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

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Two players Minnie Minoso and Nick Altrock played games in five different decades. There is a good chance these two men have accomplished something we will never see again. Minoso died on March 1 of this year. He was the first African-American player for the White Sox when he played his first game in 1949. His nine All-Star appearances earned him the title of Mr. White Sox. In three of the five decades he only played in one season, which accounts for his low total of only 17 seasons. His last game was in 1980 when he was 54 years-old. Altrock had two decades where he only appeared in one season and one decade where he appeared in two seasons. His last game was at the age of 47 in 1924.
Jim O’Rourke and Dan Brouthers, both Hall of Fame players, played all their seasons except for one season in the 1800s. What is interesting to me is that both players only season in the 1900s was in 1904 with the NY Giants. O’Rourke played in one game that season at the age of 54 and Brouthers played in two games in that season at the age of 46. It was that 1904 season that enabled both men to join the FDC. O’Rourke was out of baseball for 11 years before 1904 and Brouthers was out of baseball for 8 years before 1904. There must be a story behind why these two men returned to baseball with the same team in 1904. The most recent additions to the FDC came in 2010 when Omar Vizquel, Ken Griffey Jr. and Jamie Moyer all joined the FDC. Of the 29 players in the FDC, Moyer is one of just six whose first year in the majors did not come in one of the final two years of a given decade. Four of those six came prior to 1910, with Nolan Ryan (1966-1993) and Moyer (1986-2012) being the only exceptions since 1910. Ted Williams is the only member of the FDC to play his entire career for one franchise. On the other hand, Mike Morgan played for the most franchises 12 (1978-2002). Can you imagine moving 12 times in 22 seasons? Sharing a locker room with so many different teammates during the steroid era, he could write a very interesting book. Here is a statistical breakdown for the 29 FDC members. Of the 29 FDC members nine are in the Hall of Fame. By position we have 11 pitchers, 6 catchers, 4 first baseman, 1 second baseman, 1 shortstop, 0 third baseman and 6 outfielders. What surprised me was in spite of the wear and tear of the catcher position the six catchers represented the second most represented position in the FDC. Omar Vizquel and Ken Griffey Jr. should both eventually make it into the Hall of Fame. Tim Raines’ voting percentages for the Hall of Fame has been rising steadily from 2008 (24%) to 2015 (55%). Tim is a borderline Hall of Famer. My All-Star team from the FDC consists of Nolan Ryan pitching, Carlton Fisk catching, Willie McCovey at 1B, Eddie Collins at 2B, Omar Vizquel at SS, no one at 3B, Ted Williams in leftfield, Ken Griffey Jr. in centerfield and Rickey Henderson in rightfield. |

In the future l will examine the only 17 active players who debuted during the 1990s, meaning they could join the FDC if they continue playing into 2020.
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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.

]]>So what feat in baseball do I think about when the Grand Slam in golf is discussed? The words grand slam in baseball refers to hitting a home run with the bases loaded. So the words home run come to mind. Adding the terms batting average and RBI to home run we are now talking about the Batting Triple Crown in baseball. A batter achieves The Batting Triple Crown when he leads either league in the three statistical categories of batting Average (BA), home runs (HR), and runs batted in (RBI) for the same season. These three categories represents a batter’s hitting skill, hitting for power, and creating runs for his team. Most recently in 2012 Miguel Cabrera earned the Batting Triple Crown, replacing Carl Yastrzemski (1967) as the last player to achieve this. Yastrzemski in 1967 actually tied with Harmon Killebrew for the league lead with 44 home runs. The Career Batting Triple Crown is accomplished when a player wins or ties for the three titles of BA, HR, and RBI but not in the same season.

Since the American League joined the National League in 1901 the list of Batting Triple Crown winners include the following 12 players: Nap Lajoie (1901), Ty Cobb (1909), Rogers Hornsby (1922, 1925), Jimmy Foxx (1933), Chuck Klein (1933), Lou Gehrig (1934), Joe Medwick (1937), Ted Williams (1942, 1947), Mickey Mantle (1956), Frank Robinson (1966), Carl Yastrzemski (1967), and Miguel Cabrera (2012). Every player on this list except Cabrera (who is not eligible) has been elected to the Baseball Hall of Fame. Unlike the Grand Slam in golf two players can win the Triple Crown for the same season. The 1933 season actually had two winners, one in each league.

In the years to come will we have our first Grand Slam winner in golf or our next Batting Triple Crown winner? Since we have never had a Grand Slam winner in golf one might vote for the Baseball Triple Crown occurring first. But there are also good arguments for the Grand Slam in golf occurring first. In golf starting with the year 1934 and ending with 2014 there could have been a maximum of 81 Grand Slam winners; whereas, in baseball from 1901 to 2014 there could have been a maximum of 114*2 =228 possible winners. This makes the 14 Batting Triple Crowns to the 0 Grand Slams less impressive. Many baseball writers believe the Batting Triple Crown is much more difficult to win today because today’s batters choose to specialize in batting average or hitting with power. The gap of 45 years between 1967 and 2012 demonstrates this. Further, it is more difficult today in baseball since each league has 15 teams instead of 8 teams. What do you think?

]]>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….

