Baseball Season started this week. I want to point out that Baseball violates mathematics in two ways.
1) By the rules of the game Home Plate is a right triangle with a square adjacent to it. And what are the dimensions of this right triangle? They are 12-12-17. BUT THERE CANNOT BE A 12-12-17 RIGHT TRIANGLE!!!!
2) (Information in this point is from Bill James Article The Targeting Phenomenon.) A players batting average is what percent of the time he or she gets a hit (its a bit more complicated since some things don't count as at-bats: walks, sacrifices, hit-by-ball, maybe others). You might think that the higher the number the less players achieve that batting average. Let N(a) be the Number of players with batting average a over all of baseball history. You might think
N(296) ≥ N(297) ≥ N(298) ≥ N(299) ≥ N(300)But you would be wrong.
This would seem to violate the very laws of mathematics! Or of baseball! Or of baseball mathematics! Actually there is an explanation. Batting 300 has become a standard that players try to achieve. If you are batting 300 and it is the last week of the season you may become very selective on what balls you hit, you may ask to sit out a game, you will do whatever you can to maintain that 300. Similarly, if you are batting 296-299 then you will do whatever it takes to get up to 300.
This happens with number-of-hits (with 200 as the magic number), Runs-batted-in (with 80,90, and 100 as magic numbers), for pitchers number-of-strikeouts (with 200 and 300 as magic numbers), and wins (with 20 as the magic number).
If we all had 6 fingers on our hands instead of 5 then there would be different magic numbers.
So what to do with this information? Model it and get a paper out. Hope to see it at next years STOC.