# Which Batting Streak is More Impressive?

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