff Rating (TW*TP/100), Elo - Elo rating.
     
    Matt Duchene really surged this season.
     
    # Player FW FL FP LW LL LP TW TL TP FR Elo 1 MATT DUCHENE 239 142 62.73 214 125 63.13 453 267 62.92 285.01 2099.16 2 PATRICE BERGERON 349 262 57.12 392 254 60.68 741 516 58.95 436.82 2078.38 3 RYAN O'REILLY 383 286 57.25 315 220 58.88 698 506 57.97 404.65 2070.72 4 ANTOINE VERMETTE 350 198 63.87 265 172 60.64 615 370 62.44 383.98 2067.26 5 RYAN KESLER 442 320 58.01 300 217 58.03 742 537 58.01 430.46 2065.49 6 MARTIN HANZAL 291 254 53.39 274 185 59.69 565 439 56.27 317.95 2063.27 7 CLAUDE GIROUX 281 218 56.31 433 350 55.30 714 568 55.69 397.66 2057.67 8 JORDAN STAAL 217 170 56.07 215 130 62.32 432 300 59.02 254.95 2057.40 9 JONATHAN TOEWS 268 216 55.37 333 227 59.46 601 443 57.57 345.98 2056.26 10 PAUL STASTNY 341 267 56.09 310 253 55.06 651 520 55.59 361.91 2054.49 11 KYLE TURRIS 226 181 55.53 272 261 51.03 498 442 52.98 263.83 2049.56 12 TYLER BOZAK 201 161 55.52 311 232 57.27 512 393 56.57 289.66 2049.46 13 BRANDON SUTTER 314 261 54.61 273 211 56.40 587 472 55.43 325.37 2049.30 14 MIKKO KOIVU 394 360 52.25 295 203 59.24 689 563 55.03 379.17 2047.14 15 FRANS NIELSEN 187 165 53.12 269 214 55.69 456 379 54.61 249.03 2046.67 16 DEREK RYAN 86 62 58.11 153 110 58.17 239 172 58.15 138.98 2046.05 17 RYAN JOHANSEN 236 224 51.30 297 244 54.90 533 468 53.25 283.81 2043.37 18 TRAVIS ZAJAC 325 293 52.59 267 216 55.28 592 509 53.77 318.31 2042.99 19 JEAN-GABRIEL PAGEAU 211 178 54.24 147 111 56.98 358 289 55.33 198.09 2040.48 20 SEAN COUTURIER 199 162 55.12 170 160 51.52 369 322 53.40 197.05 2038.48 21 BRYAN LITTLE 190 168 53.07 219 157 58.24 409 325 55.72 227.90 2038.16 22 JAY BEAGLE 297 220 57.45 144 114 55.81 441 334 56.90 250.94 2035.44 23 MIKE FISHER 300 249 54.64 240 200 54.55 540 449 54.60 294.84 2034.64 24 CODY EAKIN 165 153 51.89 138 126 52.27 303 279 52.06 157.75 2034.28 25 SEAN MONAHAN 214 189 53.10 346 310 52.74 560 499 52.88 296.13 2031.43 26 ERIK HAULA 163 141 53.62 156 129 54.74 319 270 54.16 172.77 2030.95 27 TOMAS HERTL 67 55 54.92 55 34 61.80 122 89 57.82 70.54 2029.31 28 TORREY MITCHELL 218 209 51.05 120 81 59.70 338 290 53.82 181.92 2028.69 29 JOHN MITCHELL 113 105 51.83 128 90 58.72 241 195 55.28 133.21 2027.15 30 HENRIK ZETTERBERG 207 194 51.62 275 248 52.58 482 442 52.16 251.43 2026.42
  11. More Hockey Stats
    It looks like I've forgotten to translate a couple of entries.
    Correcting that.
     
    Original post.
     
    Part I
    Part II


    Once again, driven by idea that if you want to encourage goal scoring, you need to reward the goal scoring in standings directly, not indirectly through winning. Then, based on the idea of a fellow hockey fan and blogger, a new suggestion was born in my mind.

    Not so long ago I was involved in another discussion on the subject on Twitter, where an interesting alternative, 2-1-0-0 was described. The idea is that you still get two points for a win in regulation, just one point for a win in OT, but nothing if you lose, and, the key, both teams get nothing if the game is tied at the end of regulation (shootouts are abolished). This is a very sharp idea, but for me something felt very wrong, and then it crystallized:

    It's not fair to reward a hard fought 5-5 tie with zero points, just like a lazy-skated 1-1. We still want to encourage goal scoring, and the simple 2-1-0-0 just unbalances the game. And so it dawned on me. We should reward goals with extra standings points!

    The formula that first came to mind, and which seemed fair: give each goal a 0.1 point in the standings, while the win-scoring system shall be 2-1-0-0. If you or your database have an aversion against decimals, assign 20 points for a win, 10 points for OT loss, and 1 extra point for each goal scored. This will encourage goal scoring in any situation, and for both sides, including the games that go into garbage time pretty quickly. So, a 7-2 win will give the winner 2.7 points, and the loser 0.2 points. A 2-0 win will give the winner 2.2 points, the loser 0. A 4-3 OT win will give the winner 1.4 points, the loser 0.3 points. A 5-5 OT tie will give each side 0.5 points.

    Wait, there's a caveat.

