• the most dangerous lead in hockey

    by  • June 3, 2012 • Hockey • 22 Comments

    There’s pretty broad agreement that coaches of NHL teams have their teams play more conservatively when protecting a lead. It’s reflected in the data – virtually every team in the NHL sees its share of the shot attempts at 5v5 get worse when it’s winning. The thinking goes that coaches have carefully sussed out that they can maximize their chances of victory by playing a defensive game, clogging up the neutral zone and taking advantage of any odd-man rushes that might present themselves as the other team pushes. TACTICS.

    I’ve copied the table that Gabe has on Behind The Net, just to illustrate what I’m talking about, in case any of you are less familiar with score effects. 29/30 teams have a lower Fenwick share when up a goal than they do when they’re tied. The reverse is true. The same effect is also visible when up or down two goals, although it’s less consistent, likely because of sample size. Not a lot of hockey is played with a two goal deficit.

    NHL teams that were up two goals entering the third last year were pretty dominant: they had a regulation time record of 257-6-27, taking a very impressive 93.3% of points available in regulation. (Aside: if you mostly watch the Oilers, this might surprise you. They took 12 points out of a possible 16 in this situation.) We have pretty solid evidence that those teams, as a collective, became less aggressive when they had the lead and, presumably, in crunch time, were less aggressive still. Get it out, get it deep, one man forecheck (if that), repeat.

    We need something to compare this too. There’s a useful way of doing this by assuming that goal scoring is consistent with a Poisson function or distribution (I’ve never learned the exact way of saying this): basically, that it’s random, in accordance with underlying probabilities. Update: Commenter “E” points out that many non-nerd types may be encountering this idea for the first time. I recommend the paper linked here. There’s lots of research that supports this idea, with some caveats – if you apply it to predict a team’s record as a whole, you tend to significantly under-predict the number of games that will end up tied after regulation, because teams respond to the incentives and will play for the tie if they’re tied in the third period.

    What I did was take each team’s GF/G and GA/G and calculate the probabilities of winning, losing and ending up tied in a game in which they led by two after two periods. As you can see, even terrible teams are awfully likely to win. I then multiplied those probabilities by the number of games in which they actually had a two goal lead after two. It’s the row at the bottom that’s really of interest.

    On this way of calculating things, all of that Get it out, get it deep, one man forecheck, repeat resulted in teams winning virtually exactly as many games as we’d expect with a two goal lead after two, losing two and a half fewer and drawing two and a half more. In 290 games. It doesn’t seem like much of a reward for playing less fun hockey.

    There are, of course, a couple of confounding factors here. It’s entirely possible that there are other factors at play. Maybe, for example, referees are way more likely to give penalties to the leading team and third periods for teams up by two have a much tougher row to hoe, in that they face more PP against. Wouldn’t shock me. It’s also possible that teams trailing by two shorten the bench significantly and that using their overall goal differential isn’t really appropriate, in that the players who are on the ice are a sort of a better team.

    That runs both ways though – teams protecting a lead are known to shorten the bench as well. Moreover, it’s implicit in the math here that teams are playing against the average team that they faced; in fact, the average game where one team leads by two entering the third features opposition that’s weaker than usual.

    I ran the same table for teams with one goal leads entering the third period. It’s a little more interesting.

    You can see that the Poisson Excel function significantly overestimates the number of wins and underestimates the number of ties. It also overestimates the number of losses, although not by a huge amount. This is, presumably, teams responding to the incentives that are before them – if the team that’s trailing scores, everyone’s happy to go to overtime and put a point in the bank. My suspicion is that the team leading the game becoming more conservative probably changes the odds of a tying goal from what they otherwise would be, making it more likely that the trailing team will tie to score the game than they otherwise would.

    The really funny thing about this is that playing conservatively seems to have little in the way of benefits for the team leading. If you calculate the points on the basis of regulation win being worth two points and a regulation tie being worth 1.5, you would expect the teams leading by one to average 1.66 points. Actual average points collected by teams leading by one heading into the third: 1.67. The real beneficiaries are the teams trailing by one heading into the third period. Their expected points per game is 0.56. They actually averaged 0.64 points per game.

    As with two goal leads though, I’m not sure that this suggests that playing a more defensive game is actually an optimum strategy or that it’s worth doing, when you consider that hockey’s not just a game but also supposed to be entertainment. On last year’s data, teams pick up an extra 1 point per 100 games in which they have a one goal lead (subject to all my caveats above about how the data might be influenced by other factors.) They give up an extra point per ten games though which can’t be good – I’ve found before that it was weaker teams who benefited disproportionately from the OTL rule; this might help explain why.

    In any event, the point I’m really interested in this: we’re told that defence wins games and that settling into a defensive shell is the way to go about doing things when you have the lead. If this was really true, shouldn’t it show up in the data? (Subject, again, to the caveats above ways in which the data might be misleading.)

