A baseball lineup in descending order of on-base average is superior to the traditional batting order.  

Your lead off hitter should be your best hitter.  If I could pick any player in history to lead off it would be Ted Williams.  Why?  He had the best on-base average in history.  Not only did he have a high batting average, but he walked a lot as well.  I would put the player with the second-best on-base average in the second spot.  And so on.  Almost all websites recommend batting the highest average player third and the best home run hitter fourth.  All those who advocate the traditional batting order are wrong.  I will admit that the difference between their batting orders and mine are small.

More than one billion computer simulated games were used to prove that no lineup is better than one ordered from best to worst in on-base batting average.  Over fifty years ago major league manager, Bobby Bragan, experimented with his lineup.  He lead off with his best hitter and ordered the rest of the lineup in descending batting average order.  In 1968 I read a newspaper article about a professor from MIT who showed, using a computer, that the batting descending average batting order was superior to the traditional batting order.  I wrote a computer program that simulated baseball games trying to prove the professor wrong.  Amazingly, my program indicated he was right!

Earnshaw Cook published a book, "Percentage Baseball", with the MIT press.  He taught at Johns Hopkins University, not MIT, as the newspaper article reported.  Many of his suggestions have been implemented today.  The concept that batting order should be the best hitter to the worst hitter is on that has not been implemented.

I challenge students, baseball enthusiasts and programmers to prove Professor Cook and me wrong.  The difference between Cook's lineup and the typical lineup used in the major leagues is small.  Modern managers are less likely to put their best hitters in the sixth position like the 1961 Yankees.  Cook estimated teams would win 1 to 2 extra games a season with his lineup.  I estimate current major league teams would win an extra game every 2 seasons.  Because there is likely more variation in hitting ability in amateur baseball teams Cooks lineup will be more beneficial to high school and little league teams.

The following conclusion has implications in drafting players for professional baseball or for awarding scholarships in college.  Assume use of a designated hitter. If one takes any given lineup and calculates the average probabilities for a single, double etc. and simulates play between the actual line and the lineup of averages, the average lineup will win more often.  This has salary implications.  Rather than shell out megabucks for superstars, it is better to upgrade all the positions.  The superstar may attract more fans at the ticket counter, but may not be a good investment if the goal is to win games with limited salary resources.

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