    Imagine a situation where a team needs just 0.1 point to pass another one in the standings for the playoff spot. They are playing an opponent whose number of points in the standings does not have any effect on them. In such a situation, the team would play without a goaltender at all, because they don't care how much they lose, they just need that goal. Now, this is not really hockey, so to prevent this kind of play a restriction needs to be introduced:

    Any goal scored without a goaltender on the ice, when not on a delayed penalty, and when trailing by more than two goals shall not yield any standings points.

    Here is an example what the final reg. season standings would look like under the suggested system:

    Team                           W  OW T  L  GF  GA  P
    --------------------------------------------------------  
    Boston Bruins                  38 04 05 35 232 209 103.2
    Montreal Canadiens             33 11 05 33 223 198 99.3
    Toronto Maple Leafs            33 06 09 34 250 234 97.0
    --------------------------------------------------------
    Washington Capitals            45 08 07 22 261 177 124.1
    Pittsburgh Penguins            40 06 09 27 278 229 113.8
    Columbus Blue Jackets          39 09 04 30 247 193 111.7
    --------------------------------------------------------
    New York Rangers               40 05 07 30 253 216 110.3
    Ottawa Senators                34 04 10 34 206 210 92.6
    --------------------------------------------------------
    Minnesota Wild                 42 04 05 31 263 206 114.3
    Chicago Blackhawks             37 09 05 31 240 212 107.0
    St. Louis Blues                38 06 04 34 233 216 105.3
    --------------------------------------------------------
    Anaheim Ducks                  40 03 06 33 220 197 105.0
    Edmonton Oilers                37 06 09 30 243 207 104.3
    San Jose Sharks                38 06 03 35 219 200 103.9
    --------------------------------------------------------
    Nashville Predators            35 04 06 37 238 220 97.8
    Calgary Flames                 32 09 06 35 222 219 95.2
    --------------------------------------------------------
    New York Islanders             33 06 06 37 239 238 95.9
    Winnipeg Jets                  33 04 04 41 246 255 94.6
    Tampa Bay Lightning            32 06 07 37 230 224 93.0
    Dallas Stars                   28 05 03 46 222 260 83.2
    Carolina Hurricanes            28 05 09 40 212 230 82.2
    Los Angeles Kings              25 12 06 39 199 201 81.9
    Philadelphia Flyers            25 07 12 38 212 231 78.2
    Buffalo Sabres                 25 06 08 43 199 231 75.9
    Florida Panthers               23 07 11 41 205 231 73.5
    Arizona Coyotes                20 04 08 50 191 258 63.1
    Vancouver Canucks              19 07 06 50 178 241 62.8
    New Jersey Devils              18 07 06 51 180 241 61.0
    Detroit Red Wings              17 07 09 49 198 244 60.8
    Colorado Avalanche             14 07 03 58 165 276 51.5

    Naturally, they would not be the same standings if the system were indeed implemented, but why not to take a look. And once again, try it in the AHL first, it won't hurt anyone.
  12. More Hockey Stats
    Original post
     
    The main page of the website shows the summary of all its features.

    The site menu features the main statistical sections:
     
    League - league-wide statistics Teams - team-based statistics Players - personal statistics Coaches - statistics for the NHL coaches Drafts - statistics for currently drafted players and the historical performance by draft Fantasy - tools to help the fantasy player
    On the top we have a ticker of the scores, as predicted by the model. The ticker is always scrolled to the current date, however you can navigate it back and forth using the two arrows at the edges. The away team is on the top, and the home team is on the bottom. The predicted score is in the Prdct column. The actual score is in the Act column. The projected winner is displayed in bold. If the prediction failed, the displayed teams will be painted red. We never adjust our predictions backwards. Only the scores for the current season are featured.

    Then, on the top right we have three very important links that would help you with understanding the pages:
     
    Learn More - about the methodology of the Website Glossary - about the terms used in the pages Blog - link to this blog which, as you see, also takes time to elaborate on the site. We also display our latest addition to the website and the latest blog entry.   Then we have three random snippets in the columns. The snippets represent excerpts from the tables published elsewhere on the site and may change after each publication, which happens overnight. The snippets currently (hopefully they would become more diverse) are: Team data snippets: Buchholz/Berger-Sonneborn coefficients Empty Net Statistics (probably our most popular page) Teams Elo Ratings and predicted standings, per division Strikebacks Player data snippets: Goaltender elo ratings Deadly pairs of the NHL (goals+primary assist tandems) Clutch players excelling scoring lead-changing goals Reverse stats (players being hit, drawing penalty, etc.) Coach data snippets: Face to face coaching records Coach challenge statistics Only current season data is displayed in the snippets. Below the random snippets we feature a permanent snippet that shows the best projected picks for the daily fantasy competitions. We provide a model-based evaluation of the expected score for players in the three most popular Daily Fantasy websites - Yahoo, FanDuel and DraftKings.   Below each snippet there is a link to the page with the full data.   At the bottom we have a collection of information links. Make sure you visit the Glossary and the About pages. The Links page has an ever-growing collection of hockey-related links. The Forum link leads to hockeyforums.net, the site we're partnering with - this blog is broadcast there as well. The Data section shows the software and the data sources this website is built with.
  13. More Hockey Stats
    Original post.
     
    Often the general managers, the coaches and the players talk about "intangible values". Sometimes it's about the "locker room contributions". Sometimes it's about "passion". In my opinion, these two are actually negligible and in certain cases even harmful. I remember such references, especially the latter one, made about Israeli soccer players, and that usually meant that the player doesn't have a lot of talent to go along, but contributes a lot of passion into the game. While a passionate play can indeed ignite the play and carry the team along, more often it indicated dumb physical low-talent execution that actually harmed the team.

