  In most popular sports leagues, like the MLB, NBA, and NFL, none of the
commonly used statistics take into account the strengths of the opponents a
player faces. One of the main reasons for this is the conventional belief that
a player's luck tends to even out over the course of a season. The other main
reason is the difficulties of finding a sensible algorithm to both quantify the
strengths of the opponents and incorporate such quantifications into a
renormalization of a player's statistics.
  In this paper, we first argue that certain statistics, such as Earned Run
Average (ERA) or Fielding Independent Pitching (FIP) can be significantly
skewed by opponents' strengths in the MLB. We then present an algorithm to
renormalize such statistics, using FIP as the main example. This is achieved by
observing that certain opponent statistics for all 30 teams in the MLB (e.g.
the collection of each game's opponent FIP value over the course of a season)
follow a universal distribution, up to scaling and shift.
  This enables us to establish a data set for a hypothetical average team and
to develop a pitching statistic based on FIP which accounts for the strength of
a pitcher's schedule through methods based on equipercentile equating. It is
called aFIP, which measures what a pitcher's FIP would have been if he had
faced a league-average offensive team every time he pitched.
  We find that there is a significant difference between aFIP and FIP for some
pitchers during the 2019 season and other seasons as well, adding a new tool
for player evaluation. This could make millions of dollars of difference in
player contracts and in profits for teams as they enhance the accuracy with
which they make player acquisitions. The universal distribution we observed
also has many possible future applications throughout the sports world.
