Unpredictable, rare, and occasionally effective…but always entertaining.

Perfect Games are Easier(?)

with 2 comments

Loyal reader Mac asked me the other day why there have been so many perfect games and no-hitters, both completed and those that came up just short.  Just in this season we’ve had Dallas Braden, Roy Halladay, and Armando Galarraga (yeah, I’m counting it) throw perfect games and Ubaldo Jiminez and Edwin Jackson throw no-hitters.  Last season there was also a perfect game (Mark Buerhle) and a no-hitter (Jonathon Sanchez).  Before I theorize why these are occurring more often, I wanted to think about how often should these things happen, and once I’ve established the parameters for a no-hitter or a perfect game, are they more likely now?

First, let’s start with no-hitters.  I’m going to simplify slightly by talking about 9 inning no-hitters only.  To do this a pitcher has to get 27 outs.  Now, this isn’t to say that you have to get 27 different hitters out.  Because we are only talking about no-hitters, the possibility exists for a runner who got there via error or walk to be thrown out on the bases (double play, caught stealing, etc.).  So we’re talking about slightly less than 27 at-bats that need to pass without a hit.  Since it’s probably not a full at-bat that we could erase by doing this, I’m going to continue given that the pitcher has to get 27 different guys out.

The league-average batting average last year was 0.263.  So the random chance of getting 27 consecutive outs is 0.0264% (meaning that each game should see 0.000264 no-hitters, or a no-hitter will occur every 3,788 games).  There are 2,430 games in a major league schedule, and each game has 2 chances for a no-hitter.  Multiplying the 0.0264% chance by 4,860  results in about 1.28 no-hitters per season.  Since 1998 (as long as there have been 30 teams), there have 23 been no-hitters (including 6 perfect games), or roughly 1.8 no-hitters per season.  Since 1875 there have been 267 no-hitters, or roughly 1.98 no-hitters per season.  Remember that for many of these seasons there were fewer than 30 teams, but the 0.263 BA is near the median of league batting averages through the history of the game.

This year the batting average is down to 0.259 so far, the lowest it’s been since 1992 (ERA is the lowest it has been since 1992 also).  In the history of baseball, the league batting average is 0.2634.  The lowest it’s been in the last 100 years was 0.237 in 1968, the famed “Year of the Pitcher.”  Anyway you slice this, there have been more no-hitters than we might expect throughout the history of the game.

Just to show what difference the change in batting average makes, here’s a table showing the number of no-hitters we would expect given the current number of games in a major league season:

BA No-Hitter? # Games Per NH
0.240 0.0605295% 1652
0.245 0.0506486% 1974
0.250 0.0423306% 2362
0.255 0.0353362% 2830
0.260 0.0294616% 3394
0.265 0.0245334% 4076
0.270 0.0204041% 4901
0.275 0.0169483% 5900
0.280 0.0140597% 7113
0.285 0.0116483% 8585
0.290 0.0096377% 10376
0.295 0.0079635% 12557
0.300 0.0065712% 15218

Looking at this a little more in-depth, strikeouts are at an all-time high also, as teams are striking out roughly 7 hitters per nine innings.  Obviously, striking out more hitters leads to fewer balls in play.  So the league is arriving at its average BA by a different route.  Examining this on a BABIP-basis, the percentages change; the following table shows what the odds are if you only have get 20 outs on balls in play.

BABIP No-Hitter? # Games Per NH
0.285 0.1219329% 820
0.290 0.1059661% 944
0.295 0.0919988% 1087
0.300 0.0797923% 1253
0.305 0.0691347% 1446
0.310 0.0598387% 1671
0.315 0.0517382% 1933

Now we’re in the realm of 2 no-hitters per season.  Every additional hitter that is struck out makes a big difference; the following table assumes a 0.300 BABIP and shows the difference based on the number of outs needed.

Outs Needed No-Hitter? # Games Per NH
22.0 0.0390982% 2558
21.5 0.0467313% 2140
21.0 0.0558546% 1790
20.5 0.0667590% 1498
20.0 0.0797923% 1253
19.5 0.0953700% 1049
19.0 0.1139890% 877

Moving to perfect games, this one is slightly easier to check.  The league-average on-base percentage last season was 0.333.  Not accounting for reaching via error, a pitcher needs to retire 27 hitters without any reaching base.  The odds for this are 0.001784% (or a perfect game every 56,053 games, roughly 11 seasons).  Like I said earlier, there have 6 perfect games since 1998, or roughly 1 perfect games every 2.1 seasons.

Since 1875 there have been only 20 perfect games (21 counting Galarraga’s), or roughly 1 every 6.8 seasons; however, 8 of the 20 (or 9 of the 21) perfect games have occurred in the last 20 years. There have also been 10 instances of a perfect game being broken up on the 27th hitter (including Galarraga); there have been 9 instances of the first man reaching base and then the pitcher retires the next 27 hitters, and there have been 8 instances of no-hit, no-walk, no-hit-batter games where the only baserunner reached via error.

The frequency is definitely increasing, and the addition of teams throughout the league helps in two ways: one is that there are more opportunities for it to happen, and the other is that hitting talent is more spread throughout the league than it’s ever been.  A good pitcher has a better chance of running into a lineup with weak spots.  The league average for BA and OBP are propped up by weak pitchers.

The increase in strikeouts, seen in the table below, has definitely helped.  The value placed on defense over the last several years has probably helped.  We could play the steroids game, but I’d rather not get into it.  There’s probably an argument for the tension of the late inning situations getting to the hitters more than the pitchers, but there’s no way to measure that.  There’s definitely a way to measure how the situation gets to umpires, relating to the possibility that the strike zone expands when a pitcher has something historic going.  As much as anything else, it could also be a lot of randomness, the same randomness inherent in every no-hitter and perfect game where every batted ball finds a glove and every throw finds it target.

Decade K/9 Year K/9
2000s 6.59 2010 6.94
1990s 6.14 2009 6.91
1980s 5.34 2008 6.77
1970s 5.15 2007 6.62
1960s 5.70 2006 6.52
1950s 4.40 2005 6.3
1940s 3.55 2004 6.55
1930s 3.32 2003 6.34
1920s 2.81 2002 6.47
1910s 3.67 2001 6.67
1900s 3.43 2000 6.45
1890s 2.55 1999 6.41
1880s 3.48 1998 6.56
1870s 1.42 1997 6.61


Written by Dan Hennessey

July 15, 2010 at 10:40 PM

Posted in Uncategorized

2 Responses

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  1. Why have strikeouts jumped up over the last decade? Is it sabermetricly acceptable to strike out more? Mark Reynolds awaits your answer.


    July 16, 2010 at 9:57 PM

  2. This blog has an east coast bias.

    – The emergence of Buster Posey
    – The struggles of Tim Lincecum and Pablo Sandoval
    – The First Place San Diego Padres
    – The managing failure that is Bruce Bochy’s career
    – The Coors Field ball switching controversy

    These are all local stories that your blog has overlooked to write a 7th and 8th entry on Roy Halladay and Cliff Lee. I know that you want to be one of the best, but all of the best start local. Judging by your IP address, you are a 1,000 miles off base, and since I just tagged you, YOU’RE OUT!!!

    Pastor Greg

    July 20, 2010 at 10:57 AM

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