Streaking surprise

The Count — Thu, 26 Nov 2009 18:44:38 +0000

I’m a football fan… well, more specifically the NFL. I hear that colleges other than the one I went to actually have their own teams and that quite a lot of people think that the outcomes of these “college football games” are important, but I never saw the appeal. Anyway, as I said, I follow the NFL. This year, as the season has proceeded, I’ve found myself noticing quite a few long winning and losing streaks occuring this year. With 2 teams reaching 10-0, and a few teams having streaks of 6 and 7 wins (or losses), I decided to track the actual numbers and determine just how abnormal this season is.

Using one of the many available NFL statistic sites, I was able to compile the number of streaks that occured at each of the 10 lengths available at week 11 (which was just completed). Note that only 10 games have been played by each team at this point, and that I ignored the bye week, allowing streaks to continue through the bye uninterrupted. The following are my results:

Streak Length	1	2	3	4	5	6	7	8	9	10
Streak Count	79	30	22	8	5	4	2	0	0	2

Now, to determine how abnormal this year is (so far), I first have to determine what the expected count for each of the streak lengths is. I must admit, I had to seek outside help determining what this should be, as my first few attempts bore rotten fruit. Luckily, there are some helpful folks at MathOverflow, one of which was able to find a solution:

Streak Length	1	2	3	4	5	6	7	8	9	10
Streak Count	96	44	20	9	4	1.75	0.75	0.31	0.13	0.06
I know, these numbers seem small, given that I’d expect HALF of the 2-game sequences to be a 2-game streak. The trick here is know that every 3-game streak has two 2-game streaks inside it which don’t count!

Now, let’s compare the two sets of values. I’ve found a great little charting tool for small sets of data over at Google. Here’s what it comes up with:

Hmmm, these don’t seem to be very different, do they? As you can see, it seems this season isn’t very abnormal at all; with only moderate drops in the number of 1- and 2-game streaks to account for the obvious outlier of having 2 undefeated teams this late in the season. Each streak length is very close to the expected count for that length.

There would seem to be several reasons one could come up with for why long streaks should occur in football: the literally outstanding talent on certain teams compared to others, the non-random nature of scheduling often pitting teams against obviously “unfair” set of opponents, even the difference between having to play certain teams at home or at the away park with largely varying weather. Yet it seems that the schedule is “fair”, that the teams are well matched. The math we’ve done here has shown that my anecdotal musings of unusually large streaks are without basis. How cool is that?

The Count

The heart of baseball, served rare

The Count — Sun, 12 Jul 2009 00:34:15 +0000

Baseball is a game of numbers. Players move from team to team, teams change cities (admittedly, less than in other sports), and sometimes even their names, but real fans always remember the numbers. This was brought home, to me at least, last Friday night when Jonathan Sanchez of the San Francisco Giants threw a no-hitter against the San Diego Padres. His feat, already a rarity, was made even more special in that he missed a perfect game by only an error by his third-baseman during the 8th inning. Let’s take a look at some of the numbers involved in baseball’s most rare occurrences.

Long ago, Major League Baseball coined the term “modern era” for games played starting in the year 1900 onward. Although the modern rules were instituted in 1893, we’ll take the following statistics from the modern era:

First, some big numbers:

The number of games played per year in MLB has changed over the years but, thanks to other helpful fans1, I’m told the number of games played since 1900 is 174,206, roughly 1600/year. Of course, each game involves two teams.
While not technically a minimum (due to shortened games), a normal game would require at least 51-54 batters (depending on whether the bottom of the 9th is played). I’m not unhappy using 54 as a valid minimum, giving us 9,407,124 plate appearances during those games… at least!
While games with fewer than 100 pitches per team aren’t all that rare, nor are they common. Yet games with 120+ pitches for a team happen all the time. At only 100 pitches per team per game on average, that’s 34,841,200 pitches thrown during those games. I believe that the real number of pitches thrown is much higher, but it gives you an idea of the scale of numbers we’re talking about.

Now, let look at some of the rarified statistics of the game:

206 times a single pitcher has thrown a no-hitter (like Mr. Sanchez)2, pitching a whole game where no opposing batter get a hit. That’s once every 3400 games or so (or every 6800 starting pitchers).
245 times a player has “hit for the cycle”3, hitting at least a single, double, triple and home run during a single game. That’s around 2 per season since 1900, or 1 every 40000 plate appearances!
15 (now 16, read on) times a single pitcher has thrown a perfect game4, a complete game where no opposing player reaches base. That’s once every 11,600+ games, or once every 7 years or so. The last was over 5 years ago, but the longest time period between perfect games was 34 years from 1922-1956, so don’t get your hopes up. edit: Of course, this isn’t true anymore, as a new perfect game was thrown on July 23rd, 2009 by Mark Beuhrle7
- 10 times, the pitcher allowed the first batter of the game on base, but then threw a perfect 27 (or more!) outs.
- 9 times a perfect game has been lost to the last (27th) batsman, who reached base.
- 8 times a perfect game has been lost when the only batter to reach base did so on an error, just like Mr. Sanchez’ game. Only once was it the pitcher himself who committed the error.
- Once, a pitcher named Harvey Haddix threw 12 perfect innings (36 batters) before an error ruined his perfect game, he even took the loss when that batter scored to end the game.
13 times a batter has hit 4 home runs in the same game. That’s once every 13,400 games. Mike Cameron hit four solo home runs (no one else was on base), and Bob Horner’s team actually lost the game where he hit his 4 dingers.

These are certainly rare occurrences, but by no means the rarest. As I said, baseball is a game of numbers, and you can find any number of special sets of circumstances that fans have only had the chance to see once or maybe twice in the last 100+ years. From hitting 2 grand slams in an inning (once, by Fernando Tatis) to pitching 21 strikeouts in a game (once, by Tom Cheney), these are records worthy of the hard-core baseball fan. Having the chance to talk about the wonderful numbers that result from one pitch, one at-bat, one inning, game, or season is some of the best fun of being a baseball fan. I hope you enjoy it as much as I do.

The Count

Discrete Ideas » Sports

Streaking surprise

The heart of baseball, served rare