I did this study at the beginning of this season based on the weights of KHL players from last season. What I created for the various weights and heights of the respective players was a linear regression model that gave us the predicted weight of a player based on their heights. For those whose weight was at least one standard deviation over their predicted weight, I put them in the "overweight" category as I did to those one standard deviation below, who were "underweight". I then found the average points per game of each player and made a histogram for each category of player.
In the KHL, we can see that players slightly overweight according to their given height tend to have more points per game. This I’ve come down to two reasons for:
1.) Most of the extra mass consists of muscle , most likely in the legs for strong, powerful strides that help them tear up defenses.
2.) It could also be that this extra mass was a prominent fuel sourced used over the course of the season (since the players’ weight were taken at the beginning of the season), in which the skinnier players didn’t have, which is why they weren’t so productive.
The underweight players are a lot less skewed towards higher points per game , given they’re not as fast and cannot hit as hard. In fact, an underweight forward is twice as likely to only have 1 point every 10 games compared to the average player.
Applying this to the NHL could be interesting. I’d expect similar results if not ones that favor heavier players even more, because of smaller rinks (more hitting).