    However, there is one intangible that I take my hat off in front. It's the one that I always admired, and myself did not have enough in my chess career. It's the ability to go for the throat of the opposition at even momentary display of weakness by it, or as Terry Pratchett put it one of its books, 'Carpe Jugulum1'.

    So what is it, in my understanding? It is the situation when your opponent puts itself into an inferior position in a volatile situation (for example, in a close score), such as by a penalty, or by an icing at the end of a long shift, or by allowing an odd-man rush, and you are able to capitalize on it, yanking any remains the carpet of security from under the feet of the opposition. And then, you continue to hammer the blows on the opposition until it collapses completely. Some also call it the 'killer instinct'. This blog (and this article too) sins with abundance of examples from chess, so let me plant one from tennis... Before the match between Lleyton Hewitt and Taylor Dent at the New York Open, 2005, the latter one complained: 'He displays a poor sportsmanship: taking joy in double errors at the opponent services as well as in unforced errors.' 'I don't care what Dent thinks about it', parried Hewitt, 'I always go for a win, and on the way to it many things are allowed.'

    Machiavelli advised the rulers and the politicians, 'Don't be kind'. Winston Churchill also knew something about achieving the goals when he was recommending: 'If you want to get to your goal, don't be delicate or kind. Be rough. Hit the target immediately. Come back and hit again. Then hit again with the strongest swing you can...'

    All the chess champions had it, the extremes going to Alexander Alekhine, Robert J. Fischer and Garry Kasparov. Many wonderful players that never got the title complained that they couldn't commit themselves to going for the throat of the opponent time after time.

    These qualities were elevated to perfection by the two best teams of the first half of 2010s, by the Los Angeles Kings and the Chicago Blackhawks that split between themselves five cups out of six from 2010 to 2015. Even when both teams seem to be struggling and wobbling, they seemed to be able to instill some kind of uncertainty into their opponents - and certainty into the spectators that these teams are going to be able to make a fist out of themselves that is going to hammer their opponents once they display any kind, and minimal level of weakness. That capability was championed by their leaders, Anze Kopitar, Drew Doughty and Jeff Carter for the Kings, and Jonathan Toews, Patrick Kane and Duncan Keith for the Hawks. When the playoffs series between the Blackhawks and their opponents were tied 3-3, Chicago has always been the favorite to win the game 7 because of their Carpe Jugulum reputation. The Kings gained even more notoriety, first by burying their sword to the hilt into each and every opponent in 2012 en route from the #8 seed to their first Stanley Cup, and then from the reverse sweep they managed against the Sharks that started their 2014 Cup run - which included two more comings from behind, 2-3 and 1-3. And even in 2016, down 1-3 to the Sharks in the first round of the playoffs somehow fans around the league were not ready to commit to the Sharks as the favorites to win the series, because the Kings were a hair away from the Sharks' throat in game 4, from 0-3 to 2-3 in the 3rd period, and then in game 5, they indeed were able to erase the 0-3 deficit into a 3-3 tie.

    Well, that tie didn't hold, the Sharks broke the stranglehold and got a boost that carried them all the way to their own first even Stanley Cup Finals, and that outcome got the Kings' reputation as the Carpe Jugulum team damaged to a degree. So did the Blackhawks' one, losing their game 7 to a team that - along with the Sharks and, for instance, the Washington Capitals - had a reputation of a somewhat nonplussed one - the St. Louis Blues.

    It would be entertaining to see whether the Carpe Jugulum landscape changes this year in the league, and whether the teams who were able to overcome their "benign" reputation will be able to go all the way to the Cup Finals - through their opponents' throats.

    Chess Grandmaster Gennady Sosonko wrote, 'A real professional, having thought about the situation on the board, acts most decisively. He knows, that during the game, there should be no place either for doubt, nor for compassion, because a thought which is not converted into action, isn't worth much, and an action that does not come from a thought isn't worth anything at all.'

    And it's important to remember, Carpe Jugulum is a necessary key to success in a competitive environment only. Albert Einstein used to say that chess "are foreign to me due to their suppression of intellect and the spirit of rivalry."

    1Carpe Jugulum (lat.) - seize the throat
  14. More Hockey Stats
    Original post.
    The goalkeeper is half of the whole team
      Soviet proverb from Lev Yashin's times.
    After a foray into the calmer lands of teams' evaluation using the Elo rating, it's time to turn our attention to the really juicy stuff - the evaluation of a single player. And we'll start with the most important one - the goaltender. DISCLAIMER: this evaluation concept is still a work in progress and one of several possible implementations of the idea.

    By coincidence, it's also the simplest evaluation to make. While many stats describe the performance of a skater (goals, assists, shots, hits, blocks, faceoff wins, etc. - and even one that is accounted usually for goaltenders) only one stat truly describe the goalie's performance: the saves percentage. Usually, whole four stats are used to compare the goalies: wins (W), saves percentage (SVP), goals against average (GAA) and shutouts (SHO), but will show you first, why three of them are mostly unnecessary. Also, the name saves percentage is a bit of a misnomer, since the values of svp are usually not multiplied by 100 to look like real percent, but are shown more frequently between 0 and 1, and therefore would be more properly named as 'Saves Ratio', or 'Saves Share'.

    Wins are truly results of team efforts. I always cringe when I read that a goaltender "outdueled" his opponent, when the both barely got see each other. The GAA is much more of an indication of how well the defense operates in front of the goalie. Shootouts are first, and foremost, a very rare thing, and secondly a 15-save shootout should not be the same as 40-save shootout, although for any of the four stats listed above they create two identical entry.

