here's a letter written to Joe in 1985:
Joe Dimaggio
2150 Beach Street
San Franciso, CA 94123
January 3, 1985
Dear Joe,
My best wishes to you for a happy 1985. I hop you had a chance to see the NOVA show in which you so kindly participated. I have received so many favorable comments, with unanimous agreement that your appearance mad eth show.
I mentioned to you in San Francisco that my colleague Ed Purcell, a Nobel Laureate and one of the world’s greatest physicists, had determined that your fifty-six-game hitting streak was, statistically, the most unusual and unexpected great event in the history of baseball. Ed recently sent me the enclosed note in which he derives the reason for his statement. The mathematical details need not be perused, but the chart on the back of the second page will give you some idea of how remarkable and unpredictable your achievement was in statistical terms. The top row labeled b represents lifetime batting averages of .400, .380, and .300. The first column, labeled n at the left indicates the number of games in a hitting streak- 40, 50, and 60 in this example.
The nine numbers in the chart itself give you the probability that a batter with lifetime batting averages of b will have a hit streak of number of games n over a career of 1,000 games. Just consider the .0096 value for a .350 lifetime average, and a 50 game hitting streak. This means that a lifetime .350 batter has only nine chances in a thousand to have a 50 game hitting streak in a career of 1,000 games. To make it more likely than unlikely that such a hitting streak would exist, the number in the chart must be great than .5- for a probability of greater than one-half.
Thus, there would have to be fifty-two lifetime .350 hitters in order to make the probability of a 50 game hitting streak more than likely (.0086 times 52 equal the crucial value of one-half). I don’t have my encyclopedia handy, but I think that only 3 people actually have lifetime averages exceeding .350 (Cobb, Hornsby, and perhaps Joe Jackson). But your streak went for 56 games, a value that would only become more likely to happen (than not to happen) if baseball included more than 100 lifetime .350 hitters.
You asked me jokingly if this analysis meant that your record would never be broken. Even us pompous academics wouldn’t dare to make a statement like that. But Ed Purcell’s analysis does suggest that of all baseball records, your hit streak is surely the one least likely to ever be broken.
Thanks again for you time and, especially, for your kindness to my son Ethan.
Sincerely,
Steven Jay Gould
Gould (2003), Triumph and Tragedy in Mudville (188-189).
Dimaggio struck out 13 times in 541 AB's that year, yet hit 30 homeruns in the worst park in baseball for right handed hitters (489 feet deep fence)
Joe Dimaggio
2150 Beach Street
San Franciso, CA 94123
January 3, 1985
Dear Joe,
My best wishes to you for a happy 1985. I hop you had a chance to see the NOVA show in which you so kindly participated. I have received so many favorable comments, with unanimous agreement that your appearance mad eth show.
I mentioned to you in San Francisco that my colleague Ed Purcell, a Nobel Laureate and one of the world’s greatest physicists, had determined that your fifty-six-game hitting streak was, statistically, the most unusual and unexpected great event in the history of baseball. Ed recently sent me the enclosed note in which he derives the reason for his statement. The mathematical details need not be perused, but the chart on the back of the second page will give you some idea of how remarkable and unpredictable your achievement was in statistical terms. The top row labeled b represents lifetime batting averages of .400, .380, and .300. The first column, labeled n at the left indicates the number of games in a hitting streak- 40, 50, and 60 in this example.
The nine numbers in the chart itself give you the probability that a batter with lifetime batting averages of b will have a hit streak of number of games n over a career of 1,000 games. Just consider the .0096 value for a .350 lifetime average, and a 50 game hitting streak. This means that a lifetime .350 batter has only nine chances in a thousand to have a 50 game hitting streak in a career of 1,000 games. To make it more likely than unlikely that such a hitting streak would exist, the number in the chart must be great than .5- for a probability of greater than one-half.
Thus, there would have to be fifty-two lifetime .350 hitters in order to make the probability of a 50 game hitting streak more than likely (.0086 times 52 equal the crucial value of one-half). I don’t have my encyclopedia handy, but I think that only 3 people actually have lifetime averages exceeding .350 (Cobb, Hornsby, and perhaps Joe Jackson). But your streak went for 56 games, a value that would only become more likely to happen (than not to happen) if baseball included more than 100 lifetime .350 hitters.
You asked me jokingly if this analysis meant that your record would never be broken. Even us pompous academics wouldn’t dare to make a statement like that. But Ed Purcell’s analysis does suggest that of all baseball records, your hit streak is surely the one least likely to ever be broken.
Thanks again for you time and, especially, for your kindness to my son Ethan.
Sincerely,
Steven Jay Gould
Gould (2003), Triumph and Tragedy in Mudville (188-189).
Dimaggio struck out 13 times in 541 AB's that year, yet hit 30 homeruns in the worst park in baseball for right handed hitters (489 feet deep fence)
