The best goalies should play for the worst teams

Last week, I described a way to look for "bad team" goalies as described by Ken Dryden. I don't think that method is going to work ... the sample sizes are too small.

But, while doing the math (which I'll spare you), it occurred to me that there IS a class of goalies that could be considered "bad team" goalies, in the sense that they're more valuable to a good team than a bad team. That class of goalies is simply ... the best goalies.

The worse the team defense, the more shots the other team gets. So the great goalie will wind up saving a lot more goals for a bad defense than a good defense. It's like how a policeman is more productive in a bad neighborhood.

I guess this isn't a new realization ... people have said that Ken Dryden was wasted, a bit, in the Montreal goal for so many years ... there was very little for him to do. He would have had more value to a team with a worse defense -- at least in terms of goals saved.

So, if teams are rational, you should see the best goalies playing behind the worst defenses.

Or maybe not. I'm surprised at how tiny the effect is. Eyeballing last year's NHL stats, it looks like bad teams gave up maybe 125 more shots than average.

The best goalie in the league might be 2 SD above average, or .008. Multiply 125 by .008, and you get ... exactly one goal. So, even a great goalie is worth only one more goal to a bad team than to an average team.

That assumes that all shots are equal. Suppose bad teams give up harder shots, and good teams give up easier shots. Maybe that doubles the effect. In that case, the advantage becomes two goals. So moving from the best team to the worst is worth four goals -- from two goals worse than normal, to two goals better than normal.

Hmmm ... maybe not as tiny as I thought. To get four goals of goalie improvement is the equivalent of 3/4 of a standard deviation in goalie talent. For a team, saving four goals should get you, what, maybe a couple of points in the standings?

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I'm sure this is old hat to hockey sabermetricians, but this is the first time it seriously occurred to me that the same player can be more valuable, in terms of influencing the score, with a bad team than a good team.

You've also got the punter in football ... the worse the offense, the more fourth downs, so the more important punting is overall. And, maybe, the safety: he's the last line of defense, so he gets more chances when his teammates fail to make the tackle before him.

In baseball, good fielders are more valuable on bad teams, since bad pitchers allow more balls in play. Also, a bad team will have a lot more men on base than normal, which means more double-play opportunities. Also, a strikeout pitcher is more valuable on a team that doesn't field well.

You might also argue for the NHL enforcer, if his job is to start fights when his team is behind, and you also accept the premise that the goonery actually helps the team come back.

Which is the strongest example, the one where the player adds the most value moving to the bad team? I'd guess the NHL goalie, but, really, I have no idea.