  Individual performance metrics are commonly used to compare players from
different eras. However, such cross-era comparison is often biased due to
significant changes in success factors underlying player achievement rates
(e.g. performance enhancing drugs and modern training regimens). Such
historical comparison is more than fodder for casual discussion among sports
fans, as it is also an issue of critical importance to the multi-billion dollar
professional sport industry and the institutions (e.g. Hall of Fame) charged
with preserving sports history and the legacy of outstanding players and
achievements. To address this cultural heritage management issue, we report an
objective statistical method for renormalizing career achievement metrics, one
that is particularly tailored for common seasonal performance metrics, which
are often aggregated into summary career metrics -- despite the fact that many
player careers span different eras. Remarkably, we find that the method applied
to comprehensive Major League Baseball and National Basketball Association
player data preserves the overall functional form of the distribution of career
achievement, both at the season and career level. As such, subsequent
re-ranking of the top-50 all-time records in MLB and the NBA using renormalized
metrics indicates reordering at the local rank level, as opposed to bulk
reordering by era. This local order refinement signals time-independent
mechanisms underlying annual and career achievement in professional sports,
meaning that appropriately renormalized achievement metrics can be used to
compare players from eras with different season lengths, team strategies, rules
-- and possibly even different sports.