]]>My first observation about these two graphs is how similar these four statistics are between the two leagues. Concentrating on the statistic SOA from 1901 to 2013, we can make these observations. From 1910 to about 1950 the SOA hovered around .100. From the early 50s to the late 60s we see our first spike in SOA to around .170. A reduction in the height of the mound in 1968 along with a tighter strike-zone caused a drop in SOA to about .150 in the 70s. From the 80s until today the SOA has spiked sharply upward to over .210. This year the SOA could exceed .220 and be the highest for any year in the history of baseball. Because of the formula which associates AVG with both SOA and IPBA one can see as the SOA increases the gap widens between the AVG and the IPBA. Specifically looking at the two periods of time 1920-1930 and 2003-2013 (about 80 games) for the AL, we have a mean SOA of .084 for 1920 to 1930 compared to a mean SOA of .193 for 2003 to 2013.

Chapter 17 of *Sandlot Stats* is titled *Mission Impossible: Batting .400 for a Season *and the entire chapter presents what is necessary for a player today to hit .400 for a season. Since 1913, there have been nine Major League players to achieve an AVG of at least .400 for a season. Of those nine, eight occurred between the years 1920 and 1930. The only other player to achieve this feat was Ted Williams when he batted .406 in 1941. Using regression analysis, I show in this chapter that the ideal numbers for a player to hit .400 are an SOA < .066 and an IPBA > .427. The nine players who batted .400 had a mean SOA of .065 and a mean IPBA of .428. To illustrate what a .066 SOA means let us assume a player has 600 at-bats. For his SOA to be less than .066 he would have to strike-out less than 40 times (never happens today).

Is it plausible for a player today to have a .427 IPBA and a .066 SOA? Well, in 2012, the highest IPBA was Trout’s .433 (SOA = .249) and the lowest SOA was Scutaro’s .079 (IPBA = .333). Posey’s pair was .410 and .181 and Miguel Cabrera’s pair was .391 and .158. In 2013, Cabrera’s pair after 82 games is IPBA =.451 and SOA = .183 with a batting average of .368. As great of a hitter as Cabrera is, his SOA will clearly stop him from hitting .400. In my opinion, the SOA will stop any of today’s players from reaching the special number of a .400 batting average.

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In Chapter 17 titled “Mission Impossible: Batting .400 for a Season” of my book *Sandlot Stats*, I use sabermetrics to analyze what I believe is necessary for a player to bat .400 for a season today. Using regression analysis, based on those players who either have batted .400 or very close to .400 for a season, a typical .400 hitter has an in-play batting average IPBA > .427 and a strike-out average SOA < .066. The IPBA is H/(AB-SO). The SOA is SO/AB. A player’s batting average BA = H/AB. It can be shown that BA = IPBA*(1-SOA). Each increase of .010 (10 points) in his IPBA raises his BA by approximately 7 points and each decrease of 10 points in his SOA increases his BA by approximately 3 points.

Since 1913, the .400 hitters club include Harry Heilmann (.403 in 1923), Rogers Hornsby (.401 in 1922, .424 in 1924, .403 in 1925), George Sisler (.407 in 1920, .420 in 1922), Ty Cobb (.401 in 1922), Bill Terry (.401 in 1930) and Ted Williams (.406 in 1941). This elite club, since 1913, includes just six players since Hornsby did it three times and Sisler did it twice. What these players had in common was the ability to make contact with the ball and not strike-out. Their SOA ranged from a low of .024 to a high of .080. Only two SOA were above .066. In 1922, Hornsby had a SOA of .080 but his IPBA of .436 gave him a BA = .401. In 1923, Heilmann had a SOA = .076 but his IPBA of .436 gave him a BA = .403. Their IPBA ranged between .420 and .450with only two less than .427. In 1920, Sisler had an IPBA of .420 but his SOA of .030 gave him a BA = .407. In 1922, Cobb had an IPBA of .420 but his SOA of .046 gave him a BA = .401.

Since 1913, of the ten times a player was able to hit .400 for a season all but Ted Williams did it between 1920 and 1930. The era from 1920 to 1930 was called the “lively ball era” due to the fact that a new tighter wrapped ball led to higher batting averages. Also, before 1930 since pitchers were expected to pitch the entire game the strike-out was deemphasized. Like marathon runners, pitchers wanted to pace themselves by throwing fewer pitches and letting their fielders create their outs.

The four players, since 1941, who came the closest to the magic .400 average were Ted Williams (1957, BA = .388), Rod Carew (BA =.388 in 1977), George Brett (BA = .390 in 1980) and Tony Gwynn (BA = .394 in 1994), Williams, Carew, Brett and Gwynn had corresponding IPBA of .432, .426, .410 and .413. Their corresponding SOA were .102, .089, .049 and .045. Williams and Carew failed to bat .400 because their SOA were too high. Brett and Gwynn failed because their IPBA were too low.

Since 1913, the Triple Crown winners include Rogers Hornsby (1922 and 1925), Jimmie Foxx (1933), Chuck Klein (1933), Lou Gehrig (1934), Joe Medwick (1937), Ted Williams (1942 and 1947), Mickey Mantle (1956), Frank Robinson (1966), Carl Yastrzemski (1967) and the newest member Miguel Cabrera (2012). The exclusive Triple Crown Club, since 1913, includes just 10 members.

Please read my next posting where I examine what it will take for Miguel Cabrera to accomplish both of these feats in 2013 and whether I think Cabrera can and will do it. News Flash: Cabrera is now on pace for 198 RBI which would break Hack Wilson’s single-season record of 191.

]]>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*.