Hitting Streaks Dont Obey Your Rules: Evidence That Hitting Streaks Arent Just By-Products of Random Variations

📝 Abstract

There have been more hitting streaks in Major League Baseball than we would expect. All batting lines of MLB hitters from 1957-2006 were randomly permuted 10,000 times and the number of hitting streaks of each length from 2 to 100 was measured. The average count of each length streak was then compared to the corresponding total from real-life, when the games were in chronological order. The number of streaks in real-life was significantly higher than over the random permutations. Non-starts (such as pinch-hitting appearances) were removed since these may be unduly reducing the number of streaks in the permutations; the number of streaks in the permutations increased but was still significantly lower than real-life totals. Possible explanations are given for why more streaks have appeared in real-life than we would expect, including possibly the hot hand idea. Contact at trentm@email.unc.edu

💡 Analysis

There have been more hitting streaks in Major League Baseball than we would expect. All batting lines of MLB hitters from 1957-2006 were randomly permuted 10,000 times and the number of hitting streaks of each length from 2 to 100 was measured. The average count of each length streak was then compared to the corresponding total from real-life, when the games were in chronological order. The number of streaks in real-life was significantly higher than over the random permutations. Non-starts (such as pinch-hitting appearances) were removed since these may be unduly reducing the number of streaks in the permutations; the number of streaks in the permutations increased but was still significantly lower than real-life totals. Possible explanations are given for why more streaks have appeared in real-life than we would expect, including possibly the hot hand idea. Contact at trentm@email.unc.edu

📄 Content

Hitting Streaks Don’t Obey Your Rules Evidence That hitting Streaks Aren’t Just By-products of Random Variations Trent McCotter, UNC Chapel Hill, Jan 2009, contact: trentm@email.unc.edu . Professional athletes naturally experience hot and cold streaks. However, there’s been a debate going on for some time now as to whether professional athletes experience streaks more frequently than we would expect given the players’ season statistics. This is also known as having “the hot hand.” For example, if a player is a 75 percent free-throw shooter this season and he’s made his last 10 free throws in a row, does he still have just a 75 percent chance of making the 11thfree throw? The answer from most statisticians would be a resounding Yes, but many casual observers believe that the player is more likely to make the 11th attempt because he’s been “hot” lately and that his success should continue at a higher rate than expected. Two common explanations for why a player may be “hot” are that his confidence is boosted by his recent success or that his muscle memory is better than usual, producing more consistency in his shot or swing. As it relates to baseball The question is this: Does a player’s performance in one game (a ‘”trial,” if you will) have any predictive power for how he will do in the next game (the next trial)? If a baseball player usually has a 75 percent chance of getting at least one base hit in any given game and he’s gotten a hit in 10 straight games, does he still have a 75 percent chance of getting a hit in the 11th game? This is essentially asking, “Are batters’ games independent from one another?” As with the free-throw example, most statisticians will say that the batter in fact does still have a 75 percent of getting a hit in the next game, regardless of what he did in the last 10. In fact, this assumption has been the basis for several Baseball Research Journal articles in which the authors have attempted to calculate the probabilities of long hitting streaks, usually Joe DiMaggio’s major-league record 56-game streak in 1941. It was this assumption about independence that I wanted to test, especially in those rare cases where a player has a long hitting streak (20 consecutive games or more). These are the cases where the players are usually aware that they’ve got a long streak going. If it’s true that batters who are in the midst of a long hitting streak will tend to be more likely to continue the streak than they normally would (they’re on a “hot streak”), then we would expect more 20-game hitting streaks to have actually happened than we would theoretically expect to have happened. That is, if players realize they’ve got a long streak going, they may change their behavior (maybe by taking fewer walks or going for more singles as opposed to doubles) to try to extend their streaks; or maybe they really are in an abnormal ‘hot streak.’ But how do we determine what the theoretical number of twenty-game hitting streaks should be? In the standard method, we start by figuring out the odds of a batter going hitless in a particular game, and then we subtract that value from 1; that will yield a player’s theoretical probability of getting at least one hit in any given game: 1-((1-(AVG))^(AB/G)) For a fabricated player named John Dice who hit .300 in 100 games with 400 at-bats, this number would be: 1-((1-(.300))^(400/100)) = .7599 = 76 percent chance of at least one hit in any given game With the help of RetroSheet’s Tom Ruane, I did a study over the 1957–2006 seasons to see how well that formula can predict the number of games in which a player will get a base hit. For example, in the scenario above, we would expect John Dice to get a hit in about 76 of his games; it turns out the formula above is indeed very accurate at predicting a player’s number of games with at least one hit. Thus, if games really are independent from one another and don’t have predictive power when it comes to long hitting streaks, this means that John Dice’s 100-game season can be seen as a series of 100 tosses of a weighted coin that will come up heads 76 percent of the time; long streaks of heads will represent long streaks of getting a hit in each game. This method for calculating the odds of hitting streaks was used by Michael Freiman in his article “56-Game Hitting Streaks Revisited” in BRJ 31 (2002), and it was also used by the authors of a 2008 op-ed piece in the New York Times: Think of baseball players’ performances at bat as being like coin tosses. Hitting streaks are like runs of many heads in a row. Suppose a hypothetical player named Joe Coin had a 50–50 chance of getting at least one hit per game, and suppose that he played 154 games during the 1941 season. We could learn something about Coin’s chances of having a 56-game hitting streak in 1941 by flipping a real coin 154 times, recording the series of heads and tails, and observing what his longest streak of heads happened to be. Our simulations did something ver

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