Perfection

So jamesd asked why we’re getting more perfect games than we used to. Between stampton, hsmith and jamesd the question actually got answered, but I’m not going to let that stop me making a graph out of it.

So I made a simple model. Perfect games happen when you get, in the first 27 batters faced, no walks and no hits. (I’m going to ignore stuff like hit-by-pitch and errors and interference, but they could be added by anyone really interested.)

For every season in the Retrosheet database, I took the top 50 pitchers in batters faced. Overall, they average right around 30 starts each, a number that hasn’t varied a lot in 120 years. For each of them, I I looked up walks, strikouts and babip and calculated the associated rates: walks/batter faced, strikeouts/battter faced and hits/(batters faced-strikeouts-walks). Now, looking across those top 50 starters for each season, I calculated the mean and standard error of these three quantities for each season.

With these quantities, I can simulate every game of the season. First, you sample from the distribution to get two pitchers in the game. This is probably somewhat better on average than the pitchers in an average game, but you don’t want to use guys with very small samples. Now there’s a pretty simple equation that gives the probability that a particular pitcher with strikeout rate k, walk rate w and babip rate b throws a perfect game:

P = (k + (1-k-w)x(1-b))27

We simply perform this calculation for every random pitcher draw for the whole season. That gives us 2 2 x #of games probabilities. With these, we can do some statistical wizardry to calculate the probability that in that particular season you see any particular number of perfect games across the whole season. In practice, I calculate p(0), p(1), p(2), and p(3). These four calues almost sum to 1, so I make p(4)=1-p(0)-p(1)-p(2)-p(3)-p(4). Using these values, we can calulate the expected number of perfect games in a year: p(1)+2xp(2) + 3xp(3) + 4xp(4).

I then graph the mean k,w, and ba by season along with the expected number of perfect games. Here it is:

As was surmised, the rise in strikeout rates explains the increase in perfect games pretty much oerfectly. (Expected perfect games are plotted on the right y-axis, the rest are on the left y-axis.)

Repeat After Me

In Thursday’s game, both Mauricio Dubón and Michael Harris II had hits in the 6th, 7th and 8th innings. Brandon Gaudin asked about this, so I’ll assume he was asking me.

Before answering that, I answered a different question: what’s the most consecutive innings in which a player had a hit? The answer is 5. On July 31, 1928, Taylor Douthit of the Cardinals got hits in each of the 5th through 9th innings, four singles and a double. That feat was repeated by Doc Cramer of the A’s on July 13, 1935. And that was the last of it for over 50 years, until Rickey Henderson hit in five straight innings on September 29th, 1991. Amazingly, Rickey was 5-for-5, one hit in each of the first five innings, did not bat in the 6th and then was pinch-hit for in the 7th.

Hits in four consecutive innings by a batter are fairly rare, but hits in three consecutive innings is not. All you really need is a lot of people to come to the plate in the middle inning of the three, some hot hitting, and luck as to where the inning creaks come in the order. It’s happened over 5000 times.

Two players getting three consecutive hits in the same three innings is considerably rarer, but not all that rare. It’s happened just over 500 times, including 12 times by the Braves. But twice the Braves had three players get hits in three consecutive innings in the same game:

The Game

It started with an hour and 45 minute rain delay, followed by an offfensive delay from both teams. Max Fried in his first outing against his ring-giving team, should have given up a run in the first, but sloppy baserunning negated it. After that, he was Max Fried.

But hoping to make us forget Max Fried, and Deadline Angst, was Tyler Mahle. He was great. he gave up no hits for the first two times through the order and worked around a couple of doubles later. He gave way to Fuentes, who was fine.

Because of the delay and because of an early committment on Saturday, I had to leave Yankee Stadium. But I told ububba, “It’s no problem. I think my presence is holding back the offense. After solo homers from Riley and Olson, I was proven right.

So that brought Iggy in with a two-run lead in the 9th. He was… not good. He was lucky to give up only the tying runs. Our pessimistic friend Mr. Insect Overlords thinks we have a closer problem. Methinks we have a 2021 Will Smith problem. The only way out is through. Keep thowing him out there until he gets it back.

The extra innings were random, and we lost. Late afternoon game tomorrow.