    Therefore we feel ourselves on a firm ground evaluating goalie's performance through SVP only (with a slight input from shootouts, as described below) - and the Elo function, of course. For the start, each goaltender is assigned an Elo rating of 2000 for his first career appearance. We discard performances in which goalies faced less than four shots, because these usually are late relief appearances in the garbage time, not really an evidence of goaltending in a true hockey game. We only account for them to display the real SVP accrued in the season so far, and we consider dropping these appearances completely.

    After the game we get the pure SVP from the real time stats. We adjust it in two ways: If, in the very rare case, the performance is below 0.7, we set it to 0.7 . If there was a shootout (not the shootout as defined by the NHL, but a performance where a goaltender was on the ice for at least 3420 seconds and did not let a single goal in during that time), we add a shootout bonus for the performance:   Bonus = (Saves - 10) / 200   If there were less than fifteen saves in the shootout, the bonus is assigned the minimum value of 0.025. We consider adding this bonus necessary, because the opposing team is usually gives an extra effort to avoid being shut out even during the garbage time.

    Then, given the actual performance we can calculate the "Elo performance rating":
      Rperf = 2000 + (SVP - SVPvsopp) * 5000   Where SVPvsopp is the SVP against the opponent the goalie is facing - effectively the shooting % of that team minus the shots resulting in empty-net goals, sort of "Expected SVP against that opponent". That means that for every thousandth of the SVP above the expectation, the performance is five points above 2000 (the absolute average).

    Wait, there seems to be an inconsistency. Don't we need ratings of opponents for Elo changes calculation? Actually, no. Given an Elo performance of a player, we can calculate the rating change as a "draw" against a virtual opponent with that Elo performance, i.e.
        ΔR = K * (0.5 - 1 / ( 1 + 10 ** (( Rperf - Rg)/ 400)) ) )   Where K is the volatility factor mentioned in the earlier posts. Right now we are using the volatility factor of 32, but that may change - including introducing a dependency of this factor on goaltender's experience.

    And the new rating, is naturally,
      Rg' = Rg + ΔR   Now we can calculate the expected remaining svp:
      SVPrem = SVPavg + (Rg' - 2000) / 5000   Where SVPavg is the league average SVP. It would be more correct to substitute that value with the weighted averages of the remaining teams to face (with accordance to the matches remaining), and we'll be switching to this index soon.

    We can also calculate the SVP expected from the goalie at the start of the season:
      SVPexp = SVPavg0 + (Rg0 - 2000) / 5000   where SVPavg0is the average SVP of the league during the previous season and the Rg0 is the rating of the goalie at the conclusion of the previous season (including playoffs), or the initial rating of 2000.

    We post a weekly update on our Elo ratings for goaltenders, and their actual and expected SVPs on our Twitter feed. You can also access our daily stats on our website page.

    It looks like we're ready to try to take on the skaters' performances. But I'm not sure it's going to fit into one posting.

    To be continued...
  15. More Hockey Stats
    Original post.
     
    While the series "Website - A Page A Day" is being delayed by all kinds of things, here comes a short post on a different topic.

    Last year, in my opinion, the accuracy shooting competition which included shooting the pack from the goal line into a small hole was, in my opinion a total failure. Mike Smith's spectacular score across the rink did the injustice and provided a false impression this skill contest was any good. Otherwise, the competition was not exciting to say the least.

    Therefore, here's a suggestion to replace it: reverse shootouts.

    Let the goaltenders shed their equipment for once, and let the skaters don it instead. Let's have a competition where the goaltenders skate and attempt to score in shootout, while the skaters try to stop them. I am sure that somewhere in the back of their minds that would fulfill a little dream both parties would have!    
  16. More Hockey Stats
    Original post.
     
    Goodhart's law is the bane, the safeguard and the watchdog of everyone who tries to make conclusions from sample data. The "Schroedinger Cat of Social Sciences" practically says, if you want people to do X, but you reward them for doing Y, they will be doing Y rather than X. We start seeing that in the "possession analytics", based on shots taken, that the players begin to shoot from everywhere to get their possession ratings up. But we digress - the topic is the scoring system, we'll save that note for another blog entry.
     
    We want the NHL hockey to be spectacular. That's the main objective (beyond being fair and competitive, otherwise look for Harlem Globetrotters). In the past the spectacular was fighting as much scoring and winning games, but that taste of the public changed, and the fighting went away. It was not directly related to scoring and winning, it was just an extra free show provided.
     
    Now we're left with scoring and winning. These two are closely tied, and not necessarily as a positive feedback, since not allowing your opponent to score also helps winning. A 2-1 win is practically just as valuable as a 7-2. So in the mid-2000s, the winning objective, the points objective took over the scoring objective. And from the previous post we see that the existing 2-2-1-0 points system encourages low-intensity game preferably slipping into the OT. On the other hand we also noted that the 3-2-1-0 points system would encourage teams to clamp down and protect their minuscule leads. Looks like a circle to break...
     
    Well, here comes Goodhart's law. You want teams to score, or at least try to score, but you reward them for achieving points. So what they do is concentrate on getting points. Therefore, if the NHL want to see score-oriented hockey, the NHL needs to reward scoring, and not points. Still, the points have been used to determine playoff spots, so something has to give.
    First, let's take a wild ride by suggesting that we rank teams by the amount of goals scored. That would lead to a pretty drastic change and the end of hockey as we know it. This will lead to situations where a team might play for a period without a goaltender in a playoff race. In general, the goaltending position will deteriorate, and aren't we loving the spectacular saves just as we love slick goals? Probably, that would be too much.
     
