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# Equality =/= Quality

Bill James once theorized that given enough chances right-handed batters would begin to form split stats similar to left-handed hitters with at-bats favoring them the opposite handiness. Why is that at all relevant? The idea suggests that a lineup must be balanced in terms of lefties and righties in order to reach their performance ceiling consistently. We often hear about how teams should re-arrange their lineups so ideally the opposing manager can't send out a handed-specialist to gain multiple outs - Tony LaRussa spits in that statement's face - but just how valid is the idea that the best teams are the ones with heavily mixed lineups?

To begin our study I took each of the 30 teams and ranked them by runs scored per game, then using Baseball-reference's batting order sorter took the most prominently used lineup and assigned each lineup slot a handiness.

The raw data doesn't tell us too much, partly because staring at just a bunch of single letters can strain your eyes. Taking the amount of righties in each lineup I stole the idea of a hitters' K:BB and turned it into RHB:LHB. Theoretically the teams with the best offenses would be near 1.00 while the worst offenses would reach upwards of 3; again when you consider the ratio similar to a K:BB ratio you get the idea of what we're looking for, in theory at least.

Now to compare the orders in terms of leaders in each category.

One of the main issues with the data is ignoring switch hitters completely, someone with more ambition than I currently have with this project could go through and use the majority of at-bats taken for each switch hitter and figure that data in, I didn't but may in the future. Another thing is we're assuming every lefty and righty is equal in terms of quality. A question that isn't possible to answer with any level of certainty is whether the league has a bias towards lefties - in other words is a marginal lefty better than a marginal righty due to scarcity issues? That's something I'll try and answer at a later date, but for now it seems like diversity in any given lineup is a fraud in terms of easily improving your run scoring chances throughout the season.