For most of Sunday afternoon, Justin Verlander looked unhittable. As Tigers fans can attest, when his curveball is working and he doesn’t rely too heavily on his fastball, looking unhittable is nothing new for Verlander. This particular no-hit bid unraveled in the eighth, due in part to a preening ex-star, an ejected hothead and poor fielding by Verlander himself. The knockout blow came off the bat of Maicer Izturis with two outs in the inning, ending Verlander’s chance for a second no-hitter of the season four outs short.

Beyond his unhittable-ness, Verlander has shown an amazing ability to start games strong this season. Twice (including Sunday), Verlander has lost a no-hit bid after seven innings, once more after five and four other times after three innings. Additionally, he has begun his day with three perfect innings—one full time through the opposing batting order—five total times. These numbers see quite impressive, but how do they compare with other pitchers throughout history? *(Because of the limitations of the available data, the rest of this article will deal only with the 1960 season and later.*)

First, let’s look at Verlander’s 2011 season and how deep into each game he took his no-hit/perfect game bid. The listed number of outs is the last out before the no-hitter ended. For example, his first start’s listed six outs indicates that he pitched two full innings of no-hit baseball and the 10 outs in his second start indicates three full innings plus one additional out (3.1 innings).

To determine how Verlander’s season of strong starts compares historically, a simple scoring method will be applied to pick out other great seasons. Since a no-hit bid becomes more difficult and unlikely the deeper into the game it goes, a strictly linear score will not do. Most would probably agree that a nine-inning no-hitter is more than three times more difficult than a three-inning one. To compensate for this, a simple compounding element will be added. Additionally a bonus will be added to reward a pitcher for how deep into the game he stayed perfect (no walks, errors, hit batsmen, etc.). The formula for our “Strong Start Score,” then, is simply:

{exp:list_maker}Take number of outs the no-hit bid lasted

Multiply by the last full inning of no-hit baseball completed

Add the number of full innings pitcher stayed perfect for, squared {/exp:list_maker}As an example, Verlander’s no-hit bid on Sunday lasted 23 outs or 7.2 innings, making his base Strong Start Score equal to 161 (23*7). His perfect day lasted until he walked Bobby Abreu with two outs in the fourth. Since his bid for a perfect game lasted three full innings, we’ll add nine points (3*3), making the total Strong Start Score for this game 170 points. By tying our score to both the number of outs and number of full innings we reward pitchers for every out while also reflecting how the excitement and tension of a no-hitter is ratcheted up with each full inning that passes.

Now that the mathematical housekeeping is taken care of, we can look at some of the greatest seasons of strong starts since 1960. The following list was compiled by applying the previously described scoring method to every game, then adding together all of a pitcher’s starts over the course of a season. The seasons are sorted by total score but a per-game average is also shown. The number of times each pitcher took a no-hit bid past the fifth through ninth innings is also listed:

It’s certainly no surprise that Nolan Ryan—the owner of seven career no-hitters—features prominently on this list, although it is somewhat surprisingly that his best season is one that didn’t feature a no-hitter. Of all pitchers with more than 10 games pitched, Jose DeLeon in 1983 has the highest per-game average (39.6), but starting only 15 games prevented him from making the list. In those 15 starts, however, he took four different no-hit bids into the sixth inning.

How does Justin Verlander’s 2011 season compare to this list? In just 24 starts, Verlander already ranks No. 5, with a per-game average below only the aforementioned Jose De Leon season. Here is his current line:

If we project this line to include 10 more starts, he will reside at the top of the list by a wide margin:

Whether he achieves this ambitious projection or not (how exactly does one throw 0.4 no-hitters?) Verlander’s 2011 season is already one of the greatest of all-time, making each of the rest of his starts must-watch events, not just for Tigers fans but for baseball fans everywhere.

For those interested in seeing the distribution of every partial no-hit bid since 1960, the following chart shows the total number of no-hit bids that lasted up until a certain point in the game. As an example, 2,953 pitchers had a no-hitter after 15 outs (five innings), but only 2,273 of them were able to get that first out of the sixth inning.

Interestingly, there are two instances where a no-hitter lasted into and through the 10th inning and both were achieved by Jim Maloney in 1965. In the first game, his no-hit bid was lost (along with the game) when he gave up a solo home run to lead off the 11th. In the second, his teammates came through with a solo home run of their own in the top of the 10th and Maloney finished off the no-hitter in the bottom half of the inning.

