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Streaks, slumps and the Law of Averages

Recommended reading for Sportscasters
Copyright Iain Fyffe, 2002

 Please visit Puckerings for more hockey stuff by me

 

There is nothing sportscasters like to talk about more than streaks, slumps and the law of averages.  And, as they are wont to do, many sportscasters demonstrate their ignorance of all things statistical when they do so.  The purpose of this article is to demonstrate why you should ignore any mention of streaks, slumps, and the law of averages.

Streaks and slumps are related.  A player who does a good thing a lot over some period of time is said to be on a streak (or is "hot"), while a player who does something bad over a period of time is in a slump (or is "cold").  These concepts are very popular in the sports media. Unfortunately, they are of little meaning and of less use.

What does a streak tell you?  In hockey, for instance, scoring streaks are often mentioned. Why is it important to know that Player X has five goals in his last four games?  While it is true that the best predictor of future performance is past performance, any streak mentioned is of such a short time period as to be of no predictive use whatsoever.  That is the main problem with streaks and slumps; you can select any period of x number of games to examine.  Streaks and slumps are merely the result of choosing your endpoints carefully.

For example, let's compare two players, over a period of 10 games.  Player A scores a goal every second game, for a total of five goals.  Player B goes scoreless for the first three games, then scores a single goal in each of the next four games, then goes scoreless for the final three games, for a total of four goals.  Player A scored five goals compared to Player B's four, but you can bet someone in the media will mention Player B's "four-game scoring streak" at some point.  Attention is directed to where it should not be.

Really, the only appropriate time period to examine is the full season.  This is the basic unit of sports. A team's record over the entire season is used to determine if it makes the playoffs (though sportscasters like to stress the importance of winning games late in the season).  Thus, we should use a player's full season when evaluating him.  It is a fact that all players will go through a series of "streaks" and "slumps" during a season, on his way to his final level of production.  Breaking down performances into arbitrary sets of games has no value.

Streaks and slumps are also very subjective in their definition; that is, there is no actual definition.  The judgment on whether a player is on a streak or in a slump depends on the perceived quality of that player.  The subjectivity of streaks and slumps is best demonstrated when one is "broken".  For instance, say a player has gone 20 games without scoring a goal, and this is considered a slump for that player. The media will surely mention his "20-game scoreless drought" or some such thing.  In his next game, the player scores a goal, and it will be mentioned that he has "broken out" of his slump.  This is supposed to mean he is no longer in a slump.  But if you look at it, he has still only scored one goal in his last 21 games, which would also be considered a slump.  He has broken out of a slump, yet he is still in a slump.  This is arbitrary and silly.

Streaks also do not necessarily indicate the quality or caliber of the player.  For instance, say we have two players.  Player A has had a 10-game goal-scoring streak.  Player B never has; his career best is five games.  Is player A a better player, or even a better goal-scorer? We cannot say.  Streaks are useless in this sense as well, since we have other stats that reflect the quality of a player much better.  For instance, a player's total goals is a much better indicator of his goal-scoring ability than his best goal-scoring streak.

The "law of averages" is often invoked when a player breaks out of a slump, particularly by baseball announcers.  Strangely, it is never mentioned when a player "breaks out"(?) of a streak.  There are two major problems with the law of averages.  First, it does not exist. What sportscasters think they're talking about is called the Law of Large Numbers.  Second, they use this law when it does not apply.  It has absolutely no application in sports.

The Law of Large Numbers states that if you know the final average of a large sequence of numbers, and the average after a large number of observations is either above (or below) the final average, then each subsequent observation is more likely to be below (or above) the final average.  If you think about it, this makes sense.  Say you have a series of a million numbers, and you know the average of these numbers is 10.  If, after 800,000 observations, the average is 9.5, then each subsequent observation is more likely to be above 10.  Note that this has no use whatsoever in the world of sports statistics.

First of all, even though a "large number" in this sense has no absolute definition, rest assured it will never be reached in a single season of sports statistics.  Secondly, and most importantly, we never know the final result of numbers in sports statistics until they are final.  We couldn't use the Law of Large Numbers with a player hitting .250 in baseball, because we don't know what his final average will be.

In summary, when a sportscaster speaks about a statistical matter, it's usually safe to assume he doesn't know what he's talking about.  Then, examine his statement to determine if it's valid; don’t be surprised when it isn’t. There are many popular misconceptions about statistics in sports; streaks and slumps and the law of averages are all good examples.  Beware these misconceptions, and don't be led into believing they have any validity at all.

Please visit Puckerings for more hockey stuff by me

 

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