In Chapter 16 of my book, “Sandlot Stats: Learning Statistics with Baseball,” I developed a new formula which uses a player’s seasonal batting statistics to assign a probability of that player duplicating any batting streak. Then I apply my formula to calculate which players had the highest probabilities of duplicating special batting streaks. Of course, the most talked about batting streak is DiMaggio’s 56-game hitting streak. Another interesting streak belongs to Ted Williams when in 1949 he reached base successfully in 84 straight games. Which streak was harder to achieve? My formula assigned DiMaggio a probability of .0001 (1/10,000) and assigned Williams a probability of .0935 (935/10,000) of achieving their respective streaks. This says that, using their batting statistics for 1941 and 1949, for every 10,000 seasons DiMaggio would duplicate his streak one time while Williams in 10,000 seasons would duplicate his streak 935 times. Clearly, DiMaggio’s streak was the harder to achieve.

I also applied my formula to many other batting streaks such as the most consecutive games with at least one home run, the most consecutive games without striking out and many other streaks. If you are interested in seeing the mathematics I used to develop my formula and the players who actually own these records, please read Chapter 16—titled ‘Streaking’— in my book.

Below are the players with the longest hitting streaks in both the Major and Minor Leagues. Observe that Joe is the only player that appears on both lists.

In a recent article Sara Lang looked at the streak by the numbers:

**.408:** DiMaggio hit .408 (91-for-223) during the streak with 15 home runs and 55 RBIs.

**.375:** He entered May 15 (the first game of the streak) with a .306 batting average. That rose to .375 after the July 16 game, the final game of the streak.

**4:** DiMaggio faced four future Hall of Fame pitchers: Lefty Grove, Hal Newhouser, Bob Feller and Ted Lyons.

**10:** DiMaggio extended the streak in his final plate appearance 10 times, as Elias research notes.

**16:**DiMaggio started a 16-game hitting streak the game after the 56-game one ended. So he hit in 72 of 73 games total. In those 73 games, he had 120 hits, 20 home runs and six strikeouts.

**44:** The longest hitting streak since DiMaggio’s is a 44-gamer by Pete Rose in 1978.

**29:** The longest hitting streak by a Yankees player since DiMaggio’s streak ended is a 29-gamer by Hall of Famer Joe Gordon in 1942. Derek Jeter’s longest hitting streak was 25 games in 2006. Don Mattingly’s longest was 24 in 1986. Those are the three longest for the Yankees since DiMaggio.

I also apply my formula to many other batting streaks such as the most consecutive games with at least one home run, the most consecutive games with at least one extra base hit, the most consecutive games with at least two or more hits, the most consecutive games without striking out and many other streaks. If you are interested in seeing the mathematics I used to develop my formula and the players who actually own these records, please read Chapter 16—titled ‘Streaking’— in my book.

A discussion of DiMaggio’s 56-game hitting streak always resurfaces whenever a player starts approaching DiMaggio’s record. The Cleveland Indians 20-year old catcher Francisco Mejia, ranked their number four prospect, playing for the High-A Lynchburg Hillcats entered August batting .344. On Aug.4, he extended his hitting to 45 games by doubling in the 9^{th} inning after going 0-4. As of this writing his hitting streak stands at 47 games. This ranks his streak as the 7^{th} longest in Minor League history.

Below are the players with the longest hitting streak in both the Major and Minor Leagues. There are many observations that can be made from these two tables. DiMaggio is the only player that appears on both lists. In fact, his 61-game streak in the Minors was longer than his 56-game streak in the Majors. Yes, Joe D. was a very special player. Except for Joe the other players listed in the Minor League Table had limited Major League success. In contrast, the Major League players listed are all Hall of Fame caliber players. What conclusions can you draw from this?

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In an article by Herm Krabbenhoft which appeared in the Baseball Research Journal, he compares DiMaggio’s 56-game hitting streak to Williams’ 84-game on-base streak. Krabbenhoft gives his answer in terms of approachability. He states, “Since DiMaggio achieved his streak in 1941, the closest any major league player has come to it was the 44-game hitting streak by Pete Rose in 1978. Forty-four is 78.6% of the way to 56. Since Williams achieved his 84-game streak in 1949, the closest any player has come to it were the 58 consecutive game on-base streak by Duke Snider in 1954 and Barry Bonds in 2003. Fifty-eight is 69% of the way to 84. So, with the above approachability considerations in mind, it can be argued that Teddy Ballgame’s 84 game on-base safely streak may be the greatest batting achievement of all.” Since Krabbenhoft’s article was published in 2004, Orlando Cabrera recorded a consecutive game on-base streak of 63 games in 2006. Sixty-three is 75% of the way to 84. This blows a hole in the approachability argument.