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    22 Responses to the most dangerous lead in hockey

    1. E
      June 3, 2012 at

      There’s a useful way of doing this by assuming that goal scoring is consistent with a Poisson function or distribution (I’ve never learned the exact way of saying this): basically, that it’s random, in accordance with underlying probabilities.

      Despite the internal disclaimer, it would be enormously helpful if you could explain this point in more depth or link to the previous research.

    2. Tyler Dellow
      June 3, 2012 at

      Link added to text.

    3. speeds
      June 3, 2012 at

      Interesting article Tyler. It lead me to wondering about something kind of related I’ve wondered about before – shooting from your own end at the empty net when leading in the last minute.

      The prevailing hockey wisdom suggests you should softly dump the puck out of your zone to avoid an icing. I’m not really sure if teams do that because they’ve exhaustively studied the matter and concluded that it’s not worth the risk, or if they are just continuing to do what they’ve always done over the years?

      I obviously don’t actually know which is the correct tactic, but I have to admit I have a bit of a hard time believing that it would be a truly terrible play to shoot for the other team’s net when you’ve got time, space, and a clear shot from your own blueline. Maybe the data would suggest that it is (if there is/were any)? Obviously if you can get to the red line first, there’s good reason to do so, but I’m talking about the situation where you have room and time to shoot but can also see you won’t be able to clear the red line.

      What are the chances of scoring and ending the game right there? How does that relate to the increased risk of a goal against if you miss and the other team gets an offensive zone faceoff?

    4. Locky
      June 3, 2012 at

      I think your final point is really interesting in the context of the extra number of games played against a team in your division, and divisional playoff seeding.

    5. Paulus
      June 3, 2012 at

      Great read. Reminds me of the advice my old Dad gave me about driving: the best defense is a good offense

    6. PDO
      June 3, 2012 at

      Or more simply…

      “You’re up two-nothing! Great job! Now throw everything you did to get this lead out the window and play completely differently!”

      • Doogie2K
        June 7, 2012 at

        I wonder how much of it is direct coaching and how much of it is risk aversion on the part of the players. Like, “we have the lead now, let’s not fuck it up.”

        Either way, it seems self-evident in hindsight that playing conservatively produces worse results, since lower Fenwick/Corsi is associated with poorer performance, and I’m a little surprised that connection hasn’t been made as explicitly as this before now. Neat study.

    7. dog
      June 4, 2012 at

      great stuff as always and thanks to you and Gabe for putting it together.
      Minor thought – if you are up by two I dont think you would shorten your bench – if one then sure – but when its two you would still be looking to spread the load I reckon

      But regarding going defensive – I’m reminded of the French national football (soccer) team – reputedly the stats guys, 20 years ago, studied the games and they determined that the most likely way to score was on the break (not sure if that created the emphasis on a surging midfield that led to France winning the 98 World cup with possibly the worst forward a world cup winner has ever had) – but you get the idea – I saw a similar thing on the Copper and blue recently – you are more likely to get quality scoring chances from transition play than cycling in the zone, I think it said

      But basically its human nature to be conservative when you have something you want to keep and few if no attempts at requests for entertaining hockey, will change that

      Incidentally any chance for more stories from mc52tennis – sounds like there could be some interesting stories there ….

    8. Tom Benjamin
      June 4, 2012 at

      In any event, the point I’m really interested in this: we’re told that defence wins games and that settling into a defensive shell is the way to go about doing things when you have the lead.

      I think you are mixing up two ideas here. I don’t think this is a good way to test whether playing defensive hockey as a primary strategy really pays. That’s a different thing than whether teams should go into a shell when they get the lead.

      I suspect that playing a game that is designed to keep the score down does pay, at least in the regular season. Teams that are involved in low scoring games will tie more often and therefore play in more three point games. This is a strategic choice made by the coach.

      But I’ve come to believe that most of Fenwick swing toward trailing teams will come about no matter what the coach wants. The Canuck coaching staff has often said they want the team to play the same way all the time regardless of the score. The system does not change when the team is ahead and coaches seem to get frustrated when the team turns cautious with a lead.

      The problem is with human nature and the way we assess risk. Losses loom larger than gains. A goal against that ties the score is perceived to be worth more than a goal for that extends the lead. When a team has a lead to lose, a d-man won’t pinch as often as he will when the score is tied because the same pinch is perceived to be riskier. A forward will peel back instead of dash for a loose puck. Players on a team that is winning can’t help themselves from playing more cautiously even when the lead was built with aggressive play.

      • PopsTwitTar
        June 4, 2012 at

        “The problem is with human nature and the way we assess risk. Losses loom larger than gains. A goal against that ties the score is perceived to be worth more than a goal for that extends the lead. When a team has a lead to lose, a d-man won’t pinch as often as he will when the score is tied because the same pinch is perceived to be riskier. A forward will peel back instead of dash for a loose puck. Players on a team that is winning can’t help themselves from playing more cautiously even when the lead was built with aggressive play.”

        damn well said.

