数学英语 15 What Are Averages?

by Jason Marshall

In the last few articles, we’ve talked about decimals and how they’re related to fractions through the process of division. Now, it’s time to turn our attention to some practical applications of these tools. Up first today we’re talking about statistical 1 averages—in particular: batting averages.

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Who is the Best Hitter in Baseball?

Who is the best hitter in baseball? Or, if you’re not a baseball fan, feel free to replace this question with an analogous 2 one from the sport of your choosing. Those of you who are baseball fans probably have a favorite player. And, for many of you, this favorite player is probably also the person you claim to be the best hitter. If that’s the case, it’s also pretty likely that your opinion has been swayed by your passion. Now, there’s certainly nothing wrong with having a little passion and an opinion, but it sure would be nice if we could determine the best hitter in baseball in a way that isn’t biased 4 by your feelings. Well, I have good news for you: there is a way—it’s called statistics.

What is Statistics?

Statistics is the set of ideas in math that deals with collecting and analyzing 5 sets of numerical data. From analyzing poll results that tell us who is winning an election, to determining whether a person taking a lie detector 6 test is telling the truth, statistical analysis gives us a way to understand sets of observations in a consistent and unbiased way. So let’s see how we can use it to figure out which player is the best hitter in Major League Baseball.

What is a Batting Average in Baseball?

What number should we use to determine if somebody is a good hitter? How about the total number of hits they’ve had in their career? Well, a large number of career hits could be a good sign; but there’s a problem: a mediocre 7 player blessed with unusual longevity—and many at bats—could, over the course of sufficiently 8 many seasons, amass 9 a large number of hits. Clearly, it wouldn’t be fair to use total career hits to compare the skills of an average player in his tenth season to a phenomenal player in his first. We need to figure out a way to remove the bias 3 introduced by the total number of at bats a player has had. In other words, a true measure of a hitter’s skill is measured not by his total number of hits, but by the rate at which he succeeds at the plate. The number we’re looking for here is called the player’s batting average.

Now, you’ve probably heard the term “batting average” before, and you’ve also probably heard game announcers make statements like “[so and so] is batting 275 this season,” but what exactly does that statement mean? Well, there’s a big clue in how batting averages appear in print—namely, the above average would not be written “275”, but would instead be written “.275”. You’ll recognize that .275 is a decimal number, which may also be thought of as a percentage. And that’s the interpretation 10: batting averages in baseball represent the percentage likelihood, also known as the probability, that a batter 11 will succeed in getting a hit. So, a .275 batting average means that a batter hits safely 27.5% of the time—which might not sound too great, but actually isn’t bad in baseball.

How to Calculate Batting Averages

But we’re missing one very important piece of the puzzle: How are batting averages actually calculated? Well, as we discovered earlier, to compare the skills of two players, we need to take into account the total number of at bats they’ve each had to accrue 12 their hits. That is, the number we’re interested in isn’t the total number of career hits, but is instead the total number of hits divided by the total number of at bats. For example, if a player has 275 career hits in 1000 at bats, his batting average is the fraction 275/1000—275 hits per 1000 at bats. That fraction has an equivalent decimal representation of .275—which is what we call “batting 275.” So, if two players have the same number of career hits, but one of them has batted half as many times, that player’s batting average will be twice as big—and it’ll be obvious that that player is a much better hitter.

Why is Statistics Useful?

So, let’s return to our original question: Who is the best hitter in baseball? Well, there are several factors to consider (for example: are you more interested in home runs or overall hits?), but you could make a pretty good argument that the best hitter is the player with the highest batting average. After all, that’s the player who, on average, has the highest number of hits per 1000 at bats. And that is the beauty of statistics—it gives consistent and unbiased answers. It doesn’t matter who you think the best hitter is; you can use statistics to calculate the answer.

Wrap Up

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Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!