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March 13, 2010

Between The Numbers

The Rounded Slash Line

by Eric Seidman

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Chris Coghlan of the Florida Marlins burst onto the scene last year and put together a fantastic rookie season with the bat, compiling a .321/.390/.460 slash line in 504 PA en route to the NL Rookie of the Year award. Take a closer look at that slash-line, as Coghlan came within one-thousandth of a batting average point of finishing the year with a perfectly rounded slash line. There are no awards to commemorate such an achievement, but, c'mon, you know it would have been fun if he ended the season hitting .320/.390/.460. His numbers got me thinking -- how often does a rounded slash line occur? And, of the players in this hypothetical sample, have any achieved their "feat" in a significant number of trips to the dish?

Querying from 1974-2009, I found 1,227 batter-seasons with a rounded slash line, a sample accounting for approximately four percent of all seasons in the span. Not all 1,227 lines were created equally, however, as a pretty penny of the seasons belonged to players who hit, say, 1.000/1.000/2.000 in one plate appearance. Paring the list down to those who actually, you know, played the game, only 21 players rounded their lines while amassing 100 or more plate appearances. Of this group:

  • Only 15 had 250+ PA
  • Only 11 had 400+ PA
  • Only 8 had 500+ PA
  • Only 4 had 600+ PA
  • Only 1 had 700+ PA

That one? Well, that would be none other than the Centaur himself, Alex Rodriguez, who hit .310/.360/.560 in 748 plate appearances back in 1998. His compadres with 600+ PA:

And that's it -- nobody aside from these four has finished a season with a rounded slash line while playing all year. But, as you'll notice, their TAv's weren't rounded, and that darn A-Rod finished at .302 in 1998 as well. That being said, has anyone ever achieved a quadruple-round, with BA/OBP/SLG and TAv rounded? Well, yes and no. Players have technically accomplished this but not in any meaningful number of plate appearances. Of the 103 to produce a quadruple-round, only two players did so in 100+ PA:

Coghlan finished with a .299 TAv, meaning that he was one-thousandth of a point from becoming just the 9th player in the last 40 or so years to have a rounded slash line and another thousandth of a point away from having the most PAs for any quadruple-round player. He won the Rookie of the Year but he has to be disappointed about this.

Eric Seidman is an author of Baseball Prospectus. 
Click here to see Eric's other articles. You can contact Eric by clicking here

Related Content:  Quadruple-A Player

12 comments have been left for this article. (Click to hide comments)

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I would expect it would be ~1 in 1000 players with a triple rounded slash score (10% x 10% x 10%). What were the number of player seasons in each cohort?

Mar 13, 2010 17:43 PM
rating: 3

That was pretty much my thought upon reading the question. There are 14331 player seasons with > 100 PA over 1974-2009. So the naive assumption would be 14 such seasons. 21 is certainly in the ballpark for that, and you could even speculate that final day efforts to reach/maintain BA thresholds like .300 would be a influence increasing their share.

Mar 13, 2010 19:02 PM
rating: 0
Brock Dahlke

Yes, he must be just devastated....;)

Mar 13, 2010 17:43 PM
rating: 0
Benjamin Harris

I haven't looked at it at all, but I'm wondering if it may actually obey Benford's law.

Mar 13, 2010 21:46 PM
rating: 0
BP staff member Eric Seidman
BP staff

Well, I've got ACL, so I can see what pops up!

Mar 14, 2010 06:58 AM

I don't see how having your anterior cruciate ligament will help in this matter. :-P

Mar 15, 2010 07:42 AM
rating: 1

Fun...and dumb. But mostly fun.

Mar 14, 2010 20:32 PM
rating: 2

Uhm, it's 1 in 1000 lol... clearly... regardless of what history has shown, the results are irrelavent, it's 1 in 1000.

Mar 14, 2010 20:52 PM
rating: 0

No, there's no reason to expect 1/1000 odds. The rounded third digit of ratios of random three-digit whole numbers are almost certainly not randomly distributed.

For example, I can do this exercise.

- Suppose that the number of ABs is a uniform distribution bound by 100 and 650.
- Suppose that batting averages are distributed normally with a mean of .270 and a variance of 0.20.
- Using the above distribution, generate an integer number of hits H. Then the third digit in the ratio H/AB has the following distribution (10 million Monte Carlo realizations):

0: 10.3%
1: 9.0%
2: 9.0%
3: 9.3%
4: 9.0%
5: 9.1%
6: 9.1%
7: 9.1%
8: 9.2%
9: 9.0%

(I checked my random number generator. It returns 10.0 % for each possible value of the first digit of a uniform distribution between 0 an 1.)

(But the whole discussion is kind of moot, as the third digit in a ratio stat for an individual's single-season baseball performance means absolutely nothing, as the result of a single plate appearance in a full season affects the rate stat by more than 0.1%.)

Mar 15, 2010 20:38 PM
rating: 0

Sorry, errors to the numbers above. (I entered the variance of the average as 0.20, instead of 0.020.)

The actual distribution is:
0: 10.1%
1: 9.9%
2: 10.0%
3: 9.9%
4: 10.0%
5: 9.9%
6: 10.0%
7: 10.0%
8: 10.1%
9: 9.9%

The 0.1% is statistically significant. However, I think the real effect is that denominators in AVG and SLG coincide, i.e., If you have a number of ABs that results in an average with a 0 in the 3rd digit, then you are much more likelier than 10% to also have a 0 in the 3rd digit in the slugging percentage.

Mar 15, 2010 20:50 PM
rating: 0

Updating, the odds of getting a AVG and SLG both with a 0 in the third digit appears to be in the neighborhood of 1.2%, not 1.0%.

Mar 15, 2010 21:05 PM
rating: 0

Well, it may SEEM like its 1 in 1000, but isn't it also true that certain denominators are more likely to result in a percentage ending in 0 than others. (I'm thinking of 0,5,2 in that order)

Mar 15, 2010 04:35 AM
rating: 0
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