Friday, February 22, 2013

A record chase

Question:  Predicting the number of future hits

A major league player nearing the end of his career needs 200 hits to break a record.  He has promised his wife that he will retire after two more full seasons.  His production is falling but he remains a good hitter and analysts believe that the batting average in his final seasons will range from 280 to 300.  His playing time is falling because he now shares his position with younger players.  He will play in around 50% to 75% of all regular season games.  (There are 162 games in the regular season.)  Analysts believe that he will have approximately 3.1 at bats in each game that he plays.

Do you expect that this player will get the 200 hits needed to break the record?

Come back tomorrow for answer. 

Answer:  The batter needs 200 hits.  At a 0.280 batting average this requires 715 (200/0.280) at bats.  At a 0.300 batting average this requires 667 (200/0.300) at bats.  In both cases, I rounded up.   Why?

He has two more years left in his career.   If he plays in 75% of all games and has an average of 3.1 at bats he will have approximately 753 (2x162x0.75x3.1) at bats.  This is greater than the 715 at bats needed to break the record based on a 0.280 batting average.

If he only plays in 50% of all games he will have around 502 (162*0.5*3.1) at bats, not enough to get the record even if he hits 0.300.

For fun calculate the breakeven points - - the percent of games the player must play in his last two years in order to break the record – at batting average 0.280 and batting average 0.300.

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