This post was inspired by the work of Eric Tulsky, Geoffrey Detweiler, Robert Spencer, and Corey Sznajder (of the esteemed Broad Street Hockey) in a paper that will be presented at the forthcoming Sloan Sports Analytics Conference, March 1-2, 2013 in Boston, as well as a post over at NHL Numbers.

When I first started taking my girlfriend to hockey games, I had to explain some of the tactics to her. As a former soccer player, nothing befuddled her more than dumping the puck. "After expending so much energy to get the puck, why on earth would a team voluntarily give that up?"

It’s a damn good question, and one which teams probably ought to reexamine. For instance, I think a smart coach with a steady, puck-possession roster could probably ditch the "dump and change" routine for more of a "skate around in neutral and change" strategy.

Back to my story though. . . I explained dumping the puck thusly:

There are reasons that teams dump the puck in, and most of the reason comes down to hockey’s offside rule and how it diverges from soccer. In soccer, being offside is defined by the positioning of the opposition, whereas in hockey, it’s defined by a discrete line on the ice. The blueline creates a "chokepoint" on the ice – a virtual barrier if you will. This allows the defenders to crowd the blueline, safe in the knowledge that nobody can be behind them without being offside.

This brings us to the second big difference between hockey and soccer (and other sports for that matter) – forward to backward transitions in skating are really, really difficult and incredibly slow, even compared to backward to forward transitions. This is the reason for the clichéd-but-true adage that turnovers at or near the blueline are the most dangerous. Why? Because once the puck reaches the blueline, everyone on the team with possession of the puck is anticipating that the puck will cross the line and is behaving accordingly. On defense, all of the forwards and defensemen are skating forward to lead, join, or support the rush, otherwise they’re skating for a change. They’re anticipating that the puck will clear the zone – if it doesn’t, they suddenly have to hit the brakes and try to accelerate backward. Predictably, this gets ugly.

The same thing applies for turnovers at the offensive blueline. The forwards are all (presumably) skating hard to back the defense off and gain the zone with speed. Turning the puck over here virtually guarantees an odd-man rush the other way as the forwards put on the brakes and skate back toward their net (or in the case of Ovie, take a wide, looping rink turn).

So we’ve established that the bluelines create a chokepoint, and that this chokepoint, combined with the inherent physics of skating, makes turnovers near the blueline extremely dangerous. This is where we get into the game theory.

From the offensive player’s perspective, the optimal play is to carry the puck into the offensive zone. From the defensive player’s perspective, the optimal play is to prevent the offensive team from carrying the puck into the zone, preferably by creating a turnover at the blueline. This leads to a situation wherein the offensive player tries to enter the zone with possession, and the defensive player challenges him at the blueline. Unless the offensive player is Pavel Datsyuk, Nick Backstrom, or someone similar. . . or unless the offensive team has a strong odd-man advantage, most offensive coaches don’t like this. The chances for a bad turnover are high, and the upside is low, particularly if the offensive players involved are bottom-six forwards. This is in large part why you see third and fourth lines play so much dump-and-chase, and in all likelihood it’s partly responsible for their lower relative Corsi ratings.

This brings us to the next option – the offensive players observe the defenders challenging the blueline and choose to dump the puck into the zone. (There’s more to playing good dump-and-chase hockey than this, but I’m simplifying). This has the advantage of bringing the probability of a dangerous turnover to virtually nil, but it has the disadvantage of raising the probability of losing the puck – albeit 200 feet from your own net. By dumping the puck, the offensive players can carry speed into the zone, while forcing the defenders to execute a tough backward-to-forward pivot. This disparity in momentum is why the offensive players can often recover the puck on a well-executed dump-in. It’s also why the ability of the goaltender to play the puck is so crucial. If the goalie can move the puck away from the forechecker, it’s much easier for the defenders to counter the dump-in. Think back to the Devils of the late 90s and early 00s. Scott Stevens, Ken Daneyko, and Colin White could aggressively challenge forwards at the blueline because they knew that Brodeur would negate the dump-in. This is a big reason why I’m not a proponent of eradicating the trapezoid.

Let’s say the defenders observe that the fourth line is on the ice, and they guess (correctly) that these knuckle-draggers will get stapled to the bench in perpetuity if they even think about trying to carry the puck into the zone. The defenders can then "cheat" a little by backing off the blueline and readying themselves to retrieve the dump-in. Or the defenders can play "one-up, one-back," with one defender challenging the puck and the other heading back to retrieve the dump-in. Not surprisingly, the more likely it is that a line will dump the puck into the zone, the less likely it is that the tactic will be successful. This is why teams that primarily play dump-and-chase tend to be pretty poor at puck possession; they become predictable.

Boiled down to its essence, zone entries entail two competing sets of binary choices: carry the puck or dump it in for the offense, and challenge the blueline or back off for the defense. The result is a two-by-two decision matrix that looks like this:

The numerical rankings are derived for the offensive team, and intentionally ignore the skill of the players on the ice. Obviously, if the offensive player with the puck is Pavel Datsyuk and the defender challenging him is John Erskine, you probably want him carrying the puck anyway. Same thing goes in reverse if that player is D.J. King and the defender is Nick Lidstrom.

There are two important observations that can be gleaned from this analysis. First, that for most coaches in most situations, the dump-in is the preferred zone entry, even though it’s suboptimal. This is because dump-ins minimize risk. Even if you dump the puck in and the opponent is backing off, the worst thing that happens is a turnover behind the opponent’s net. Above all things, most coaches abhor risk.

The second observation is that the best results occur when the players on the ice do the opposite of what the opponent expected; carry when the defenders back off and dump when they challenge. This is why even good puck-possession teams will dump the puck when they’re on the power play – when the four penalty killers are stacking the blueline, the best option is to dump the puck rather than try to force your way through.

Ultimately, I think that the zone entries paper is an excellent contribution toward better understanding and analyzing hockey, and particularly the effectiveness of certain players and systems. Still, I think viewing the decision between carrying the puck and dumping it in as a static choice made in isolation detracts from a full understanding of how and why teams choose to enter the offensive zone in different fashions. By applying game theory and considering how the opposition’s choices affect what the offense chooses to do, I believe we get a better sense of the decision-making process, and we can therefore better examine the relative merits of different tactics.