    Thus, we can mitigate to allow the goal differential to be the ranking criteria. At the end of the season, the teams with the higher goal differentials will be ranked at the top, and the wins-ties-losses, well, they get relegated to tie-breaks. The incentive to score rather than to hold the opponent increases, because while now the competitors in their games cannot score more than two points, they still can score a bigger goal differential! All the lazy skating to finish the game after it's 4-0 or 5-1? Gone.
     
    This idea is actually not novel. It's been used for a long while in team chess tournaments. Such tournaments consist of matches, where each player of one team plays against an opponent of the opposing team at the same time. Each player's individual score (win, draw or loss) is accumulated into the total score. So a match of 8-player teams, where one team had 5 wins, 1 draw and two losses ends up with 5.5-2.5 score, essentially "the goal differential". At the end of the tournament, the scores accumulate, and the teams are ranked according to them. You can see the crosstables of historical chess tournaments at the wonderful Olimpbase website.
     
    And if you feel that the fact of winning or losing the game should be have more weight than just a tie-break (by the way, there will be less tie-breaks on goal differential), that is easy to factor in, just add a bonus "goal" to the winner, like it is done in the shootout now. Or, add two bonus "goals" for winning in regulation, one bonus "goal" for winning in the OT, abolish shootouts.
  17. More Hockey Stats
    Website A Page - A Day, Part VI - Warm Welcome
      Original post

    Prologue
    Part I
    Part II
    Part III
    Part IV
    Part V

    With nothing else to do for about half an hour, why not to resume the series?

    Have you wondered if it is your team, or your goalie, who always has the first career goal scored against them? Now you can check if your feeling is right. On the page 'Warm Welcome' of the League section on the website we present a look at the first goals scored against different teams and goalies.

    With the two left items in the top menu you can select the span over which you want to see the statistics. Want one season only? Select the same season for the start and for the end. Then you can toggle the view by the team or the goalie the first goal is scored against.

    For example, for the 2016/17 season, team view:
      # Team Goals Allowed 1 Dallas Stars 7 2 Carolina Hurricanes 7 3 New Jersey Devils 7 4 Tampa Bay Lightning 6 5 Ottawa Senators 6 6 Detroit Red Wings 5 7 Pittsburgh Penguins 5 8 New York Rangers 5 9 San Jose Sharks 5 10 Vancouver Canucks 5 11 Colorado Avalanche 5 12 Nashville Predators 4 13 Boston Bruins 4 14 Buffalo Sabres 4 15 Winnipeg Jets 4 16 Arizona Coyotes 3 17 Columbus Blue Jackets 3 18 Edmonton Oilers 3 19 Montreal Canadiens 3 20 Anaheim Ducks 3 21 St. Louis Blues 3 22 Los Angeles Kings 2 23 Washington Capitals 2 24 Calgary Flames 2 25 Minnesota Wild 2 26 New York Islanders 2 27 Toronto Maple Leafs 2 28 Chicago Blackhawks 2 29 Florida Panthers 2 30 Philadelphia Flyers 0
    Take a look. You might be surprised. Or not.
  18. More Hockey Stats
    Original post.
     
      Wild thing, you make my heart sing You make everything groovy, wild thing   Also inspired by Twitter, and because I can, I decided to gather statistics on games with most lead changes* most lead swings** Here, for the 2016/17 season: By most lead swings: AWAY    HOME   Date        Sco LC LS CHI  vs DAL  on 2017/02/04: 5-3 7 3 CBJ  vs OTT  on 2017/01/22: 7-6 11 3 PHI  vs STL  on 2016/12/28: 3-6 7 3 MTL  vs PIT  on 2016/12/31: 3-4 7 3 CHI  vs NYI  on 2016/12/15: 5-4 7 3 ARI  vs PHI  on 2016/10/27: 5-4 9 3   with 60 games at 2 lead swings. Dallas leads the way with 8 games with at least two swings, and Carolina, Chicago, NY Islanders and Winnpeg follow with 7 each.   By most lead changes:       AWAY    HOME   Date        Sco LC LS CBJ  vs OTT  on 2017/01/22: 7-6 11 3 TOR  vs WSH  on 2017/01/03: 5-6  9 2 TOR  vs NYI  on 2017/02/06: 5-6  9 2 NYI  vs DET  on 2017/02/03: 4-5  9 1 CHI  vs COL  on 2017/01/17: 6-4  9 2 CAR  vs NYI  on 2017/02/04: 5-4  9 2 CHI  vs STL  on 2016/12/17: 6-4  9 1 BUF  vs OTT  on 2016/11/29: 5-4  9 1 ARI  vs PHI  on 2016/10/27: 5-4  9 3   with 31 game with at least 7 lead changes. Here we've got Carolina, Chicago and NY Islanders at the lead with at least 6 games with 7 or more lead changes.   And what do we get historically?
      The wildest games, regular season, by lead swings: AWAY    HOME   Date         Sco LC LS   PHI  vs BOS  on 2011/01/13: 5-7  11 5 COL  vs CGY  on 1991/02/23: 8-10 11 5 ARI  vs CGY  on 1991/01/15: 5-7  11 5 PHI  vs COL  on 1988/11/19: 5-6  11 5   with 30 games at 4 lead swings.   The wildest games, regular season, by lead changes: AWAY    HOME   Date        Sco LC LS   DET  vs SJS  on 2005/11/26: 7-6 13 4 MTL  vs COL  on 2002/12/06: 6-7 13 2 COL  vs SJS  on 1997/04/04: 6-7 13 2 ARI  vs PHI  on 1990/01/25: 6-8 13 1 TOR  vs PIT  on 1989/10/25: 8-6 13 3 COL  vs WSH  on 1997/11/18: 6-6 12 3 PIT  vs NJD  on 1993/04/14: 6-6 12 1 BUF  vs CAR  on 1991/12/07: 6-6 12 4 CAR  vs TOR  on 1990/02/14: 6-6 12 2 VAN  vs TOR  on 1988/01/04: 7-7 12 3   with 65 games at 11 lead changes (even numbers can only occur in the ties era).   The wildest games, playoffs, by lead swings: AWAY    HOME   Date        Sco LC LS   STL  vs DAL  on 1999/05/08: 4-5 9 4 MTL  vs COL  on 1993/04/26: 5-4 9 4 EDM  vs LAK  on 1992/04/20: 5-8 9 4   with 33 games at 3 lead swings.   The wildest games, playoffs, by lead changes: AWAY    HOME   Date        Sco LC LS   BUF  vs OTT  on 2006/05/05: 7-6 13 2 PHI  vs CHI  on 2010/05/29: 5-6 11 3 COL  vs SJS  on 2010/04/16: 5-6 11 1 PHI  vs WSH  on 1989/04/11: 8-5 11 3   with 42 games at 9 lead changes (only odd numbers can occur)   The data is presented since the year 1987 - the earliest boxscores from the NHL.com Now this one is going to make it into the website, I just haven't decided in which form.   *   Lead swing is defined as when a team takes the lead after the other team had it.  ** Lead change is defined as when a team loses the lead, even if only temporarily to a tied score.    
  19. More Hockey Stats
    Original post.
     