As a sabermetrician, I give my answer using probability theory. Which player DiMaggio or Williams, based on their statistics for that year, had the smallest probability of achieving their streak? Using the number of games played, number of plate appearances and number of successes of any player combined with the length of the streak, I created a probability formula which gives the probability of any player, based on their season’s batting statistics, duplicating any batting streak. The development of my probability formula for different batting streaks can be found in two books. In my book, *Sandlot Stats: Learning Statistics with Baseball*, published by John Hopkins Press I devote the entire Chapter 16 to comparing different batting streaks. My research on streaks was also published as Chapter 4 in the book *Mathematics and Sports*, published by the Mathematical Association of America.

Applying my probability formula to both players’ streaks, here are the results.For the year 1941, the probability of Joe DiMaggio achieving his 56-game hitting streak was 0.0001 or 0.01%. For the year 1949, the probability of Ted Williams achieving his 84-game on-base streak was 0.0944 or 9.44%. For every 10,000 seasons, we would have expected DiMaggio in 1941 to accomplish his streak once while we would have expected Williams in 1949 to accomplish his streak 944 times. Ted Williams himself said, “I believe there isn’t a record on the books that will be tougher to break than Joe DiMaggio’s 56-game hitting streak.”

Based on the probabilities calculated above, I agree with Williams that DiMaggio’s 56-game hitting streak is the more impressive.What about the probabilities associated with the 2016 streaks of Bradley and Ozuna? As for Bradley’s 29-game hitting streak his probability was 0.00281 or 0.281%.

Ozuna probability of a 36-game on-base streak was 0.0125 or 1.25%. Bradley’s streak is the more impressive one.

If you are wondering why Williams’ 84-game streak had such a high probability of occurring in 1949 the lengthy answer is in my book

]]>Below is pictured Snider, DiMaggio, Mays and Mantle walking in from centerfield on July 16,1977, at Shea Stadium on Old-Timers Day.

I have chosen facts from Carl’s book that are related to my past blog postings. I wrote a blog posting about Dale Long, the left-handed power hitting first baseman for the Pirates in the 1950s. The reason for my blog about Dale Long was his grandson, also named Dale Long, was a student in one of my biostatistics classes at Quinnipiac University. Dale Long was also featured in my book, *Sandlot Stats: Learning Statistics with Baseball*, because of his record setting 8 consecutive games with a home run. Later, this record was tied by Don Mattingly and Ken Griffey Jr. However, what I did not know was that it was Carl who gave up the 8th home run in game number 8. In writing a blog about the Dodgers and Giants moving to Los Angeles in 1957 I failed to mention that it was Carl who pitched and won the opening day game in front of 78,000 fans in LA on April 18, 1958, the first game for the Dodgers as the LA Dodgers. The Dodgers defeated the San Francisco Giants 6-5 and Carl pitched 8 innings giving up 4 earned runs.

Still in another blog posting I wrote about, “The Shot Heard Around the World,” the Bobby Thomson 1951 playoff home run that gave the NY Giants the 1951 NL pennant. The Giants won playoff game 2. In the deciding 3rd playoff game with Bobby Thomson at the plate representing the winning run in the bottom of the ninth inning, Dodger manager Charlie Dressen called the bullpen coach where Ralph Branca and Carl Erskine were both warming up. The bullpen coach said they are both ready but Erskine is bouncing his curveball. Dressen chose to bring Branca in to face Thomson. On Branca’s second pitch Thomson delivered a three-run home run to win the game and the pennant for the Giants. Whenever Carl was asked what his best pitch was he said, “The curveball I bounced in the Polo Grounds bullpen.” In his book there is a picture of Carl with Bob Feller, Sandy Koufax, and Bob Gibson. These four pitchers totaled 10 no-hitters (Koufax 4, Feller 3, Carl 2, and Gibson 1). Carl writes, “The only distinction I can claim that the other three cannot—- I’m not in the Hall of Fame.” Carl’s 1956 no-hitter was the first nationally televised no-hitter. He also set the record for most strike outs 14 in a World Series game in 1953. This record was later broken by Koufax and then by Gibson at 17.

