I may, after all this time, finally have understood the question. The data, if I'm correct, are a set of tuples $(i, j, y(i,j))$ where $i$ is one player, $j \ne i$ is another player, and $y(i,j)$ is the number of attacks of $i$ on $j$. In this notation the objective is to relate $y(i,j)$ to $y(j,i)$. There are some natural ways to do this, including:
Analyze the data set $\{(y(i,j), y(j,i))\}$ by means of a scatterplot or PCA (to find the principal eigenvalue). Note this is not a regression situation because both components of each ordered pair are observed: neither can be considered under the control of an experimenter nor observed without error. It is this scatterplot, I believe, that appears triangular. This already suggests that any attempt to describe it succinctly, such as by means of a principal direction, is doomed.
Model $y(i,j)$ in terms of characteristics of $i$ and $j$. This is a classic regression situation. The solution provides an indirect, but possibly powerful, way to relate $y(i,j)$ to $y(j,i)$.
In this case, also consider re-expressing the data in terms of relative numbers of attacks. That is, instead of using $y(i,j)$ use $x(i,j) = y(i,j)/\sum_{j}{y(i,j)}$.
In this case, also consider re-expressing the data in terms of relative numbers of attacks. That is, instead of using $y(i,j)$ use $x(i,j) = y(i,j)/\sum_{j}{y(i,j)}$.
