Is a Team of Average Players an Average Team?

Depending on who you are, you'll have one of three responses to this question:

1. That's so obvious I don't even know why you're asking it.
2. That's so obvious I-- well, now that I think about it a little more...
3. Click on nearest link to Kate Upton bikini pictures[1].

Because I fell in the category #2, I felt the need to test this with the simulator. And really what I mean with this question is "Does a lineup of average players produce an average number of runs?" The argument for "yes" has the backing of the stats community---the statistic wRC (weighted runs created) works. It predicts with high accuracy the number of runs a team will produce. And all you need to calculate it is the number of times each player reached base and how; a walk, a double, etc. And that statistic doesn't care about whether one player got those hits more than another.

The argument for "no" is that statistics like wRC aren't perfect; there's a dispersion[2] of 25 actual runs for teams that have the same wRC value. And different slots in the lineup matter more than others--- a better hitter in the 2-spot will help the team more than a better hitter in the 8-spot. So if you swap in an above-average player in the two spot and a below average player in the 8-spot, don't you end up with a better team?

Really, this all depends on how you define average. If you take all qualified players and sort by wOBA, and take whoever is smack in the middle... that's not actually an average player. An average player would have the statistics of what happens during an average plate appearance. That means that you take every single, double, triple, walk, etc, that happens during an MLB season, and divide by the total number of plate appearances that occurred. Thus the extra at-bats that high-slot players get are taken into the definition of "average":

• 700 plate appearances
• 141 strikeouts
• 109 singles
• 31 doubles
• 3 triples
• 18 home runs
• 54 walks
• 6 times hit by a pitch

The total runs achieved by a lineup of nine clones of this player is identical to the average runs from all lineups created from actual players. So, chalk one for the statheads.

This implies that most of the variance of team performance at fixed values of wRC can be attributed to "luck". This means that even though the number of hits+walks is the same, their distribution within each inning is different. If an average MLB team reached base 8 times per game, the fewer innings you bunch those baserunners into, the more runs you'll score. More on that in a later post.

This is not related to the shenanigans that managers engage in when constructing lineups. Although lineups shuffle around the same players, the shift in runs created is (mostly) due to the fact that a team will produce fewer baserunners when putting crappy players in the first two spots, and this will be reflected in their wRC.

[1] But really... are there any other kind of Kate Upton pictures?

[2] For those of you not familiar, "dispersion" here is the same as "standard deviation" (which is the square root of variance). It means that about 34% of teams will be up to 25 runs above what wRC predicts, and 34% will be up to 25 runs below what wRC predicts (assuming Gaussian statistics). Converting that into wins, there's over 5 wins separating teams at the high and low of one standard deviation. The remaining 32% of teams will be even farther apart. Just ask Cardinals fans this year.