    One "intangible" being tossed around is "motivation" of the players. Which brings memories of an episode I was witness to.
     
    In 2003/04, in the Israeli Top Tier Chess League (which is indeed no slouch) our club managed to assemble an outstanding team, featuring, among others, a former Champion of Russia and a former Champion of Europe. I was part of the management team, and orchestrated bringing the first of the two, who also happened to be my childhood friend back in Leningrad, Soviet Union.
     
    And so, in round III we were to face our main rival for the title, and the club's GM (also a pedestrian chess player) gathered the team and carried out a pronounced motivational speech, how we have to beat the team we're facing, and so on, and so on.
     
    We lost 1½-4½ without winning a single game and lost any chance for the championship we could have.
  20. More Hockey Stats
    Why does the cat lick his balls? Because it can.   Recently I saw a request on a stats of goal posts / crossbars hit per game. While I do have that statistic per player, I haven't one for games, so - since I can - why shouldn't I produce one?

    About half an hour of Perl-ing created the following summary:
      Irons altogether, top:
    AWAY    HOME                P C T OTT  vs BUF  on 2011/12/31: 8 0 8 VAN  vs FLA  on 2010/02/11: 7 0 7 WPG  vs FLA  on 2009/12/05: 6 1 7 TOR  vs BUF  on 2007/10/15: 6 1 7 TBL  vs FLA  on 2006/04/01: 6 1 7 PHI  vs PIT  on 2006/03/12: 7 0 7 COL  vs NYI  on 2005/12/17: 7 0 7 NSH  vs DAL  on 2016/03/29: 4 2 6 PIT  vs NSH  on 2014/03/04: 5 1 6 NYI  vs TBL  on 2014/01/16: 3 3 6 DAL  vs VAN  on 2013/02/15: 5 1 6 STL  vs CAR  on 2012/03/15: 5 1 6 WPG  vs MTL  on 2011/01/02: 6 0 6 OTT  vs VAN  on 2011/02/07: 6 0 6 MTL  vs CAR  on 2011/11/23: 6 0 6 LAK  vs DAL  on 2010/03/12: 4 2 6 NJD  vs TBL  on 2009/10/08: 6 0 6 LAK  vs DAL  on 2009/10/19: 5 1 6 DAL  vs CBJ  on 2009/01/31: 5 1 6 COL  vs CHI  on 2009/11/11: 6 0 6 PIT  vs WPG  on 2008/01/30: 5 1 6 NYR  vs NJD  on 2008/04/09: 4 2 6 STL  vs ARI  on 2007/01/15: 5 1 6   followed by 109 games with 5 irons hit.   Crossbars, top: AWAY    HOME                P C T
    CGY  vs CBJ  on 2008/11/08: 1 4 5 NYR  vs FLA  on 2007/11/23: 0 4 4 PHI  vs FLA  on 2006/12/27: 1 4 5 BUF  vs DAL  on 2017/01/26: 1 3 4 EDM  vs DAL  on 2016/01/21: 2 3 5 TOR  vs STL  on 2015/01/17: 1 3 4 CHI  vs ANA  on 2015/05/19: 1 3 4 BOS  vs VAN  on 2015/02/13: 1 3 4 NYI  vs TBL  on 2014/01/16: 3 3 6 CHI  vs ANA  on 2008/01/04: 2 3 5 CAR  vs FLA  on 2007/11/12: 1 3 4   followed by 50 games with 2 crossbars hit.   The data is extracted from the PBP files of NHL.com, from the year 2005 on.

    However I consider this a one-time effort and will not add this to the website itself.  
  21. More Hockey Stats
    Original post.
     
