LATE-GAME STRATEGY

WHEN TO PULL THE GOALIE

Pulling your goalie swaps a goaltender for a sixth skater. You get a 6-on-5 advantage, and you give the other team a shot at an empty net. Two things make that trade better than it looks.

First, losing by two costs the same as losing by one. In the standings, a 3-1 regulation loss and a 2-1 regulation loss are both zero points. If you're trailing late, an empty-net goal against usually changes nothing that matters. A tying goal changes everything: it gets you to overtime and at least one point.

Second, the extra skater really does help. Teams score at a much higher rate 6-on-5 than 5-on-5. They also give up empty-net goals at a high rate, but see the first point.

Put those together and the math says to pull earlier than tradition does. For decades the default was around the one-minute mark. Analysts who modeled the trade-off, including a widely cited 2018 paper by Clifford Asness and Aaron Brown, found that a team down one should pull with roughly five or six minutes left, and a team down two much earlier than that. NHL coaches have been moving in that direction. Pulls with three or more minutes left, once rare, are now common.

What our model says. The win probabilities in the game come from the last three NHL seasons, and they put the sweet spot for a team down one a little later than that paper: about three to two minutes left. The reason is how fast empty-net goals come now. In the last two minutes, a team with its goalie pulled gives up about 18 goals per 60 minutes and scores about 6. Down one from 7:00, pulling around 2:30 wins about 13.6% of the time, pulling at 5:00 about 13.2%, at 1:00 about 12.4%, and never about 10.7%. Down two, earlier is better: anywhere from 7:00 to 4:00 is about the same, and every minute you wait after that costs you. Either way, the old one-minute pull leaves chances on the table.

WHAT CHANGES THE ANSWER

• Where the puck is. The cleanest pull is at a whistle before an offensive-zone faceoff. You get a set play with six attackers and the puck 180 feet from your empty net.
• Who has the puck. Pulling on the fly only works when you have possession heading the right way. Pulling while the other team is breaking out is how you give up a 190-foot goal.
• Down two. Go earlier still. You need two goals, and you need time to score them.
• Standings context. Late in a season, a team that must win in regulation, or that values a single point very differently, may shift the math.

Going back in. Pulling isn't permanent. If there's a neutral- or defensive-zone faceoff and you're worried about losing it clean, putting the goalie back in for the draw and pulling again on the fly is a real option. It costs you the sixth attacker for a few seconds and buys insurance against a quick empty-netter.

THE ICING RULE: A TRAP FOR TIRED LEGS

Icing happens when a team shoots the puck from its own half of the ice all the way past the other team's goal line without anyone touching it. Play stops and the faceoff comes back to the offending team's end.

The key detail for late-game strategy: the team that ices can't change lines before the faceoff. The players on the ice are stuck there, however long their shift has been. The NHL also lets the non-offending team choose which faceoff dot to use.

That matters a lot when you're trailing with the goalie pulled:

• The team protecting the lead wants to fire the puck down the ice to relieve pressure. If it ices, its tired skaters have to stay out for an offensive-zone draw against your six.
• You can change. They can't. Send out your freshest legs and your best faceoff player.
• If you're the one protecting a lead, clearing the puck high off the glass or chipping it out to the neutral zone is often better than a long icing that traps your own unit.

WHEN TO USE YOUR TIMEOUT

Each NHL team gets one 30-second timeout per game. Once it's gone, it's gone, which is why so many coaches save it for the last few minutes.

The best uses late in a game:

• Rest your top unit. After a long shift in the offensive zone, a timeout gives your best players 30 seconds of air before an important draw.
• Draw up the 6-on-5 set play. Who takes the faceoff, where the shooters stand, who covers the empty net if the draw is lost.
• Settle the room after a goal against or a bad sequence.

Remember that a timeout rests both benches. If the other team just iced the puck and their players are stuck on the ice, calling your timeout hands them 30 seconds of rest. Let the icing rule do its work and save the timeout.

Using your timeout earlier in the game, say to stop a bad stretch in the second period, is a real choice with a real cost: you won't have it in the last two minutes. In Pull the Goalie, a scenario tells you up front whether your team still has its timeout.

FACEOFF MATCHUPS

With the goalie pulled, every offensive-zone faceoff is a possession coin flip worth a lot. Win it and your six set up in the zone. Lose it clean and the other team can fire at an empty net.

• Season numbers versus tonight's numbers. A center who wins 55 percent of his draws over a season is a good bet. One who is 0 for 4 tonight might be off, or might just be in a small sample. Four draws is not much information. Lean on the larger sample, but don't ignore a player who's clearly struggling against tonight's opponent.
• Have a backup. Officials can throw a player out of the faceoff circle for a violation, and then a teammate has to take it. Make sure there's a second player on the ice you trust on the dot.
• Changing to get a better center costs something. Bringing a faceoff specialist off the bench means taking someone else off, and it can mean giving up a skill player for the rest of the shift.
• Plan the lost draw. Decide in advance who goes back to defend the empty net if the draw is lost cleanly.

BUILDING THE EXTRA-ATTACKER UNIT

Once the goalie is out, you have six skater spots to fill. There's no single right shape, just trade-offs.

• Six forwards: maximum skill and scoring touch around the net. Nobody is a natural on the blue line, so pucks that get past your point can turn into empty-net chances.
• Five forwards, one defenseman: the most common choice. One player at the point to hold the line, move the puck and shoot from distance, with five scorers below him.
• Four forwards, two defensemen: the safest version. Better at keeping the puck in the zone and at getting back, with less finish.

Whatever the shape, fatigue matters. The empty-net push often comes at the end of a game where your best players have already logged heavy minutes. A slightly less skilled player with fresh legs can be the better choice than a star on the last of his energy. That's exactly the trade-off the legs meter in Pull the Goalie asks you to make.

Faceoff ability matters too. If your unit has no strong center, every offensive-zone draw becomes a gamble.

COACH'S CHALLENGE MATH

A coach can challenge certain goals, most often for offside on the zone entry or for goaltender interference. In the NHL today, a failed challenge costs a two-minute minor penalty for delay of game.

Whether to challenge comes down to a simple comparison:

Late in a close game, both sides of that comparison get bigger. Here's an illustrative example with made-up round numbers. Say you're down one with eight minutes left and the other team scores to go up two:

• Down two with eight minutes left, maybe you tie it 10 percent of the time.
• Back to down one, maybe you tie it 30 percent of the time. Overturning the goal is worth about 20 points of tying chance.
• If the challenge fails, you're down two and killing a penalty. Maybe your chances drop from 10 percent to 6 percent. That's a cost of about 4 points.

With those numbers, a challenge only has to succeed about one time in six to be worth it. The exact figures vary game to game, but the shape of the math usually favors challenging a goal when there's a reasonable case, especially late. A goal that puts you down two costs far more than a short penalty kill.

Pull the Goalie doesn't include challenges yet. They're on the list.