Why is batting average calculated to three decimal places?
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M$3 Answers
I just did a bunch of research - I think the best answer is that baseball is a game that reveres statistics and tradition. When the statistic was created in the 1800's by Henry Chadwick, he termed it a "per cent" and carried it out to three decimal places. (Thus, he has probably confused thousands of people over the years between "percents" and "decimals". Damn him! ;-) )
Chadwick came to the United States from Great Britain, where he had covered cricket games. He became the father of baseball journalism, and adapted the cricket "batting average" ("per centage") to create the "batting average" for baseball. Here's a link to the "Spalding's Baseball Guide and Official League Book for 1889" (an interesting peek into baseball's past), where he (as editor) talks about and charts "the leading players of the league". He ranks them with his "Per cent of Base Hits" statistic, carried out to the thousandths place. http://www.gutenberg.org/catalog/world/readfile?fk_files=18196&pageno=26
Chadwick is also credited with developing the box score that we still see largely intact today, as well as the "Earned Run Average." And, lest we think that he only dealt with the most simplistic of ranking statistics, the Baseball Guide also shows that he came up with many of the more-specialized stats we toss around these days (on base "per centages", slugging, etc.)
Chadwick was elected to the Baseball Hall of Fame back in 1938, for his contributions to the game. http://baseballhall.org/hof/chadwick-henry
And, I must say, I think that his decision to carry it out to the thousandths remains a good one. As you suggest, mcduff, two places isn't enough and four is more than necessary to evaluate the players' comparative values.
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M$For example, if you had 157 hits for 500 at bats, you would have a batting average of .31, rounded to the nearest tenth. Now, other players could have the same batting average as you, even if they had poorer performance. For example, if you had 153 hits for 500 at bats, you would still have a .31 batting average, (.306 rounded to the nearest tenth). That means that you got 4 less hits than me, but we are statistically the same.
Now consider this problem accruing over a career. Babe Ruth had 8,399 at bats over his career, with 2,873 hits, for a career average of .342. If this were rounded to .34 instead, you could drastically change the stats and receive the same result. I could have the same career at bats with only 2,814 hits and still have a batting average of .34. That's a 59 hit difference!
So the short answer is, "Three decimal places give you higher accuracy."
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M$
Still, good answer. Is there a source out there somewhere, though?
To use your Babe Ruth example, the Babe could have hit anywhere from 2,869 hits to 2,876 hits with a .342 average in 8,399 at bats. So why not four digits to have it at .3421? I'm sort of assuming it's due to space in the newspaper; over a season that four digit is unlikely to be significant. It could have been written as 34.2 as well...
I agree, but a 7 hit difference over an entire career cannot compare to a 59 hit difference if we only used the tenths place for stats. I also think @doubleminaz did not answer your question, but you gave him the Best Answer anyways.
In Major League Baseball, it just happens that if you use just two decimal places, you won't be able to distinguish between the good and the bad batters. Too many batters will have similar "rounded off" batting percentages. If you use three decimal places, you will then be able to distinguish among the players. If you use four decimal places, then you'll be able to distinguish between them too much that it becomes impractical for most purposes; the differences between consecutive players in the rankings would be insignificant.
Three decimal places is like the optimal solution to rank the pros according to batting percentage for most purposes. Four decimal places are only used in comparing thousands or tens of thousands of players, like calculating the best batters in baseball history.
Take for example the top ten best hitters of all time:
1 Ty Cobb * 1905–1928 11434 .3664
2 Rogers Hornsby 1915–1937 8173 .3585
3 Joe Jackson 1908–1920 4981 .3558
4 Lefty O'Doul 1919–1934 3264 .3493
5 Ed Delahanty * 1888–1903 7505 .3459
6 Tris Speaker * 1907–1928 10195 .3447
7 Ted Williams * 1939–1960 7706 .3444
8 Billy Hamilton * 1888–1901 6269 .3443
9 Dan Brouthers * 1879–1904 6711 .3421
10 Babe Ruth * 1914–1935 8399 .3421
If you use just three decimal places, Williams and Hamilton would both score .344, thereby making the fourth decimal place necessary in this case.
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M$
:-)
While this gives a nice history behind baseball statistics, it does nothing to answer the question of WHY 3 decimal places is used in the statistics.
Ahhh, Brendon. I agree that it is frustrating that we don't have a definitie quote from Mr. Chadwick as to why he used 3 places. Believe me, I searched that entire 1889 Baseball Guide today.
But, the answer does explain who came up with it, where his head was at, etc. And, the sentence about baseball - and baseball fans - being loath to tinker with tradition attempts to explain why it has not changed even post-Chadwick.
And, I added that 3 seems to be the right number to best compare batting averages. In that part, I agree with your analysis. But, it seemed to me from the wording of the Q that mcduff was looking more for the history than the mathematical. And, while this seems like a natural question for a typical baseball stat fan/junkie, I was surprised that I didn't find this question has been asked (and answered) all over the internet.
If only Chadwick knew "permille"...