1 Comment(s):

Marty Cobern said…
Why ISN’T Carl Erskine in the HoF? It’s a disgrace! May 30, 2016 07:57:29 |

The title of this blog comes from the book *Joe DiMaggio and the Last Magic Number in Sports *by Kostya Kennedy. His book takes the reader through each game of Joe DiMaggio’s 56-game hit streak at a time when America was preparing for war with Japan. Joe’s streak began on May 15, 1941 when he blooped a single to right field in a game against the White Sox. The streak ended two months later at Cleveland’s Municipal Stadium, in front of 67,000 cheering fans. That day Joe had 4 plate appearances. Joe walked once and hit 3 ground balls. The first ground ball was a rocket hit down the 3rd base line which was backhanded by Cleveland’s Ken Keltner throwing Joe out by a step. Joe Walked in the 4th inning. In the 7th he ripped another rocket to Keltner who threw him out again. In his final plate appearance he hit a routine grounder to the shortstop. Joe’s greatness showed when he promptly started a new hitting streak which lasted for 16 games. All told Joe produced at least one hit in 72 of his 73 games. Both his 56-game hitting streak and hitting safely in 72 out of 73 consecutive games have never been duplicated. Without Keltner’s great fielding, the consecutive game streak might have reached 73 games.

The year 1941 also marked the last time a Major League hitter batted over .400 when Ted Williams batted .406 for the season. The year 1941 witnessed two remarkable baseball feats that many baseball experts say will never happen again. The baseball writers had a tough choice for the 1941 AL MVP Award. They chose the Yankees’ DiMaggio over the Red Sox’s Williams.

In my book, *Sandlot Stats Learning Statistics with Baseball*, I devote Chapter 16 to the study of many different types of batting streaks. In that chapter I develop a new probability formula which uses a player’s actual batting statistics for a season to calculate his probability of duplicating any of these batting streaks. These calculated probabilities allows us to compare different batting streaks seeing which streak would be the hardest to duplicate.

The rivalry between DiMaggio and Williams also extended to batting streaks. Ted Williams possesses 2 amazing on-base streaks. He holds the record for getting on-base in 84 consecutive games (1949) and the record for getting on-base in 16 consecutive plate appearances (1957). To be credited with getting on-base a player must either get a hit, a walk or be hit by a pitch. Using my probability formula, I calculated the probability of Joe and Ted achieving their 3 streaks. DiMaggio had a 1 in 10,000 chance of achieving his 56-game hitting streak while Williams had a 1 in 10 chance of achieving his 84-game on-base streak and a 1 in 25 chance of achieving his 16-plate appearance on-base streak. Which streak was the hardest to achieve? From a probability point of view the answer is clear. Yes, Joe DiMaggio’s streak was the hardest to achieve. In fact, Ted Williams said, “I believe there isn’t a record on the books that will be tougher to break than Joe DiMaggio’s 56-game hitting streak.”

In Chapter 16 of my book I provide 4 lists of special baseball and softball players. The lists include the players with the longest hitting streaks in the Major Leagues, the Minor Leagues, the college baseball leagues and the college softball leagues. In the Major Leagues Pete Rose (1978) and Willie Keeler (1897) are tied for second place with 44-game hitting streaks. For the Minor Leagues, Joe Wilhoit (1919) had a 69-game hitting streak followed by would you believe Joe DiMaggio with a 61-game hitting streak in 1933 for the San Francisco Seals in the PCL.

Considering the thousands of players in the history of professional baseball, for Joe to have 2 of the 3 longest hitting streaks speaks to the greatness of Joe D.

]]>Many of my past blogs had the same theme. That theme was “Baseball follows me where ever I go.” It was three years ago when I was meeting my new biostatistics class at Quinnipiac University that baseball did follow me into my classroom. Reading from my new class list I came across the name Dale Long. The name Dale Long belonged to a Major League first baseman in 1951 and 1955-1963. Clearly, this Dale Long could not be the ballplayer I watched. When Dale Long the student raised his hand acknowledging his name I of course had to ask the question: Are you related to the Dale Long that played baseball? I am sure he was shocked that his Biostatistics Professor would have known about Dale Long the baseball player who played over 50 years ago. His answer was Dale Long was his grandfather.

Dale Long was a Major League first baseman. He was 6’ 4” and weighed 210 pounds. He played most of his years with the Pirates, Cubs, and ended his career with the Yankees. For his 10 year career he had a BA of 267 with 132 home runs and 467 RBIs. Yes, not awesome numbers.

So you might ask the question: Why did I remember Dale Long? There are two reasons. First being a Yankee fan, I watched him play in 1962 and 1963. The second reason is the connection between Dale Long and my book: Sandlot Stats: Learning Statistics with Baseball. I have a chapter in my book devoted to a mathematical formula I developed to compare various batting streaks. Using the batting statistics of a ballplayer for a given year my formula assigns a probability of that player achieving his batting streak. Of course the most famous batting streak belongs to Joe DiMaggio when in 1941 he had a 56-game hitting streak.

