A look at Batting orders

There is one Blog I read on sports statistics religiously and the is Phil Birnbaum's Sabermetric Research. It is a great read, and he looks at many aspects of lots of different sports as opposed to just baseball. If you have not looked at his stuff before check it out.

One of his recent postings dealt with a paper written by Nobuyoshi Hirostu who looked at if using expected runs was always the best way to determine the batting order or could a lineup with a lower expected runs produce more wins because of lower volatility. Nobuyoshi used a cut down version of the game to calculate the expected runs and ran a MC calculation to determine the winners of each potential matchup. For this experiment he used the 2007 season.

Out of the 600,000 potential matchup guess how many instances he found where the lineup with the lower expected runs won more than 50% of the games? 13! I was surprised there were not many more than that. I expected there would be a fair number of lineups of high batting average singles hitters that might have a lower expected number of runs but wins against a lineup of power hitters who score more runs on average but have great volatility due to lower batting averages.

Based on Nobuyoshi's approach to this problem I think the results are surprising, but correct. However, I can see some potential problems with how he constructed his model for analysis. First, by building a cut down model for expected runs he may have reduced the volatility of the various lineups and made the winning potential for a lower expected run lineup less likely. Second, the lineups were based on the player makeup of the various teams. For whatever reason, ( in baseball I usually assume tradition) most MLB have a lineup consisting of Power Hitters and Reliable Hitters. I think a very interesting question to ask is if this type of lineup is optimal. What type of lineup gets the highest expected wins, and does it do it with highest expected runs or some balance between high expected runs and lower volatility?