Data from: Luck, skill, and depth of competition in games and social hierarchies

Patterns of wins and losses in pairwise contests, such as occur in sports
and games, consumer research and paired comparison studies, and human and
animal social hierarchies, are commonly analyzed using probabilistic
models that allow one to quantify the strength of competitors or predict
the outcome of future contests. Here we generalize this approach to
incorporate two additional features: an element of randomness or luck that
leads to upset wins, and a "depth of competition" variable that
measures the complexity of a game or hierarchy. Fitting the resulting
model we estimate depth and luck in a range of games, sports, and social
situations. In general, we find that social competition tends to be
"deep," meaning it has a pronounced hierarchy with many distinct
levels, but also that there is often a nonzero chance of an upset victory.
Competition in sports and games, by contrast, tends to be shallow and in
most cases there is little evidence of upset wins.