Probability of a No-Hitter

              With the influx of no hitters over the past couple of years, the writers at Hawks Report wanted to take a deeper look of the likelihood of both perfect games and no hitters. To do this, we had to use our knowledge attained from high school Probability and Statistics for the first time in our adult lives. We decided that we would do two probabilities for no hitters as well as two for perfect games. The first probability relies on the assuming that every outcome in baseball has an equal probability. We determined that there were 36 distinct but simple results of an at bat. Those results are single, double, triple, home run, reach on error to every season, groundout and flyouts to each position, catcher’s interference, hit by pitch, and both striking out looking and swinging. Of those, 4 of them will break up a no hitter while 16 of them will ruin a perfect game.

                Since a perfect game or no hitter depends on each out being preceded by another out or in the case of a no hitter each hitless at bat being preceded by a hitless at bat, the formula for dependent events. After punching the numbers, we figured out that a perfect game should be thrown .0000128 of the time. That is an infinitely small percentage that is smaller than the actual amount of perfect games that have been thrown since 1900. 0.000109 of major league baseball games since 1900 have ended in perfect games which means that they happen more than you would expect if based on our first set of math. Now, what happens if we find the probability using baseball statistics. We took the all time major league On Base Percentage which is around .340(for simplistic purposes) and subtracted it from one. That number, .660, represents how often a pitcher gets an out and it will be used to determine the probability of throwing a perfect game. The number we got was .0000058 which is much smaller than the actual number of perfect games. This can be attributed to the fact that once a pitcher gets in a certain groove the outs start to come easier.

                When calculating for a no hitter there is only 4 events that could put it to an end. When doing the math based on outcomes the probability of throwing a no hitter is .04 which means that no hitters don’t happen as often as they should. After that we decided to calculate the probability of throwing a no hitter based off of the average batting average. .266 is widely accepted as the number that batting averages will fluctuate around. According to batting average the probability of throwing a no hitter is .00023. However, when you go to the numbers a no hitter happens in the major leagues at a rate of .0013. According to the numbers no hitters are thrown more often than expected based off of batting average but less so than based off of the book.

Anibel Sanchez ending the no hitter drought

                The recent surge of no-hitters and perfect games can be attributed to batting averages going down as well as players swinging for the fences instead of making contact which results in outs that don’t have to rely defensive players. During the steroid era, no hitters were far and few between but as soon as drug testing became standard in the major leagues, pitchers were able to start achieving the feat starting with Anibel Sanchez.