Recently we had a look at the evolution of positions in hockey. We noted that from about 1892 to 1911, the standard lineup could be called 1-1-1-4, being a goaltender, a point, a cover and four forwards. Even though this formation persisted for about 20 years, the results on the ice varied quite a bit over this time. In 1894, AHAC teams scored an average of 3.03 goals per game. This number trended upward, and spiked around 1904, reaching a high of 7.73 goals per game in the ECAHA in 1907.
Obviously there must be some reason for this, and looking for some answers should be interesting. I've got one hypothesis already: as time went on, the defensive players (point and cover-point) became more and more involved in the offence. As the seasons progressed, the proportion of goals scored by points and cover-points increased largely in step with the increase in goals-per-game. Note that I don't mean that as teams scored more goals, defencemen scored more goals in step with the forwards; I mean that as teams scored more goals, defencemen scored more goals relative to the forwards.
This does make sense; if your defensive players are focusing more on offence, your team will score more goals because you have more men trying to put the puck in the net. But of course, your opponents will also tend to score more goals, since you have less focus on preventing goals as well. For whatever reason the back players started to play offence more and more, resulting in more goals by their side and more goals by their opponents as well.
The following chart shows the year-by-year rate of team goals per game, divided by the average goals per game over the time period, and the proportion of goals scored by defencemen (which serves as a proxy for the defenders' relative involvement in the offence), divided by the average proportion over the time period. The goals per game ranges from a low of 3.03 in 1894 to a high of 7.73 in 1907. The percentage of goals scored by defencemen ranges from a low of 2.4% in 1892 to a high of 15.5% in 1908.
The relationship certainly isn't perfect, suggesting that there is more going on (not surprisingly), but it is quite a strong one. You can see this by looking at the chart; as goals per game increases, so does the percentage of goals scored by defencemen. The coefficient of correlation for these rates for this time period is 0.75, which is a very strong positive relationship.