      • Hawerchuk
        June 8, 2012 at

        Tom,

        Defensive shell does not reduce the other team’s offense – it only reduces your own. I have a piece on this somewhere.

    9. sacamano
      June 4, 2012 at

      Yeah, I’m not at all convinced that this can be laid at the feet of coaches. Unless you mean the pee-wee coaches who really do try to protect leads by changing tactics. It seems to me that players naturally become more conservative *despite* what non-peewee coaches want.

      It is considerably more common to hear a professional coach in any sport lament that “we starting playing not-to-lose rather than playing to win” than “we really needed to start backing off there in the third period to protect the lead”.

    10. June 4, 2012 at

      My father coached hockey for years, including top teams in peewee and bantam, and what Tom mentions above is correct – even if he stressed to his team the need to keep pressing when they were ahead, they would almost always naturally fall back.

      Not that NHL coaches don’t often change their tactics while up in the third – I’ve seen it first hand. But there is probably a strong psychological component as well.

    11. Darrell
      June 4, 2012 at

      All the comments and the article attribute the change in tactics to the team with the lead. However, I do not believe that it is obvious that the team with the lead is the one really initiating the change in tactics (even though at a certain level I agree with Tom). The trailing team, especially later in the third period, is the team who will REALLY change there style of play.

      For example, lets say two teams pinch with probability x when the game is tied. In the third period (and particularly, late in the 3rd period), both teams will have adjusted their pinching probability, with the team leading having decreased it (by y) and the trailing team increasing it (by z). I would suggest that z is actually considerably larger than y.

      The change of tactics is also really evident at the end of the 3rd period where the trailing team pulls their goaltender, which basically initiates a completely different game for the final 60-90 seconds.

      Finally, speaking of pulling the goalie, I predict that the poisson models error is due to goalie pulling. My guess is that the poisson model is over-predicting 1 goal wins, and hence, under-predicting “ties” and 2 goal wins.

    12. Tyler Dellow
      June 4, 2012 at

      E will find this hard to believe but I’m open to changing my mind on the “what does it mean” questions, as long as we’re using decent evidence of what.

      What Tom, Kent and sacamano are saying sounds compelling to me and it wouldn’t surprise me if it played into it to some degree. At the same time, as you’ll see from the table above, this doesn’t affect all teams equally. The Sens in the early aughties were notorious for keeping the pedal down when up a few goals, to the point that I think it caused people to overrate them. Ottawa would blowout more teams every year and always seemed to underperform their goal difference in terms of record. If you went through and looked at the shots, you saw that they didn’t back off. Detroit in the mid aughties was the same, IIRC, and they look similar last year.

      So it’s not a leaguewide thing.

      As for the frequency of ties: I think the value of a defensive strategy is overblown. Take two teams, one of which averages 2 GF and 2 GA per game and the other which averages 4 GF and 4 GA per game. The former can expect 17 regulation ties per year, the latter can expect 12. Each regulation tie is worth an extra half point. So 2.5 points difference. And we’re talking about teams that are basically beyond the bounds of what the NHL currently produces.

      • Tom Benjamin
        June 4, 2012 at

        At the same time, as you’ll see from the table above, this doesn’t affect all teams equally. The Sens in the early aughties were notorious for keeping the pedal down when up a few goals, to the point that I think it caused people to overrate them.

        I think most of the variance between teams is just randomness. Another factor that may partially explain the Sens or the Wings back then is found in the blowouts. At a certain point the trailing team becomes the losing team and the rest of the game is garbage time. The game is over even if there is ten minutes to go. The lead can’t be lost and fear of losing it doesn’t impact on the player decisions. I’d guess that the bigger the lead, the less the Fenwick will swing toward the losers.

        The science on this stuff is pretty clear. We are hardwired for loss avoidance and we consistently opt for strategies to avoid losses even when we know the math says a more optimum strategy is available. It is irrational, a reasoning error we make all the time. A football (or hockey) coach who calls for a prevent defense is probably making that error. Even if the coach does not call for a prevent defense, the players will give the ground to try and make sure no one gets behind them – basically because he is human.

        As for the frequency of ties: I think the value of a defensive strategy is overblown. Take two teams, one of which averages 2 GF and 2 GA per game and the other which averages 4 GF and 4 GA per game. The former can expect 17 regulation ties per year, the latter can expect 12. Each regulation tie is worth an extra half point. So 2.5 points difference. And we’re talking about teams that are basically beyond the bounds of what the NHL currently produces.

