If you have any ideas for topics, please email me. Thanks,Stan!
Posted By Dr. Stan, the Stats Man

For the fifth consecutive year, I attended the Joint Mathematical Meeting of the Mathematics Association of America (the MAA) and the American Mathematical Society (the AMS). This year the meeting was in San Diego from January 7 through January 10. This meeting is the most important meeting for both these organizations. At this joint meeting, universities and industries hire new PH.D Mathematicians. In addition, at this joint meeting, mathematicians present their new research under specific topics. My presentation was under the topic “Sports and Math.” The title of my presentation was New Theorems to Predict Winning Percentages and Compare Parity in the MLB, NBA, and NFL. You can read about my research by Googling “Stanley Rothman and the Pythagorean Theorem of Baseball.” This research is described on the website www.baseball-reference.com.

Other sample presentations on Sports and Math included:

Predictive Modeling and Analysis of Golf and Softball Teams Using Linear Algebra.

Statistical Modeling of a Mercy Rule in College Football to Reduce Major Injuries,

,A Search for Champion Boxers,

Modeling and simulation of a bicycle race,

What can a jump tell us about a pitcher? 

The convention is also a time for reconnecting with former students, graduate school friends, colleagues, and family.

For convention pictures, check out my Facebook Page: 





Posted By Dr. Stan, the Stats Man

Monday, May 15, 2017 marks the 76th anniversary of the beginning of Joe DiMaggio’s record 56-game hitting streak, which ran from May 15 to July 16, 1941. The streak ended On July 17 when he went 0-for-3 against the Indians, with third baseman Ken Keltner making two outstanding plays to stop the streak.

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.

Hitting Streaks

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.

Posted By Dr. Stan, the Stats Man

Read what my student Greg considers the biggest surprise in the MLB for 2017 is so far. 

Every year there are storylines between teams and players, and surprises that come out of the league. The biggest surprise so far in 2017 has been one in the name of Eric Thames. Thames is a 30-year-old left-handed hitter who is currently doing wonders for the Milwaukee Brewers. Thames burst onto the MLB scene in 2011 with the Toronto Blue Jays and was an average hitter at best. Thames played the following year with the Toronto Blue Jays and Seattle Mariners. His average over this time was a dismal .250 and his OBP was only .296. The following year Thames was not given another shot at the MLB. In 2013 Thames spent time between AAA and Rookie ball, which is not where you want to end up. Things were looking down for Thames and it seemed as if his MLB career would be over. What happened next would surprise almost everyone. Thames headed to the KBO (Korean Baseball League) to try to revive his playing career. The KBO is not a very well-known league, a step down from the well-known NPB (Nippon Professional Baseball League in Japan), so the hitter’s success there is taken with an asterisk next to it.

What Thames did was unbelievable. He turned himself into one of the most feared hitters in the KBO and became a world-class slugger. Over the next three years, from 2014-16, he went on to have gaudy numbers of a .349 BA, .451 OBP, and a .721 SLG. In 3 years he accumulated 124 Home Runs and 382 RBIs, averaging 41.3 Home Runs a year and 127 RBIs. After these unbelievable numbers an MLB team would have to give him at least a tryout, correct?

That is exactly what happened. On November 29, 2016 Eric Thames would get his shot again at the MLB when the Milwaukee Brewers signed him to a 3 year $16 million dollar guaranteed contract. For a player who had only played in a lower level international league over the past three years, this was a big gamble for the Brewers. The Brewers were very intrigued to see how this would work out.

Fast forwarding to the start of the 2017 season Thames arrives at Spring Training hoping to make the Brewers big league club. People were skeptical of Thames numbers because of the KBO being a low level league, but the Brewers gave him a shot regardless. During the spring Thames hit a respectable .263 with only 1 Home Run. He attributed a very solid .368 OBP over 57 At Bats. This was good for the Brewers and it looked like their gamble signing might work.  

Through the first 7 games of the MLB season Thames was struggling power wise, hitting only one Home Run, but still had a respectable .318 BA. Since then, Thames is absolutely demolishing MLB pitching hitting .348 with 10 Home Runs and 17 RBIs. Thames has become a hitting machine that cannot be stopped. In games versus the Cincinnati Reds, Thames hit an astounding 8 Home Runs.

Now, when any player comes out of the blue and starts hitting unbelievably, the thought of “Is he taking steroids?” becomes a question. The Chicago Cubs “jokingly” suggested that maybe he is on steroids and then the entire thing got blown up. Thames was quick to shut it down saying that in Korea the drug policy is run by the IOC, which is even more strict than the MLB. Thames has been drug tested numerous times since the start of the season, and has come up clean every time.

