# Streaking (not what you may think)

On April 22, 2013, I was invited to speak at Amity Regional HS in CT. Unlike some other trips this was a short excursion of 30 minutes from my house. I was told that I would be talking to an AP Statistics Class, other math students and teachers. I wanted to choose a statistics topic in baseball that was both interesting and understandable. The topic I chose was from Chapter 16 of my book Sandlot Stats. Chapter 16 (entitled Streaking) depends only on the basic probability theory covered in Chapter 7 of my book. Using these probability concepts, I derive a formula for predicting the odds of any player duplicating any streak. Some of the famous batting streaks in baseball include: Ted Williams’ 84-game on-base streak, Joe Sewell’s streak of appearing in 115 consecutive games without striking-out, hitting at least one home run in eight consecutive games (shared by Dale Long, Don Mattingly, and Ken Griffey Jr), Ted Williams getting on-base in 16 consecutive plate appearances, and the most famous of all streaks Joe DiMaggio’s 56-game hitting streak. What elements are needed to talk about a streak? Let’s look at Joe’s 56-game hitting streak. The event is a game, success is getting at least one hit in a game, and the length of the steak is 56 games. For Ted Williams’ streak of getting on-base in 16 consecutive plate appearances, the event is a plate appearance, success is getting on–base, and the streak length is 16. Streaks are discussed in all sports. Some examples are Drew Brees’ streak of throwing a touchdown pass in 48 straight games. In basketball, playing for Minnesota in 1993, Michael Williams connected on 97 straight from the foul line. Just this year the Miami Heat came close to tying the consecutive winning streak of 33 games.  Streaks also appear outside of sports. On a business channel, a reporter may report that for 15 consecutive days the Dow 500 was positive.

The numbers 714, 755, and 762 are instantly recognizable to many Americans as the lifetime home run totals hit by Babe Ruth, Hank Aaron, and Barry Bonds. Point 406 or just 406 evokes the name Ted Williams, the last player to average more than four hits in every 10 at-bats over a full season. Even a rather ordinary number like 56 has baseball significance to it—for Joe DiMaggio’s 1941 hitting streak, a 71-year record that no one in the major leagues has ever come close to breaking. The best-selling book, 56: Joe DiMaggio and the Last Magic Number in Sports by Kostya Kennedy, provides a day by day account of Joe’s streak with the buildup to WW II in the background. In the history of baseball (from 1876 to today) only six men: three college players, 2 minor league players, and one ML player have hit safely in at least 56 consecutive games. Of course, Joe was the only ML player but he also had a 61-game hitting streak in the minors. The two closest ML players to Joe’s streak were Pete Rose (1978) and Willie Keeler (1897). Both had 44-game hitting streaks.

Using my probability formula , the odds of any player duplicating DiMaggio’s 56-game hitting streak can be calculated. In 1941, the odds of Joe achieving his streak were 1 in 9545. In spite of batting .406 in 1941, Williams’ odds of duplicating Joe’s streak was 1 in 50,000. The main reason why Joe was 5 times more likely is their difference in walks. In 1941, Joe had 76 walks and Ted had 147 walks. Unfortunately, every walk hurts your chances for a getting a hit. Pete Rose’s odds in 1978 were 1 in 100,000 and Willie Keeler’s odds in 1897 were 1 in 40. Keeler had an AVG of .424 in 1897; whereas Rose’s AVG in 1978 was .302. The modern day player with the best odds was Ichiro Suzuki who in 2004 had a 1 in 274 chance of duplicating the streak. After the success of the movie 42 the time has come for a new movie called 56.