Minimum at bats for specific batting average

I got to wondering what would be the minimum number of at bats needed to have a specific batting average in baseball. For this purpose, consider batting average to be hits divided by at bats and rounded to 3 places. For example, a .271 average would be anything greater than or equal to .2705 but less than .2715. So what I would like to know is how many times would a player have to bat before it would be possible for him to have a .271 average. I need a general formula to calculate this minumum for any batting average. Something I could use in Excel would be a bonus. Thanks for any help.

Note: I have been able to get some answers to this problem using historical baseball statistics. As an example, since 1901, there have been over 200 instances of a player hitting .228. Seventeen of those had exactly 57 at bats, but none had fewer. So 57 appears to be the fewest at bats one can have to get a .228 batting average. Some others: .237 is 38 AB, .215 is 65 AB. This method is tedious and doesn't guarantee accuracy.

Ken

I discussed this a while ago here. We did not derive a general formula, but it might be possible to get one. It is certainly possible to calculate those values with a macro (and implement this macro as function in excel). Brute force, if you do not find anything better.

As alternative, you can generate a lookup table for all 1001 possible batting averages once.

Thanks for the quick reply and link to the interesting discussion. On May 23rd, Boesch achieved his .249 BA at 181 AB and Scutaro at 177. It looks like the minimum AB required for this average is 169. Also appreciate the suggestion to create a lookup table. At this point, I plan to continue to get these values using an excellent baseball database program called National Pastime Almanac. I've already got all of them from .137 to .152 and from .199 to .251.

Ken

This should do the job. Each line is "batavg,requiredbats", generated with 10 lines of code and brute force.

Thank you! I created an Excel file to calculate these (also using brute force), but it does only one at a time, and I had quite a ways to go. I appreciate you doing this.