    Part I
      After completing the first part of the lemma research - penalty box - the second part was shorter, easier, but just as useful. I decided to find out the share of time teams spend on average while at even strength, on power play/shorthanded and with empty net. Then given this number, and the number of goals scored in each such situation, I was able to calculate the frequency of EVG/PPG/SHG/ENG or the reverse of it which I called the difficult of such goal.   I scanned the database of all games between the 1999/00 season and today, and all the goals extracted from these games. Penalty shot goals were ignored, regardless if during the game itself, or in post-game shootout. The EN time was calculated as total game time minus goaltender TOI. PP/SH time was deducted from the recorded PP TOI of the players. The EV time would naturally become the total game time minus EN minus PP of both teams.   Then I calculated the difficulty of scoring a goal in each of these situations through the following formula:   DiffTYPE = ( GOALSEV /  GOALSTYPE ) x ( TOITYPE / TOIEV )   where the difficulty of the EV goal is considered "1". Here are the combined results of the difficulties in a table: Season EV PP SH EN 1999 1.000 0.502 3.506 0.162 2000 1.000 0.473 3.387 0.146 2001 1.000 0.492 3.635 0.153 2002 1.000 0.468 3.585 0.167 2003 1.000 0.445 3.127 0.221 2005 1.000 0.535 4.247 0.272 2006 1.000 0.506 4.000 0.228 2007 1.000 0.458 3.597 0.187 2008 1.000 0.438 3.745 0.183 2009 1.000 0.456 4.044 0.192 2010 1.000 0.450 3.517 0.177 2011 1.000 0.460 3.568 0.169 2012 1.000 0.430 3.890 0.169 2013 1.000 0.453 3.209 0.198 2014 1.000 0.427 3.564 0.171 2015 1.000 0.415 3.284 0.158 2016 1.000 0.419 3.252 0.178 2017 1.000 0.427 3.052 0.168
    If you divide 1 by these values you can get the relative frequency of goals scored in each situation.   The dataset containing this data is available on the website, on the Request Analysis page.   So why did I need these two lemmas? That blog post won't be ready any time soon, and I better resume the "Page A Day series'.
  22. More Hockey Stats
    Prologue
    Part I
    Part II
    Part III

    And now we're putting two in a row with West vs. East.

    PART IV

    This page shows the results of games between Eastern and Western Conference teams. The data is available from the year 1993, when Western and Eastern Conference were formed, from the Boxscore files.

    Shown from left to right: 
    Regular West wins OT/SO West wins Ties(up to year 2005) OT/SO East wins Regular East wins Stanley Cup Winning Conference A total tally is available as well. As of the date of this post the standings are:
    WEST 2802 Reg. W - 595 OTW - 444 T - 541 Reg. W - 2570 Reg. W EAST
    West holds a formidable lead which eroded a bit in the 2015/16 and 2016/17 seasons. Before that the last time East won the count was back in 1998/99! The 2009/10 was the most lopsided season with the final score of 155-115 in West's favor.
    West won 14 times, East - 6. Once, in 2011/12 there was a tie with 134 wins apiece.

    The Stanley Cup winners are divided more evenly, however, with West holding the edge 13-10.

    There is no data for seasons 1994/95, 2004/05 and 2012/13 because of full or or partial season lockout. Also, the win-loss count from the Finals are not included.

    WE NEED YOUR HELP!
    If you are an experienced Webmaster, especially with Javascript and CSS we would greatly appreciate the potential tidy-up and enrichment you could provide to these graphs. Your work will be credited for future reference! Write to us, or get in touch with us on Twitter. Thanks!

