Findings

Two edges the data says are there, measured on all 9 AHL seasons in this database

Pull the goalie about two minutes earlier

A goal down, AHL benches pull with 1:04 left. The model says 3:20 — and two goals down, 8:23 rather than 2:18.

3:20when to pull, a goal downbenches go at 1:04
+33.8standings points left on the table2025-26, across the league
10,705team-minutes of six-on-five measuredand 3,226 empty-net goals behind the rates

Win probability gained over never pulling, in percentage points · filled dot = model optimum, hollow = league median

Every curve is flat across its top, so the model is not asking anyone to hit 3:20 on the nose. It is saying the league median of 1:04 sits on the wrong side of the peak.

Every deficit in detail

Down 1

3:20

left in regulation

Benches pull at: 1:04 left
Win probability, never pulling: 23.2%
…pulling when they do: 24.5% (+1.2 pts)
…pulling at the optimum: 25.3% (+2.1 pts)

Down 2

8:23

left in regulation

Benches pull at: 2:18 left
Win probability, never pulling: 7.4%
…pulling when they do: 8.5% (+1.0 pts)
…pulling at the optimum: 9.4% (+2.0 pts)

Down 3

20:00+

before the third period starts

Benches pull at: 1:18 left
Win probability, never pulling: 1.9%
…pulling when they do: 2.3% (+0.5 pts)
…pulling at the optimum: 3.3% (+1.4 pts)

The rates the model runs on
Deficit	Goalie in net				Goalie pulled				6v5 min
	GF/60	GA/60	xGF/60	Shots/60	GF/60	GA/60	xGF/60	Shots/60
Down 1	2.63	2.22	2.71	30.5	9.59	29.42	7.60	70.4	2,839
Down 2	2.62	2.60	2.78	31.3	6.94	19.28	6.05	57.1	4,424
Down 3	2.77	2.94	2.82	31.7	4.77	7.18	4.09	38.8	3,442

A goal down, the extra attacker buys 3.8 times the scoring rate at 13.9 times the rate against. A terrible exchange on its face, and still worth making: a goal against when you are already losing costs far less than the goal you need is worth. That asymmetry is the whole reason the trade pays.

A 2025-26 season replayed this way

Games with the decision

1,056

someone was behind late enough to pull

Extra wins

+12.7

one more per 83 such games

Where the points come from
Deficit	Games	Pulled earlier by	Points gained
Down 1	384	2:00	+18.8
Down 2	303	5:33	+8.1
Down 3+	369	18:42	+7.0

Most to gain
Club	Games	Points taken	Gain
IA	43	9	+1.46
RFD	41	4	+1.39
TEX	35	8	+1.27
BRI	36	6	+1.26
TOR	39	9	+1.25
SD	36	11	+1.23
CV	35	7	+1.23
TUC	33	10	+1.19

No game is simulated from the opening faceoff. Each is replayed only from the first moment the optimal rule and current practice disagree — real score, real clock — and only that first moment counts, because after it the two worlds have separated. The replay maximises standings points rather than win probability, which pushes the thresholds a little later, to 3:04 and 7:51: reaching overtime banks a point.

How this is measured, and where it is weakest

Does the model know what it is talking about? Run it over every season on file under the policy benches actually use and it expects 1124 standings points from those 8,389 situations. The teams took 1,111 — a miss of 1.1%. The counterfactual is only worth reading because the factual lands.

The feed never records the goalie leaving the net, so six-on-five ice time is inferred. A team with an empty net cannot concede an ordinary goal, so the rate at which ordinary goals against go missing — against a baseline from the same teams minutes earlier — measures how many nets are empty. Two checks on it: goaltender time on ice, an entirely separate column of the box score, implies about the same 11,000 team-minutes without being used here; and the goals this says were conceded with a goalie in net average thirty feet of shot distance, exactly like ordinary goals.

Down three is the weak case. By three goals the leading team has stopped hunting the empty net — it scores into it at 7 per sixty rather than 30 — which is what pushes the answer past the edge of the period. Read that one as “far earlier than anyone does” rather than as a time. Hold the leading team to its up-two rate and the model says 5:19; to its up-one rate, 3:19.

Pull the goalie about two minutes earlier

Every bench in the league waits too long, and it costs them standings points.

A lead flatters the club holding it

Clubs in front outscore their opponents 52.6% of the time. Take empty-net goals out of both sides and it is 47.9% — at even play the club protecting a lead is being outscored.

47.9%goal share with a lead, empty net removed52.6% with those goals counted
4.7points of goal share the empty net is worththe entire margin, and then some
5.35 → 5.58goals per 60, tied then a goal aheadthe game does not slow down when someone leads

League, 2025-26	GF–GA	GF%	GF% without empty-net goals
With a lead	2641–2378	52.6%	47.9%
From behind	2378–2641	47.4%	52.1%

Why a lower goal share can still be the right trade

A leading club is not trying to win the next ten minutes, it is trying to run out of them, so trading goal share for a slower game can be correct. It is finding 01 in reverse: the trailing club wants variance badly enough to hand over an empty net, and the leading club should want to kill variance for the same reason. A shell is the posture that goes with it — collapse into a 1-3-1 or a box around the slot, concede the outside, kill anything from the middle.

Holding a one-goal lead, twenty minutes to go
How the leading club plays	Source	Goals/60, both	Its goal share	P(win)
What AHL leaders do	measured	5.58	46.8%	.744
Like a tied game	measured at level	5.36	50.0%	.774
A shell: scoring −40%	hypothetical	3.35	42.1%	.783
A deeper shell: −60%	hypothetical	2.23	39.9%	.829

The hypothetical shells win, so the logic is sound. The trouble is that the game does not slow down: to justify a 46.8% share, total scoring would have to fall about 18%. It rises 4%.

The honest limit on this

Those rates are an equilibrium — the leader sitting back and the trailer pushing — so part of the extra scoring is the trailing club’s doing rather than a failure by the leader. Nothing here observes what would happen if a leading club played it differently, so read the table as the price of the trade, not as proof that any particular bench is getting it wrong.

What is safe to take from it. Judge a club that spends the season in front on its even-play numbers rather than its goal share, and the reverse for one that spends it chasing — that part needs no counterfactual. Regulation only; overtime is three-on-three and always starts level. Per-club versions are on each club’s page.