On the Randomness, or Lack Thereof, of a Baseball Linescore

Last night, the Texas Rangers beat the Baltimore Orioles by a score of 30 to 3. In a baseball game. The last major league baseball team to score 30 or more runs in a game was the Chicago Colts, in 1897.

If you had to guess when the Rangers scored their runs over 9 innings (the game was in Baltimore, so Texas batted in the top of the 9th), how would you distribute the runs? If I had to do it, my linescore would probably look about like this:

1 2 3 4 5 6 7 8 9

4 3 1 0 5 6 3 5 3

But here is the actual linescore:

1 2 3 4 5 6 7 8 9

0 0 0 5 0 9 0 10 6

The Rangers scored 30 runs in just 4 innings! It’s a good reminder, once again, that the way data plays out in real life is often nowhere near as orderly, predictable, or consistent as you might imagine it to be. Even though runs scored per inning isn’t quite a matter of random distribution, this linescore did call to mind the common exercise of predicting coin flips. Levitt wrote about this topic a while ago: if you ask most people to predict how a sequence of 100 coin flips would come out, they would rarely have long streaks of heads or tails. Their answer, in other words, would end up just as fake as my imagined linescore above.

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COMMENTS: 104

  1. ryan says:

    Finaly something us Ranger fans can cheer about. Now when does the Maverick’s season start???

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  2. ryan says:

    Finaly something us Ranger fans can cheer about. Now when does the Maverick’s season start???

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  3. Tyler says:

    I actually would have guessed something close to the actual linescore. Baseball has a tendency to score in bursts, not in an even distribution.

    The amount of runs scored in any given inning has a lot to do with the opposing team’s pitcher, and where in the batting order each inning begins and ends.

    A particular late relief pitcher could be having a bad day and give up four or more runs before being pulled and replaced by someone else, who may or may not be a ‘better’ pitcher (or may not be fully warmed up!) As for the batting order, if your top of the order hitters are great, and your bottom-order hitters are of less quality, you’re more likely to score when your ‘good’ hitters are up immediately at the start of a new inning. Also, the weaker hitters may have an easier time batting another player around (by sac fly, etc) than getting a multi-base hit themselves.

    Looks like a lot of these (and probably other) factors lined up in the 4, 6, 8, and 9 innings. It was also a double header, so the Baltimore manager may have been trying to get every pitch out of his bullpen.

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  4. Tyler says:

    I actually would have guessed something close to the actual linescore. Baseball has a tendency to score in bursts, not in an even distribution.

    The amount of runs scored in any given inning has a lot to do with the opposing team’s pitcher, and where in the batting order each inning begins and ends.

    A particular late relief pitcher could be having a bad day and give up four or more runs before being pulled and replaced by someone else, who may or may not be a ‘better’ pitcher (or may not be fully warmed up!) As for the batting order, if your top of the order hitters are great, and your bottom-order hitters are of less quality, you’re more likely to score when your ‘good’ hitters are up immediately at the start of a new inning. Also, the weaker hitters may have an easier time batting another player around (by sac fly, etc) than getting a multi-base hit themselves.

    Looks like a lot of these (and probably other) factors lined up in the 4, 6, 8, and 9 innings. It was also a double header, so the Baltimore manager may have been trying to get every pitch out of his bullpen.

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  5. TWstroud says:

    A disappointing column. The nature of baseball encourages the clustering of runs. There are casual factors at play. Pitcher fatigue. The impact of full queues (loaded bases). Batting order. It is not the proper setting for a lesson on random numbers.

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  6. TWstroud says:

    A disappointing column. The nature of baseball encourages the clustering of runs. There are casual factors at play. Pitcher fatigue. The impact of full queues (loaded bases). Batting order. It is not the proper setting for a lesson on random numbers.

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  7. Richard Simon says:

    This is less surprising than you might think. A number of studies have shown that not only do runs most-often score in clumps (i.e. more than one run per inning) but that the winning team most-often scores more runs in one inning than its opponent scores in the whole game!

    In this case, the Rangers simply took this to the extreme.

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  8. Richard Simon says:

    This is less surprising than you might think. A number of studies have shown that not only do runs most-often score in clumps (i.e. more than one run per inning) but that the winning team most-often scores more runs in one inning than its opponent scores in the whole game!

    In this case, the Rangers simply took this to the extreme.

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