    Possible future additions:
    Season aggregation More compact design Your ideas are welcome!
  23. More Hockey Stats
    Part I. Part II.   Sherlock Holmes and Dr. Watson are camping in the countryside. In the middle of the night Holmes wakes up Watson: 'Watson, what do you think these stars are telling us? 'Geez, Holmes, I don't know, maybe it's going to be a nice weather tomorrow? 'Elementary, Watson! They are telling us our tent has been stolen!   Iconic Soviet joke.   Estimating a hockey player via Elo ratings is a highly complex task. Therefore, we shall wield the dialectic approach of getting from the simpler to the more complicated, and will tackle a seemingly simplistic task first. Let's work out the Elo ratings for the NHL teams as a whole first. After all, it's the teams who compete against each other, and the outcome of this competition is a straightforward result.   So, let's examine a match between Team A and Team B. They have ratings Ra and Rb. These ratings, or, more precisely, their difference Ra-Rb, defines the expected results Ea and Eb on the scale from 0 to 1. The teams play, one wins (S=1), another loses (S=0). To adapt this to the Elo scale, let's consider win 1 point, loss 0 point. The new ratings Ra' and Rb' will be (K is the volatility coefficient):   Outcome Sa Sb Sa-Ea Sb-Eb dRa dRb Ra' Rb' Team A Wins 1 0 1-Ea -Eb K-K*Ea -K*Eb Ra+K-K*Ea Rb-K*Eb Team B Wins 0 1 -Ea 1-Eb -K*Ea K-K*Eb Ra-K*Ea Rb+K-K*Eb     and the teams are ready for usage in the next meeting with their new ratings Ra' and Rb', reciprocally.   'Wait!', will ask the attentive reader, 'Not all possible outcomes are listed above! What about the OT/SO wins where both teams get some points.' And he will be correct. In these cases we must admit that the loser team scores 0.5 points, so unlike a chess game where the sum of the results is always 1, in the NHL hockey the total sum of results varies and can be either 1 or 1.5. Note, were the scoring system 3-2-1-0, then we could scale the scores by 3 rather than by two and get the range 1-⅔-⅓-0 where every result sums to 1. Alas, with the existing system we must swallow the ugly fact that the total result may exceed 1, and as the result the ratings get inflated. Which is a bad thing, sure.   Or is it? Remember, the Elo expectation function only cares about the differences between ratings, not their absolute values. And all teams' ratings get inflated, so all absolute values shift up from where they would've been without the loser's point. Whom would it really hurt? The new teams. Naturally, we must assign an initial rating to every team at the starting point. One way could be assigning the average rating of the previous season to the new team. But we prefer a different and a much more comprehensive solution. We claim that since the teams that at the start of the next season are different enough beasts from those that ended the previous ones, so that the Elo ratings should not carry over from season to season at all! Therefore all the teams start each season with a clean plate and an identical Elo rating Ro.   Once again, the attentive reader might argue, 'What about mid-season trades and other movements?' Well, dear reader, now you have a tool to evaluate impact of the moves on the team. If there is a visible tendency change, you can quite safely associate it with that move. Overall, the 82 game span is huge to soften any bends and curves in the progression of the Elo ratings along the season.   Speaking of game spans, we must note one more refinement being done to the ratings. In the chess world, the ratings of the participants are not updated throughout the length of the event, which is usually 3-11 games. The ratings of the participants are deemed constant for the calculation of rating changes, which accumulate, and the accumulation is actually the rating change of each participant. We apply a similar technique for the teams' Elo calculations: we accumulate the changes for the ratings for 5 games for each team and "commit" the changes after the five-game span. The remainder of the games is committed regardless of its length, from 1 to 5. Why 5? We tried all kinds of spans, and 5 gave the smoothest look and the best projections.   Now, as a demonstration, let's show how we calculate the possible rating changes in the much anticipated game where Minnesota Wild is hosting Columbus Blue Jackets on December, 31st, 2016:   Rcbj = 2250, Rmin = 2196, Ecbj = 0.577, Emin = 0.423, K = 32 (standard USCF).   Outcome Scbj Smin S-Ecbj S-Emin dRa dRb Ra' Rb' CBJ W Reg 1 0 0.423 -0.423 +13.53 -13.53 2263.53 2182.47 CBJ W OT 1 0.5 0.423 0.077 +13.53 +2.47 2263.53 2198.47 MIN W OT 0.5 1 -0.077 0.577 -2.47 +18.47 2247.53 2214.47 MIN W Reg 0 1 -0.577 0.577 -18.47 +18.47 2231.53 2214.47 Note: MIN gains rating when it gets a loser's point.   Here is a dynamic of Elo changes (without five game accumulation) for the Metropolitan Division, as an example.   See more detailed tables on our website: http://morehockeystats.com/teams/elo   Ok, we got the ratings, we got the expected results, can we get something more out of it?   To be continued...
  24. More Hockey Stats
    whoops, got the title wrong
    Original post.
    A rule change suggestion
      There's no irreplaceable people. I.V. Stalin   Rushing this one up, because this idea already came to my mind before, but I forgot about it. The age is taking its toll.

    Anyways. Everyone is talking these days about rule changes. I've already expressed a few thoughts on the scoring systems, but I am not original there. Now, however, I want to make a suggestion I haven't seen mentioned yet.

    Allow soccer (baseball, too)-like substitutions in hockey. Allow the coaches to replace players in the original lineup at the start of the game with one of the "healthy scratches", as submitted in the roster sheet, like the one Peter DeBoer recently messed up in the game against Edmonton.

    The substitution goes ONE-WAY. That means that the player that was substituted cannot return to the game. The substitutions may occur:
      During the intermissions During the commercial breaks During a time-out First and foremost this will allow teams to handle early injuries much better. Your D-man got injured at the 7:04 mark of the 1st period? Around 10:00 there will be a commercial break, you can substitute him with one of the scratches!   Second, it may allow coaches to send stronger messages to players they deem slacking. Rather than shorten the roster by benching that guy, you can send an eager healthy scratch in. Of course, then the "slacking" player is benched for the whole remainder of the game.   Third (oh, I did military service, so I have a natural obsession of providing three reasons for each thing), it may give the coaches some extra flexibility if a designated roster player gets slightly injured in the warm-ups. Then a scratch takes his place as usual, but if the original player is fixed by the 1st intermission, he can substitute the starting scratch.   The substitutes will have to come from the "scratch" list with the exception of the emergency goaltending contracts.   Oh, and I am sure the NHL website will make a mess out of it in their game reports.
  25. More Hockey Stats
    Original post.
     
    One of the greatest chess methodologists, if not the greatest one, the sixth World Champion, Mikhail Botvinnik, wrote in one of his books (about the 1948 World Chess Championship Tournament):

    A tournament must go on a uniform schedule, so that the participants would get used to a certain pace of competition. ...

    The Dutch organizers neglected that. They didn't take into account that plenty of free days (because of the holidays, and because the number of the participants was odd) may break that rhythm and take the participant out of the equilibrium.

    When I found out that one of the participants is going to "rest" for six days before the last gameday of the second round, I suggested to my colleagues Mr. Keres and Mr. Smyslov that we would submit a protest together. Alas, they didn't support me! Angrily, I told them then: "You'll see, one of us is going to rest six days in a row at the Hague, and on the seventh day he'll lose without putting up any resistance..."

    And here came true the first part of my prophecy: after the six-day rest, Keres, pale as a sheet, sat at the chess table across from me, worrying, probably, that the second part of it will also come true...

    Keres lost a rather short and lopsided game.
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