Can't think of anyone else who might enjoy these jots, and there's no certainty that you will for that matter, but what else am I going to do with them except send them your way?
A couple of days ago (which is to say in the summer of 2010), the Colorado Rockies enjoyed a run of 11 consecutive hits against the Chicago Cubs. An 11 hit streak has never happened before, it says here.
Today's baseball season consists of 30 teams playing 162 games. Previous seasons contained fewer games. I'm not enough of a fan to know if there were more or fewer teams in the early years, but a reasonable (enough) guess is that there have been on the order of 2,000 games played during every year of the modern era (since 1900). 2,000 games times 110 years is 220,000 games. Every game contains at least 54 at bats (roughly speaking—rain shortened games have fewer, games with the home team leading after 8 have fewer, extra-inning games have more, games with lots of base runners have more, etc etc). Let's call it 70 at bats per typical game. Every one of them is an opportunity for an 11 hit streak to begin. So, in the history of the modern game, there have been 70 * 220,000 opportunities for an 11 hit streak.
It's happened once, for an observed frequency of 1 in 15,400,000 opportunities.
Let b be the mean batting average of all the players in a lineup. If the likelihood of a batter getting a hit at any given at bat were independent of every other at bat (which it is not, but which is a useful approximation that nevertheless ignores 90% of a manager's reason for living), then the likelihood of any particular at bat beginning an 11 hit streak would be b raised to the 11th power. Of course, for any given player, b varies over a range of something like 0.15 to 0.40 (taking b to refer to a full season) with outliers below 0.15 and above 0.40 (where have you gone, Joe DiMaggio?). Adjusting for hot streaks and dry spells within the season becomes intractable, so let's stick with the yearly average. No entire lineup will average .400 and no entire lineup will average .150 (if god is kind).
Is that enough detail for a simple back of the envelope calculation that might allow us to get some kind of grip on just how flukey is an 11 hit streak? Crank the numbers and see if something absurd falls out:
Take b to be 0.222
1 / (0.222 ^ 11) = 15,492,349
Which is just about right.
If b is 0.209, an 11 hit streak is only half as likely (1 in 30,087,829 at bats) to have occurred in the modern era. And if b is 0.237, it is twice as likely (1 in 7,546,893, or 2 in fifteen million and change).
My untutored impression of that simple computation is that it's not that bad. Those seem reasonable estimates for the day-in day-out, season-in season-out batting average for all players for all time.
If so, then an 11 hit streak is flukey as hell on any given day, or in any given year, but if batters win their duels with pitchers between one fifth and one fourth of the time, you gotta expect this kind of thing to happen about once every century and change.
Given all this, only one thing was 100% certain: if it happened, it had to happen to the Cubs.
dc
Keith Burgess-Jackson, J.D., Ph.D. 