        Like I said, this is a different issue in my opinion. Both are very interesting but they are still separate. A defensive team becomes even more risk averse when protecting a lead. I think this is a mistake just like it is a mistake for an offensive minded team to do it. I think if an offensive team starts to trap with the lead, it is a coaching error, but even if they do not, the players will turn conservative on their own.

        I really dislike it if my coach plays Katie bar the door with a lead, and on the first issue, I agree with you. The defensive shell, the prevent defense does not pay. I’d like to believe you are correct on the second issue, too, but I’ve got my doubts. I tossed out the “more ties” argument because it is a tangible. As you showed it isn’t much, but it is something.

        I think we should be able to evaluate whether a defense-first system pays off by correlating goals for and against to wins. If it doesn’t matter whether you play offense first or defense first, I’d expect goals for to correlate against wins at about the same rate as goals against. If defense is the way to go in hockey, I’d expect goals against to consistently correlate better to wins than goals for correlates to wins. I haven’t done the work, but I’m going to guess there is a small but persistent edge to the defense.

      • E
        June 4, 2012 at

        I should just create a bot that autocomments on all your posts with, “That’s really interesting research but I have some questions about your interpretation.”

      • Triumph
        June 5, 2012 at

        If we’re going to speak of this as abstractly as has been done, I think players who push the play (i.e. score lots of goals/get lots of points) tend to be paid much more than players who don’t. Furthermore, I think it’s harder to find these players. I think people confuse cause and effect when they note that we rarely see high event teams deep in the playoffs – I don’t think that playing low event hockey is eo ipso better, I just think that worse teams tend to have a more go-for-broke attitude about the game.

        Still, I imagine it would be harder to maintain a team of players who managed to score 260 goals a season and give up the same than a team that scores 200.

    13. Ryan
      June 6, 2012 at

      But there are two teams. Both of them make a strategic choice. Even if the leading team plays exactly the same way when as they would in a tie game, the game can still look different because the trailing team can change their strategy.

      And regardless of whether it’s optimal for the leading team to sit back or not, it’s clearly optimal for the trailing team to start pinching more and playing more aggressively. That strategy will raise the trailing team’s odds of winning above what the Poisson model will predict.

      So if the observed results are bang on what the Poisson model predicts, that suggests the strategy of sitting back and protecting a lead _does_ work. Because then that strategy fully counters their opponent’s.

      • Tom Benjamin
        June 6, 2012 at

        And regardless of whether it’s optimal for the leading team to sit back or not, it’s clearly optimal for the trailing team to start pinching more and playing more aggressively. That strategy will raise the trailing team’s odds of winning above what the Poisson model will predict.

        If this is the case, then the team should not wait until they are trailing to become more aggressive. Will it raise the trailing team’s odds of winning? It both increases their chance to score and the chance their opponents will score. Presumably teams adopt the best balance between offense and defence from the outset. When they take more risks, it should help the opponents more than it helps themselves. This is not irrational because if they don’t score they will lose the game. They turn it on and it turns out to benefit them – we get more tied games than poisson would predict – but only because the leading team plays too conservatively to make the trailing team pay for their aggression.

        So if the observed results are bang on what the Poisson model predicts, that suggests the strategy of sitting back and protecting a lead _does_ work. Because then that strategy fully counters their opponent’s.

        But the results are not bang on. The trailing team benefits from the change(s) in strategy. Either the trailing team has the wrong strategy in the first place – they should adopt the more aggressive play from the outset – or the leading team is wrong to play more defensively.

        What I think is happening is that the trailing team tries to open it up and instead of taking advantage of that, the leading team screws it down even tighter. The result is more shots for the trailing team.

        • Mike
          June 7, 2012 at

          If this is the case, then the team should not wait until they are trailing to become more aggressive. Will it raise the trailing team’s odds of winning? It both increases their chance to score and the chance their opponents will score. Presumably teams adopt the best balance between offense and defence from the outset.

          Not sure this is correct – once you trail by a goal, the value of scoring a goal is large, while the cost of being scored on is reduced.

          Pretty much the same logic as pulling the goalie.

          (I’d be curious to know if anyone has actually ran the stats on whether a 6-on-5 is actually beneficial, given the increased chance of going down two)

        • Ryan
          June 29, 2012 at

          Stupidly late reply, but just to follow up:

          Mike’s right. The optimal mix of offense and defence changes depending on the score. Pressing the attack means the other team’s more likely to score. While you’re trailing, that has very little impact on your chances of winning the game. While you’re tied or leading, it has a big impact.

          But the results are not bang on. The trailing team benefits from the change(s) in strategy.

          The broader point is that we don’t have the data to even determine this. The nature of the game fundamentally changes when one team falls behind. Both teams change their strategy. You can’t compare to what happens in a tie game when both teams play normally. You have to compare to what would happen if the losing team pressed the attack and the leading team tried to play normally–but we don’t have any data on that.

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