In 1956 Dale Long had his most productive year. In that year playing for the Pirates he batted 263 with 27 home runs and 91 RBIs. During that year he had a streak of hitting a home run in eight consecutive games which broke the previous record of 6 consecutive games held by five players including Mays and Gehrig. Later on Don Mattingly in 1987 and Ken Griffey in 1993 matched Dale Long’s streak. Using my formula the probability of Joe DiMaggio accomplishing his streak was 1 in 10,000; whereas, the probability of Dale Long’s streak was 1 in 12,500. This comparison shows Long’s streak was a rarer event than DiMaggio’s streak.

Three years ago Dale Long came to my office with a scrapbook showing how the newspapers covered his grandfather’s streak. The newspaper articles had turned yellow but the words were powerful. Dale Long provided me with interesting stories about his grandfather. These stories I wrote about in my blog dated December, 2012. That blog is archived and you can pull it up and read these fascinating stories. One story is worth repeating. According to Dale Long, when his grandfather signed with the Yankees in 1960 Casey Stengel, the Yankees manager, said to Dale you will have three jobs with us. They are you will play first base occasionally, you will pinch hit, and whenever Mickey Mantle and Whitey Ford go to the city you will go with them and keep them out of trouble. I had Dale come to my office last month. He is now graduating and plans to attend medical school. He told me his grandfather’s full name is Richard Dale Long. His father is also Richard Dale Long. However, his name is Dale Long. He told me he believes his grandfather was one of the first player’s to have an African American roommate. He roomed with Willie Mays. Another story his grandfather told was when he was playing first base Ted Williams hit a line drive at him so hard that the ball hit him on the wrist before he could turn his glove. His grandfather was a heavy smoker and died tragically of Lung Cancer in 1991 four years before his grandson was born.

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I would also like to take this opportunity to thank all of you who purchased my book, “Sandlot Stats: Learning Statistics with Baseball”, published by Johns Hopkins University Press. I thank you and have appreciated and enjoyed all of your comments. “Sandlot Stats” serves as the textbook for teaching my Baseball and Statistics course at Quinnipiac University. Since the basic mathematics needed is covered within the book, anybody can use this book as a tool for learning the important subject matter of statistics. The first 15 chapters teaches the subject matter of probability and statistics. The last three chapters apply the statistics covered in the first 15 chapters to baseball research.

My last blog talked about the probability of a current player batting .400. This is one of the topics covered in “Sandlot Stats”. For those of you not familiar with my book, the two leading characters throughout the book are Henry Aaron and Barry Bonds. The supporting characters are Ted Williams and Joe DiMaggio. You can read reviews of the book and hear interviews on my websitewww.sandlotstats.com. This website also contains a wealth of baseball history and trivia. I hope you will check it out.

For the rest of my anniversary posting, I would like to talk about the wonderful baseball people and friends whose stories gave me inspiration for many of my postings.My first thank you goes to my wife, Tara, of 45 years, the designer and programmer of my web site and publisher of all my blogs. She has also put Sandlot Stats on Facebook and Pinterest so look for it there, too. Throughout this year, I have been invited to speak at mathematics conventions in Boston and San Diego, at the West Point Military Academy, at California State University at LA and at Amity High School in CT. The talks I gave ranged from my baseball research to the teaching of statistics with baseball and the history of baseball. If you would like me to talk to your group about baseball just email me. As my friends will tell you, I love to talk. Thank you to Father Gabriel Costa for the wonderful day you provided my wife and I at West Point. I really enjoyed meeting the Cadets and speaking to them on the topic of assigning probabilities to various batting streaks, including Joe DiMaggio’s 56-game hitting streak. Thank you to Nikolai Yakovenko for coming to Quinnipiac University to speak to our faculty and students. Thank you to the former major leaguer Rico Brogna for coming to my baseball and statistics class to talk to my students about the use of sabermetrics in baseball scouting, Rico, I really enjoyed spending the entire day talking baseball and hearing your baseball stories. Then there were the many friends and casual associations which led to some of my blogs. Such a casual meeting occurred with a woman outside a store in Naples, Fl. It turned out her father’s uncle was the pitcher who was on the mound when Babe Ruth pointed to centerfield. I even learned more about Dale Long from his grandson who was one of my students this year. Thank you to my many other Quinnipiac baseball students who wrote blogs about how their lives have been affected by baseball. Finally, thank you to my friends and colleagues, whom I will not name for fear of leaving someone out, for all their support and encouragement. The blog will continue….

]]>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*.