Perhaps you might have noticed that more clubs seem to be pulling their goalie earlier in matches. Traditionally, this risky tactic has been reserved for the very last minute of a match because the risk of an open net has been seen as too great. Lately, however, more and more clubs are using this tactic when they lose a player for two minutes. The logic apparently being that they are better off keeping an equal 6 on 6 balance while on offense. Typically, the extra court player plays backcourt for about 15 seconds and then substitutes out for the “real” goalie.
And sometimes the “real” goalie plays offense and as Constanta’s Mihai Popescu shows they can even score. Video: http://www.youtube.com/watch?v=uSP9w83YJ0g
So does the possibility of an 12 meter cannonball strike by your pulled goalie justify the risk of your opposition getting an easy goal into an empty net? My intuitive reaction has been that this strategy is total nonsense. After all, if pulling your goalie was such a good idea why don’t teams do it for an entire game?
But, being that I’m an Engineer (in my day job) I decided to run some numbers to back up my intuition. In doing so I was surprised to find out that this strategy isn’t as foolhardy as I thought. In fact, depending on how likely you think different outcomes are it’s a sound strategy.
For the sake of argument let’s make the following assumptions:
Likelihood of Team A scoring when:
– Down a man (5 on 6): 15%
– Pulling a goalie (6 on 6): 30% (note: this is not the same as a regular 6 on 6 since the “6th man” often stays back a little in order to be ready for the substitution
Likelihood of different Team A readiness levels on their next defense as a result of their trying to score with a pulled goalie:
– Fully ready (Made goal): 30%
– Fully ready (no fastbreak opportunity for Team B ): 20%
– Partially ready (partial fastbreak; resulting in the goalie not being fully ready to defend): 30%
– Open goal (turnover or easily recovered missed shot results in an open net): 20%
Likelihood of Team B scoring:
– When Team A is fully ready: 60%
– When Team A is partially ready: 80%
– When there is an open net: 98%
Using these percentages it can then be calculated that the pulled goalie strategy is marginally superior. (For those so inclined the math is in the in the extended text.) With the pulled goalie strategy a team can expect to be up a goal 12% of the time; tied 33%; and down 1 goal 55%. The traditional strategy results in being up a goal 6% of the time, tied 43%, and down 1 goal 51%. Or to think of it in terms of expected value, pulling a goalie results in a -.436 deficit vs. -.45 for the traditional strategy. A razor thin margin for sure, but still a slight nod to the pulling the goalie strategy.
Now we can argue if the percentages chosen are “representative”. Truth be told, they will vary greatly depending on the teams playing. Accordingly, so should the decision on what strategy should be taken. In general, if your defense is not very good under normal circumstances, the more sense it makes to pull your goalie. In other words, if they are going to score against you anyway, you might as well improve your chances to score against them. Conversely, if Thierry Omeyer is in the goal it would be foolish not to keep him in the goal where even an uncontested fast break is no sure thing. This is why I question former Norway National Team coach, Marit Breivik’s use of this tactic. With one of the best teams in the world and a more than competent goalie the odds suggests that this might have been a suspect strategy.
Another question worth contemplating is whether certain clubs might even want to consider playing 7 on 6 full time. And indeed some of the weaker Champions League clubs have done exactly this against the elite clubs for significant stretches of a match. Such a move is very disruptive, but it usually doesn’t take too long for the top clubs to adjust and punish the tactic. Reportedly, the Argentine women have been using this tactic at the World Championships in China, but based on results it hasn’t been too successful.
For more on the math involved see the extended text
For a traditional defense where the goalie stay put it’s relatively simple
Percent Team A scores (5 on 6) – Percent Team B scores (when Team A is fully ready on defense) or simply .15 -.60 = -.45
Or to think of it another way if this situation happens 100 times the resultant outcomes would be
9% Team A: 1; Team B:1
6% Team A: 1; Team B:0
51% Team A:0; Team B:1
34% Team A:0 Team B:0
The calculation for pulling the goalie is a little more complex due to the varying states of defensive readiness and the varying times they face that particular state of readiness:
Percent Team A scores (6 on 6) –
[(% Team B scores against fully ready Team A x % time Team A scores) +
(% Team B scores against fully ready Team A x % time Team B has no fastbreak opportunity) +
(% Team B scores against partially ready Team A x % time Team A is only partially ready) +
(% Team B scores against empty net x % time there is a an empty net)]
.30 – [(.60 x .3) + (.60 x .2) + (.80 x .3) + (.98 x .2)] = -.436
18% Team A: 1; Team B:1
12% Team A: 1; Team B:0
55% Team A:0; Team B:1
15% Team A:0 Team B:0