In Conclusion, it is truly great to see a hitter who was down and out, who thought their playing career might be coming to a close, getting a shot with a big league club and proving his worth. The story of Eric Thames right now is for every kid who just got cut by his travel team. Or every kid sent down to a lower step of the minors then they thought they should have. With hard work and determination, anyone can make it back. Eric Thames is proving that right now, and he is living the dream.
- by Greg Kassar

Posted By Dr. Stan, the Stats Man

Two Major League Baseball batting records were in play on Saturday, August 27th. As a side note this was the date 49 years ago that I married my lovely wife, Tara. Since I do not know the record for the longest marriage, I will return to something I do know about: baseball records. The two players connected with these records are the Yankee rookie catcher Gary Sanchez and the Red Sox veteran second baseman Dustin Pedroia. Wouldn’t you know it the 2 players come from the 2 teams that have always been bitter rivals. Pedroia entered Saturday’s games with 11 consecutive hits in 11 at-bats while Sanchez entered Saturday with 10 home runs in 22 games this season.

Pedroia started his hitting streak on Thursday when in his last three at-bats against the Rays he had 3 hits. He followed that performance on Friday against KC with a 4-for-4 game and a walk. Going into Saturday’s game against KC he had a steak of seven straight hits in seven at-bats and a streak of eight times reaching base successfully in eight plate appearances. In his first four plate appearances on Saturday he got four more hits which extended his hitting streak to 11 hits in 11 at-bats and his on-base streak to 12 in 12 plate appearances. However, both streaks ended when he bounced into a double play in his last at-bat on Saturday. The last player to have 11 consecutive hits in 11 at-bats was the Yankee Bernie Williams who accomplished this streak in 2012. The Major League record for most consecutive at–bats with a hit is 12 and is shared by Johnny King (1902 Cubs), Pinky Higgins (1938 Red Sox) and Walt Dropo (1952 Tigers). The modern era Major League record for most consecutive times reaching base successfully is 16 held by a Red Sox player you might have heard of named Ted Williams in 1957. The breakdown of his 16 successes include 2 singles, 4 home runs, 9 walks and 1 HBP. The all-time record is 17 held by Frank Ward in 1893.

In Chapter 16 of my book “Sandlot Stats: Learning Baseball with Statistics,” I presented two mathematical formulas, one developed by Michael Freiman and the other developed by me, which use any player’s batting statistics to assign a probability of that player duplicating any batting streak. The mathematics used comes from the area of mathematics called probability. If interested, please read my Chapter 16 to see what these two formulas look like and the logic used to develop them.

Using my formula, the probability of Pedroia having 11 hits in 11 at-bats was .0012 (this equates to 12 times in 10,000 seasons); his probability of having 12 hits in 12 at-bats was .0004 (this equates to 4 times in 10,000 seasons. The probability of Pedroia reaching base 12 times in 12 plate appearances was .0033 (this equates to 33 times in 10,000 seasons); the probability of Pedroia reaching base 16 times in 16 plate appearances was .0001 (this equates to 1 time in 10,000 seasons).

How does this compare to the actual record-holders? Walt Dropo’s probability of setting his record of 12 consecutive hits in 12 at-bats was .0001 (this equates to 1 time in 10,000 seasons); while Pinky Higgins’s probability of 12 hits in 12 at-bats was .0002 (this equates to 2 in 10,000 seasons). Ted Williams’ probability of his record of reaching base 16 consecutive times was .0083 (this equates to 83 times in 10,000 seasons). The very small probabilities associated with all the record holders achieving their records shows that chance and luck is a very big factor in attaining these records. The year Walt Dropo set his record his batting average was a very mediocre .279.

As for Gary Sanchez, with his home run Saturday against the Baltimore Orioles, he became the fastest player to reach 11 career home runs, doing so in just 23 games. My next blog will discuss all the other batting records approached by Sanchez in his rookie year.

Posted By Dr. Stan, the Stats Man

In 2016, 2 record batting streaks have been in the news. The 2 batting streaks are Joe DiMaggio’s 56-game hitting streak and Ted Williams’ 84-game getting on-base streak. DiMaggio’s streak means he got a hit in 56 consecutive games; whereas, Williams’ streak means in 84 consecutive games he reached base with either a hit, a base-on-balls or a hit-by-pitch. The 2 players toying with these 2 streaks in 2016 were Jackie Bradley Jr. and Marcell Ozuna. Bradley’s hitting streak ended at 29 consecutive games. Ozuna’s on-base streak ended at 36 consecutive games. How does one compare different batting streaks to choose which one is the most impressive? Most impressive means harder to achieve.

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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