A first baseman is fortunate enough for his team to be playing in the World Series. When game one is about to start, he asks the coach if he's going to play. The coach responds "despite the fact that you have a higher batting average than our rookie first baseman, we're up against a left handed pitcher today, and he has a better average against lefties than you, so I'm going to play him". Well, the fellow figures that this is fair enough, baseball being a game of averages and all, and happily sits out the first game, knowing that the team will come up against a right hander at some point, giving him a chance to play.

Sure enough, game 2 is set to start, and the opponents are starting a right handed pitcher. The fellow asks the coach if hes going to play today. The coach responds "well, I know that you have a better average overall, but today we're facing a rightie, and our rookie has a better average against righties than you do, so we're going to play him today".

So, the regular player, who has a better average against pitchers in general, has a lower average against BOTH left and right handers????? The player feels cheated. How did this happen?

For reference, the players batting average is calculated using the following formula:
average = safe hits/at bats, and is recorded to three decimal places (though announcers generally multiply this fraction by 1000 to give a integer value). A good players average will be between .300 and .350, with higher averages possible, but rare. For example a player gets 20 safe hits in 80 "at bats" then his average is .250

lets say the rookie, who doesnt get to play much, has batted 2 for 8 against lefties, but 0 for 1 against righties. This gives him a .250 lefty avg, a .000 rightie avg, and a .222 overall avg.

Now lets say the regular first baseman is 40 for 200 against lefties, but 150 for 400 against righties. this gives him a .200 avg against lefties, a .375 avg against lefties, and .317 avg overall.

So, in game one, the opposing team brings in a rightie reliever, and the rookie gets one at bat against him, which is a hit. Now his rightie avg is .500, which is better than the regular starting first baseman. That is how the situation could come about.

Bye the way, the Minnesota Twins are goin all the way this year.

Posted by ethan on 2003-05-19 17:13:06