The Physics of the Most Perfect Game

It happens. You’re walking down the street and you suddenly feel the need to straighten your tie, fix your hair, or adjust the collar on your coat. You see a weak reflection of yourself in a window and get to work only to realize the people inside the window have a clear view and are trying hard not to laugh.

Now, a normal person would just be embarrassed and walk away as quickly as possible. However, a nerd like me  would continue to stare at the window because this episode brings to mind an experiment to help me grasp the nature of the universe.

Instead of standing in front of a window, I could shine a flashlight at a piece of glass. Most of the light goes straight through, but a small fraction, about four percent, reflects back toward the flashlight. Which part of the light bounces back? Could you build a flashlight without the bounce-back light? So many questions.

The flashlight’s beam, like everything else in our world, can be broken down into smaller entities. Perhaps you have heard of the fundamental particles of light called “photons.” The beam is composed of about a billion-billion identical photons coming out of the flashlight each second.

Since the photons are identical, there is no way to distinguish in advance which ones will reflect off the glass and which will go through. Therefore, the only workable explanation is statistical. As each photon encounters the glass, it has a one-in-25 chance (four percent) of bouncing back.

This statistical behavior turns out to be fundamentally true of everything in nature and is the basis for the science called “Quantum Mechanics.” However, The Hardball Times is about baseball, not physics. So, let’s move on to understanding a bit about how statistics work.

If a billion photons encounter the glass, then about 40 million photons will reflect. However, if you look at 25 photons hitting the glass, you would most likely see one photon reflect, but you would not be surprised to see zero, or two, or maybe even three reflect. Finally, if you examine a single photon you really can’t predict which it will do at all.

The universe – like baseball – runs on statistics. So, if you look at a stat like on-base percentage (OBP) it might give you a good sense about how likely a batter is to reach base over the course of a season. However, it is less helpful if you try to use it over a given week when a hitter might be on a hot streak or in a slump. It is even less predictive for a single at-bat.

Nonetheless, when it comes to perfect games, it is really the only relevant statistic that is easy to find and apply. Below is a table listing all 23 perfect games in major league history.

There are few slouches on this list of pitchers. In fact, more than 25 percent are members of the Hall of Fame and there are few pitchers you haven’t at least heard about. The performance most worthy of note, of course, is Don Larsen’s perfecto in the World Series:

Charlie Robertson’s effort against Detroit included an 0-for-3 day by Ty Cobb. Cobb had a rough start in 1922. On that day in April he was batting only .083 with an .154 OBP. He recovered and finished the campaign with his more typical .401 batting average.

Imagine the misfortune of Ossee Schrecongost of the Philadelphia Athletics, who was blanked during Cy Young’s perfect game. He was then traded to the White Sox in time to be blanked by Addie Joss four years later.  Young’s perfect game was thrown against Hall of Famer Rube Waddell and  Joss pitched his against another Hall of Famer, Ed Walsh.

That’s fun and all, but let’s get back to statistics. We’ll start with something relatively simple like dice. Suppose you hold a single die. What are the chances you won’t throw an ace (one)? Well, you’ll throw an ace about one in six throws, so the odds of throwing an ace are one in six, or the probability of throwing an ace is one-sixth. The chances of not throwing a one then must be one minus one-sixth or five-sixths.

Suppose you are going to throw the die two separate times. What are the chances that you will not throw at least one ace? There are 36 possible combinations. Eleven of them have at least one ace. So the probability of throwing no aces is 36 minus 11, or 25 of the 36 possible outcomes. An easier way to calculate this number is to just take the five-sixths chance for the first throw and multiply by the five-sixth chance for the second throw.

Suppose you intend to throw the die 27 times. What are the chances you never throw an ace? Well, I guess it would be five-sixths times five-sixths times five-sixths…until you do it 27 times. If you care, the probability is 0.73 percent, which means the odds are once in 137 tries.

What does this have to do with perfect games? If you accept that the on-base percentage (OBP) is the probability that a batter will reach base, then the probability that he won’t get on base is one minus the OBP. If no batter reaches base, then you have a perfect game.

So, the probability of throwing a perfect game is roughly the product of one minus the OBP for each batter each time he comes to the plate. The box scores from Baseball-Reference.com include the OBP for each batter at the beginning of the game. However, they only go back to the 1920s.

For the four older games I found box scores (without OBPs) at Baseball-Almanac.com. I then went back to Baseball-Reference.com to find the OBP for each batter for the year. Finally, I could calculate the odds for each perfect game and compare them for sheer entertainment value. The table below is sorted from the most likely perfect game to the least likely, with the calculated odds for each.

Sandy Koufax was my childhood idol. I remember listening to Vin Scully call his perfect game in 1965. So, it saddened me greatly to see that he had the most likely perfecto of all. The Cubs, as usual, were not a good team. They finished eighth that year — losing 90 games.

Talk about bad timing. On the night in question, two September call-ups, Byron Browne and Don Young, played their first major league game for the Cubs. In addition Chicago’s pitcher, Bob Hendley, couldn’t hit water if he fell out of a boat. He went hitless in 14 at-bats that year, striking out 10 times. In essence, Koufax was really facing only six major league batters that night. Of the six only Ron Santo, Ernie Banks and Billy Williams had OBPs above .300.

By this methodology, Buehrle’s flawless performance in 2009 was the most difficult to accomplish. You might recall that in 2008 Tampa Bay lost the World Series to the Phillies. In 2009, the Rays they were set on returning to the Fall Classic. However, the Yankees and Red Sox were also playing great ball. On July 23, the Rays were 6.5 games behind in the AL East but had a record of 52-44.

Their line-up that day included Ben Zobrist, Evan Longoria, Carl Crawford and B. J. Upton. Only one batter had an OBP of less than .300; Zobrist boasted a gaudy .413. Of course, since it was in the American League the Rays pitcher didn’t bat.

I hope this table of odds for perfect games will start lots of fun conversations-discussions-arguments and you’ll add your thoughts to the comments below. After all, these sorts of statistical gymnastics are not just part of the National Pastime, but they are a fundamental truth about the behavior of our universe.