Hitting streaks in 7-inning and 9-inning baseball

Matt’s latest book review got me thinking about hitting streaks, and - being a fan of the sport in Britain – my thoughts naturally turned to the subject of our domestic game.

The National League South schedule consists purely of 7-inning double-headers, and it seems fair enough to state that maintaining a hitting streak across such games would be harder than doing so with the full-length variety. (As a counterpoint, innings do tend to be a little longer in the British game, but this is probably more than cancelled out by the existence of the slaughter rule, which can see games terminated after as few as 4-and-a-half frames.)

As a way of addressing the question of how much harder it might be, I will firstly put together a very crude simulation of Joe DiMaggio’s career. Over 1736 games he amassed 2214 hits in 6821 at-bats. That’s a career batting average of .325, with 3.93 at-bats per game (we’ll call it 4 to keep things simple). Assuming that every game that DiMaggio plays in a fictitious 1736-game career he has 4 at-bats and a 32.5% chance of getting a hit each time (this is what I mean by crude), then the probability of him getting at least one hit in a game is a fraction under 80%. Using this, and with a bit of code in Excel, I can simulate his career as many times as I want. Even if this doesn’t sound like fun, you might still be interested in the results.

This is the longest hitting streak in each of 50 simulated DiMaggio careers, ranked from shortest to lengthiest: 20 games, 20, 21, 21, 21, 22, 22, 22, 23, 23, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 27, 28, 28, 28, 29, 29, 29, 29, 29, 29, 30, 30, 31, 31, 32, 32, 32, 33, 34, 35, 36, 37, 38, 48.

It is interesting to note that Joe manages at least a 20-game streak in each career, and, of course, the 48-game run stands out. The number I will take from the list is 27, however, which is the 25th and 26th value and therefore right in the middle of the list (i.e. it is the median).

Now let’s - crudely once more - make Joe play out his career in a 7-inning environment (to model this we’ll use 3 at-bats per game). I won’t repeat the list, but over 50 careers, the minimum longest streak is 11 (not even worthy of a postcard to mum), the maximum is 36, and the median is 17. This is a full 10 games less than our value from above, so the shorter games do clearly have a big impact.

One of the major limitations of the simulation is that it does not throw in the odd game with just a couple of at-bats (which might easily happen, particularly if teams are pitching around you if your bat is perceived to be “hot”; Joltin’ Joe’s streak survived two games in which he had only 2 at-bats, including one in which he faced Hall of Fame pitcher Bob Feller). This could plausibly lead to an over-estimation of maximum career hitting streaks, which would make DiMaggio’s 56-game run seem all the more impressive (trumping all 50 of the simulated career maximums).

Partly to test the effect of this, and partly for fun, I’m going to plug in the number of career games and the career batting average for the nine other players at the top of the list of longest hitting streaks. I’ll assume 4 at-bats per game in each case. And for each player I’ll just run the simulation once. Here’s what I get:

• Willie Keeler 28 games (actual longest 45 games)
• Pete Rose 21 games (actual longest 44 games)
• Bill Dahlen 19 games (actual longest 42 games)
• George Sisler 34 games (actual longest 41 games)
• Ty Cobb 38 games (actual longest 40 games)
• Paul Molitor 21 games (actual longest 39 games)
• Jimmy Rollins 25 games (actual longest 38 games)
• Tommy Holmes 26 games (actual longest 37 games)
• Gene DeMontreville 23 games (actual longest 36 games)

Here the model is consistently under-estimating the longest hitting streak. This is probably through a combination of other limitations (such as assuming a flat batting talent over the whole career) and selective sampling: the longest hitting streaks are those at the luckier end of the spectrum.

To flip the selective sampling issue on its head, I’ll choose a few players who possibly should have managed a streak of more than 30 games at least once but didn’t, and then use the model to find a median value across 50 seasons once more for each one. The results are shown below.

• Tris Speaker 33 games
• Tony Gwynn 31 games
• Babe Ruth 31 games
• Ted Williams 31 games

These last findings give me at least a bit more confidence in the model.

To come back to the differences between 7-inning and 9-inning baseball, there is one way to level the playing field, and that is to look at hitting streaks across consecutive at-bats. In fact, in the National League South, Cody Cain (who has been troubling pitchers in Britain for well over a decade) recently amassed nine straight hits, with a couple of walks sandwiched in the middle.