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The Marlins and their Hitting Streak: What are the Odds?


              Before anyone gets too worked up over this 14-game streak by the Marlins of 10 or more hits, let's remember that the last team to do it -- the 1937 St. Louis Browns -- finished with the worst record in the majors that season: 46-108. You're correct to assume that those Browns couldn't pitch.

              Still, it's incredible that the Marlins are the first team in 72 years to put together a streak like the one they're riding now. It's so incredible that I asked a couple of college statistics professors who have an interest in baseball to calculate the odds of it even happening. In fairness to them, producing an answer is not as easy as plugging a few numbers into a formula.

              As James J. Cochran, a professor at Louisiana Tech University told me this morning when I provided him with the details: "It's a really messy and interesting problem." There are all sort of variables that have to be taken into consideration.

             With that in mind, here's the e-mail response I received from Jim Albert, a statistics professor at Bowling Green State University and co-author of the book Curve Ball: Baseball, Statistics and the Role of Chance in the Game. (By the way, I mentioned in my request that Marlins pitcher Burke Badenhop is a Bowling Green alum).

             Hi Clark:

            Here are some calculations which will help answer your question.

            I collected the game hit numbers for a week of games in August to how
common 10 hits was.  For these 51 National League games, the average
number of hits was 9.35 and the proportion of games where a team got
10+ hits was 0.47.  So the chance of getting 10 hits is just about
like getting heads on a flip of a fair coin.

          A naive computation would say -- since the Marlins have a 47% chance
of getting 10+ in a single game, then the chance of getting 10+ in 14
consecutive games is

         (.47)^14 = 0.00003 (pretty small)

         But this is not really right, since there are many baseball teams and
there is a long season and it is much more likely that SOME  team in
the majors will have a streak this long this season.  The number
.00003 is understating the probability by a lot.

        I did a simulation where I assume that each team is "average".  I
simulated the hits for all games for all 30 teams and recorded the
longest team streak (where long is 10 or more hits) that one sees for
some team in the season.

      What I found is the chance of finding a team hitting streak this long
by some team this season is about 0.03 or 3%.

      So the Marlins' hitting streak is unusual, but not that unusual.

      I actually am more impressed with the fact that Burke Badenhop
graduated from BGSU.

      Jim Albert

      "Unusual, but not that unusual?" I decided to call Albert directly for clarification. After some discussion, he reached the conclusion that a 14-game hitting streak of 10 or more hits is so freaky that it almost falls under the category of a purely random event, one that defies statistical definition.

      "Since it hasn't happened for so many years, it's certainly an unusual event," Albert said. "But what is the chance that some team somewhere will have a streak that long? Since it hasn't happened for so many years, it's hard to put forth a reasonable statistical model."

       Cochran agreed.

       "It's awfully complicated because it's a compound problem," he said.

       But Cochran took it upon himself to dig into some of the numbers, and what he came up with was this:

       "The 1937 St. Louis Browns hit .285 as a team while the 2009 Marlins are hitting .267," Cochran said. "So what the Marlins have done is much more impressive that what the Browns accomplished."

       The same goes for the 1929 New York Giants, the last previous NL team to put together a streak like the Marlins'. Those Giants hit .296 as a team.

       Perhaps the best way to illustrate the Marlins' hitting streak would be to use Albert's estimate that teams collect 10 or more hits in a game close to 50 percent of the time. If that's true, then a flipped coin would have to come up heads 14 straight times to approximate what the Marlins have accomplished.

      

 

   

Comments

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jason s

with some small simplifying assumptions, we can make a direct calculation.
ok, here goes some math. (skip to the bottom for the result.)
first we have to figure out the probability of a team getting 10+ hits in one game. using the team avg of .267, i figured out the probability of getting 0,1,2...,9 hits, then subtracted from 1. ( for example, the probability of getting 1 hit is .267*(1-.267)^27*C(28,1) i assumed they always have 27 outs, and ignored DP, CS, etc.) that probability works out to .3785 Thus the probability of a 14-game streak is .3785^14, or .0000012 Then we have to figure out the probability that this occurs anytime during the season, for any team. there are 149 different games in which the streak could start, and 30 teams. so the probability any team has such a streak in one season is .0000012*30*149, or .0055. thus, you would expect such a streak once every 180 seasons.
but wait! it turns out that this calculation is very sensitive to the batting average. for a batting average of .270, you expect one such streak every 88 seasons. and for a batting average of .275, you expect such a streak once every 29 seasons.
so when you consider the batting averages of the 1930s, its no surprise that was last time a streak like this occurred.

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