**References & Resources**

The information used here was obtained free of charge from and is copyrighted by Retrosheet. Interested parties may contact Retrosheet at “www.retrosheet.org”.

Dave Studeman said...

Great article, Chad. Thanks. I’m sure Verlander is due for some “regression to the mean,” but it puts his 2/3 season in perspective.

Jim Douglas said...

Interesting article. I do question your scoring, though, which is based on the assumption that “a nine-inning no-hitter is more than three times more difficult than a three-inning one.” Do you have any frequency data to back this up?

dave bristol said...

that is a really interesting article. I don’t usually like these kinds of on-the-fly stats. Seeing 0 no-hitters as the best “no-hit start” season helped to validate the stat for me as measuring dominance across all starts.

Subjectively, Verlander’s season definitely “feels special” so I’m not surprised it already ranks so highly. Ryan’s 72 is also interesting, must be he started a lot of games with a few perfect innings.

Chad Evely said...

Jim,

Good question. I’ll present the distribution in two different ways.

– The actual distribution of no-hitters after every inning in all 208,836 games from 1960-2010, including the % of total starts this occured:

1st: 84,426 (40.4 %)

2nd: 35,651 (17.1 %)

3rd: 12,267 (5.9 %)

4th: 6,736 (3.2 %)

5th: 2,953 (1.4 %)

6th: 1,356 (0.65%)

7th: 560 (0.27%)

8th: 257 (0.12%)

9th: 125 (0.06%)

– Next, we’ll calculate the expected distribution. Over the 1960-2010 seasons, the cumulative batting average was .260 (1,848,344-7,121,136). If we were going to do a comprehensive study (and if it hadn’t been so long since my last Stats class), we could introduce walks, HBP, etc into the equation. For the sake of simplicity, however, we can say that each batter has an out average of .740 (1 – .260). For a pitcher to have a single no-hit inning, then, would be the probability of getting three outs in a row (.74*.74*.74) or 40.52%. This compounds every inning, so the expected chance of remaining hitless after each inning is:

1st: 40.52%

2nd: 16.42%

3rd: 6.65%

4th: 2.70%

5th: 1.09%

6th: 0.44%

7th: 0.18%

8th: 0.07%

9th: 0.03%

As you can see, the expected and actual distribution are pretty close, although the difference grows larger as the innings progress. Part of this is no doubt due to the over-simplification of my formula. I’m sure there are other factors as well but they’ll have to wait for another day. For now, both methods give us at least a general idea of the distribution involved. In the actual distribution, there are 98 times as many no-hitters after 3 than after 9 innings while the expected distribution is more like 200x.

Admittedly, any scoring system like this is going to be somewhat arbitrary with the main goal being to make a list of the best rather than to definitively say which is the absolute best. So while I agree the method could be refined to come up with a more perfect scoring system, I think the decision to make the score compound as the innings grow later is the correct one. Otherwise we’d be left with a bunch of guys who start strong the first time through the line-up but struggle to get past the 6th, which I think is different than what we’re trying to measure. Ultimately my goal was to come up with a formula that was simple enough to understand and pretty close to correct, which I hope I’ve done.

Dave told me that for articles at The Hardball Times, there’s no such thing as “too long.” I hope that applies to comments as well.

Chad Evely said...

Dave,

I’m glad you liked it. I agree about Verlander’s season feeling special. As a Tigers fan myself, I’ve seen most of his starts this year and unlike years past where some nights he just didn’t have it, he seems to be on almost every game this year. It’s been fun to watch.

Digging a little deeper, Ryan’s ‘72 season was boosted by his early-game performance. I only listed the numbers after the 5th in the article but the scoring also includes earlier innings. In ‘72 he had a no-hitter 12 times after 3 innings and 7 times after 4 innings. That 3-inning mark is tied for the best all-time with… Ryan in ‘73. His 4-inning mark is tied for the best all-time with Ron Darling in ‘92. So his “visible” numbers after the 5th don’t look as good but his “hidden” numbers made the difference. To round out his season: in ‘72 he had a perfect game 13 times after the 1st, 3 times after the 2nd and 3rd, once after the 4th and never took one past the 5th.

When I first came up with this method, I hadn’t yet added an element to reward perfect starts. Once I did, this hurt Ryan the most since he generally walked so many guys in his great games. In ‘73 he never made it past the 4th with a perfect game and in ‘74, amazingly, never made it past the 2nd with one.