Normally I like to stick to things that happened in hockey before 1927, but sometimes fascinating things can be found in more recent season, for which of course we tend to have better data than those from long ago.
A recent thread of HFBoards got me looking into the relationship between NHL teams' man-advantage situations and their results in the standings. I wanted to look at each team's net power-plays, which we'll call their net odd-man situations (NOMS) here, and how many points they recorded for the season. As such I computed the coefficients of correlation for each NHL season from 1963/64 to the present, which is all the data that was readily available.
Remember that a positive correlation means that teams with higher point totals for the season also tend to have higher NOMS (ie, receive more man-advantage situations than they give up), while a negative correlation means that teams with higher point totals tend to have lower NOMS. The results are summarized in the table below. A correlation of zero means there is no relationship between a team's place in the standings and its NOMS.
Before the Great Expansion, at least for the seasons I have the data for, a team's NOMS were not strongly predictive of how that team did in the standing. And this held for the first season after expansion as well. But starting in 1968/69, the weaker teams in the NHL had a strong tendency to have a net positive in man-advantage situations. And this is a persistent effect, only getting close to zero for a season or two in the early 1980s, but remaining negative.
This persisted until 1988/89, when the whole thing swung to the positive. Starting in that season, strong teams had a tendency to have a positive NOMS, meaning they received more man-advantage situations than they gave up. Although it has dropped to around zero correlation in five seasons since then, otherwise it's been a positive correlation, and often strongly so.
There are at least two competing effects here, that could explain the relationship between a team's NOMS and its success in the standings.
One is that, obviously, a team with a positive NOMS should be expected, on average, to receive an advantage in net goals (which in turn results in an advantage in wins). Having a man advantage is a large advantage, almost doubling your chance to score a goal in that time and reducing your opponent's chances to almost zero. So based on this, we would expect that a team with a positive NOMS would do relatively well in the standings, which would result in a positive correlation coefficient.
Another factor, however, is score effects. A team with the lead will tend to play defensively. This is why teams with a lead will tend to be out-shot by their opponents. Additionally, I think I'm safe in saying that a team playing defensively will also take more penalties than they draw, since most penalties occur on defence. Since a team that is often in the lead will tend to win more often than one that isn't, that may lead to a good team giving up more man-advantage situations than they receive. This would result in a negative correlation between NOMS and points in the standings.
I suspect, and I haven't done any research to support this, that the first factor would have a stronger effect than the second, since the first involves actually having a higher NOMS while the second involves only the potential for a lower NOMS. That is, the skill/descipline/luck/whatever involved in drawing more penalties than you take is a stronger factor that the score effect. That's just an educated guess, of course.
So from that perspective, the results from 1988/89 to the present make sense. Teams that have a high NOMS should be scoring more goals than their opponents, on average, and therefore the positive correlation makes sense.
But two important questions would then remain: why the negative correlation between 1968/69 and 1987/88, and why the switch from negative to positive in 1988?
One thing that is very different in the NHL from the 1970s to the 1990s is the parity among teams. In the 1970s, the best teams dominated the worst (typically, expansion) teams. Dynasties like the Lafleur Canadiens, Bossy Islanders and Gretzky Oilers do not exist in the NHL today, and haven't for some time. This great disparity in team quality does suggest that, perhaps, the game's officials (knowingly or subconsciously) gave more advantages to the lesser teams in order to give them something of a fighting chance. That's a possibility. And then when relative parity arose, such things were no longer needed and were abandoned, leaving NOMS to grant the advantage that it should, as discussed above.
But there's also the possibility that the players on the better teams, knowing they were so far superior to their opponents, simply took more liberties with opposing players. Perhaps they didn't hesitate to trip the man in the slot, because they knew the resulting power-play would be relatively weak and would likely be killed off. So again, the negative correlation is a result of disparity, but this hypothesis does not require biased officials to function. As such, this is the explanation I currently prefer.
Those are a couple of hypotheses. I welcome yours.