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"I wonder what percentage of MLB pitching outings turn out to be no-hitters. How close is it to 0.0004%?"
First of all, I made the cardinal error of confusing decimal numbers with percentages... Yikes! I should have said the chances of throwing a no-hitter are actually 0.04%, which is represented as a decimal as 0.0004. Proof I was a liberal-arts major. Mea Culpa. Nevertheless, that's a slim chance.
Anyhow, to answer the question, according to the page I linked to:
"Since 1900, a no-hitter has been pitched 7.5 times for every 10,000 games -- about the same as the probability of pitching a no-hitter against a team of .235 hitters."
There's no date given for the time of that statement, so the numbers might be slightly different now. But if that holds, that would be a 0.075% chance, almost double the quickie estimate based on all batters hitting .250. But the actual overall major-league batting average isn't .235 or even .250. According to Wikipedia, "the league batting average in Major League Baseball for 2004 was just higher than .266, and the all-time league average is between .260 and .275." (The whole Wikipedia article is worth checking out!)
So, let's take the .266 figure and run the calculations again. The chance of a no-hit at-bat would be 73.4%. A no-hit inning:
0.734 * 0.734 *0.734 = 0.3954 or 39.54%
The chance of 9 consecutive no-hit innings is then:
0.3954 to the 9th power = 0.00023 or .023%
Again no-hitters actually occur 0.075% of the time -- that's about three times the statistical probability!!! Why?
Our statistical exercise leaves out all the human factors such as strategy, nerves, mis-matched talent and other wrinkles. Here are some possible reasons why no-hitters, while rare, are more common than pure chance suggests.
-- No-hitters can only be thrown by starters, who are generally better-than-average pitchers.
-- Teams will often "pitch around" or intentionally walk better hitters in a lineup, thus reducing the chances of a hit without affecting the batting average.
-- If you presume that the team working on a no-hitter is in the lead, you can also presume they will play more defensively: Moving infielders back, substituting better fielders from the bench, etc.
-- Truly excellent pitchers can be hot or "on" at certain times. They're simply better than usual, and that extra margin of performance makes them virtually unhittable (as Verlander was on Tuesday). So averages hide "lumpiness" in the data.
-- You might think nerves and pressure would make no-hitters LESS likely to happen than statistical chance suggests... But it could be that batters also feel that pressure. By the 8th or 9th inning, perhaps they feel discouraged... Could the emotion and momentum in a possible no-hitter favor the pitcher?
Any other ideas?
3 comments:
You remarked:
"Our statistical exercise leaves out all the human factors such as strategy, nerves, mis-matched talent and other wrinkles."
Perhaps this contains the answer to your earlier speculation as to how Virgil Trucks could throw two no-hitters, bang-bang: Maybe it's because he's not a statistic or probability but a person. Or maybe he just vreally, really hated those bastards, and that gave him a little extra oomph.
I'm not going to worry about the math. But wikipedia also mentions "combined no-hitters" - nine of them, including six Astros holding the Yankees hitless a few years back. Retrosheet has a giant list of them.
Otherwise, the usual bromides apply: "Past performance is no guarantee of future results", "Hitting is timing, pitching is upsetting timing" and "Ninety percent of this game is half-mental."
Not that any of that helps explain it.
To add to Jon's list of cliches:
It's a pitcher's game.
and...
Good pitching beats good hitting.
---
Here's my 2 cents, if that. For a batter with a .266 or even a .400 average, the odds always favor a no-hit at-bat. If the pitcher manages, for whatever reason, to string together 15 or 20 no-hit at-bats, I would think the psychology would generally be in favor of the pitcher. After all, the reasonable expectation of the batter, under normal circumstances, is a no-hit at-bat. But when the pitcher is "on" or "hot" or whatever, that negative expectation is amplified in every batter who steps to the plate for the second or third time during the game. At the same time, the pitcher's confidence is increasing as the game draws on (I would argue that pitchers who crack under such pressure don't often have long careers in the majors).
Note that the same logic often applies in reverse. When a pitcher makes a stupid mistake, even when his arm is fresh, it often cascades into the situation where every batter finds a way to connect.
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