## New York Yankees: Roy Halladay

### Math says Larsen > Halladay (by a lot)

October, 8, 2010
10/08/10
9:30
AM ET
Today marks the 54th anniversary of Don Larsen's perfect game, which in this Postseason of the Pitcher, takes on even greater signficance with what's happened in the playoffs the last two days.

Larsen and Roy Halladay are the only pitchers to throw no-hitters in postseason play.

Halladay tossed his no-no against a Reds’ offense that led the National League with a .272 batting average in the regular season. Larsen’s perfecto came against the 1956 Brooklyn Dodgers, who led the NL with a .342 on-base percentage that regular season.

So taking account the high level of competition in both cases, which of the two historic performances was most statistically impressive?

We're here to show you that a mathematical approach says Larsen's is better. And if you can be patient with the explanation below, you'll see that it's not close.

One way to go about evaluating this is to look at what each accomplishment entails, exactly, and calculate the likelihood of the series of events necessary for it to occur.

Let’s start with Halladay. In order to get his no-hitter, Halladay had to deny a hit to the batter in each of the 27 at-bats against him (we discount the walk he gave up since no-hitters only deal with a lack of hits).

First, he had to make sure Reds’ leadoff hitter Brandon Phillips did not get a hit. The probability of that happening can be thought of one minus Phillips’ .275 batting average in the regular season, or 0.725. Then, he had to ensure Orlando Cabrera (.263 BA this season) did not get a hit, which has a probability of 0.737.

Assuming those two at-bats are independent, the probability of a pitcher not allowing a hit to BOTH Phillips and Cabrera in the first two AB of the game is the product of those two, (0.725*0.737 = 0.534). Using this method for all the subsequent batters, we can calculate the probability of denying a hit to each one in the series of 27 batters that recorded an AB against Halladay (Phillips, Cabrera, Votto, … - obviously including repetitions for multiple at-bats by the same player).

When you get through multiplying the 27 probabilities, the likelihood of what Halladay did is quite low: 0.0001542. That number’s tininess may be difficult to comprehend, so think of it this way: one in 6,500!

So clearly Halladay’s performance is a rare feat, but how does it compare to Larsen’s?

A similar method can be used to calculate the probability of retiring each of the 27 Dodgers batters that came to the plate against Larsen in Game Five of the 1956 World Series.

The only difference is that instead of using each player’s batting average, the player’s on-base percentage is used because Larsen not only denied them hits, but also kept them from reaching base at all –- essentially, the difference between a no-hitter and a perfect game.

So the probability of retiring Dodgers’ leadoff man Jim Gilliam in his first PA is one minus his .399 OBP, or 0.601. The probability of retiring Pee Wee Reese in his first PA is .678, then there is a .601 probability of retiring Duke Snider, and so on.

Putting it altogether, the likelihood of throwing a perfect game against the lineup Larsen faced is almost nil: 0.000009! You’re reading that correctly: nine times out of a million, or about one in 111,000. By comparison, Halladay’s no-hitter against the Reds was about 17 TIMES more likely than Larsen “perfect gaming” the 1956 Dodgers!

Why is Larsen’s performance so much more unlikely, statistically speaking? As you may have guessed, it comes down to the how much more difficult it is to throw a perfect game than a non-perfect no-hitter.

The Reds’ hitters used in Wednesday’s game had a BA of about .280, so denying them a hit is a 72 percent proposition, on average. The 1956 Dodgers who came to the plate in Game 5 of the World Series had an on-base percentage of .362, so an out happens about 64 percent of the time. The eight percent difference doesn’t seem huge for a single event, but when extended to 27 straight occurrences in each case, the perfect game becomes much, much more unlikely.

Of course, this analysis doesn’t take into account that in addition to Halladay not allowing a hit, he also gave up only one walk (to Jay Bruce in the fifth inning) and didn’t allow anyone else to reach base.

This would probably make Halladay’s accomplishment look even more impressive, since he was “almost perfect”, or at least much closer than a no-hitter with several walks or other runners reaching base.

So the point of this is not to take away from Halladay’s fantastic performance Wednesday -- one in 6,500 is still quite amazing! But this statistical take shows that even after another postseason no-hitter was finally thrown 54 years later, Larsen’s perfect game back in 1956 remains in a class of its own.

Alok Pattani is a researcher for ESPN Stats and Information

### Halladay: King of the Yankee-killers

June, 14, 2010
6/14/10
8:17
PM ET
To say that Roy Halladay owns the Yankees is an understatement. To say that Halladay dominates the Yankees is a disservice as well. Even referring to him as a Yankee-killer, as old-timers do with a pitcher like Frank Lary, doesn't necessarily convey his skill.

It's hard to describe just how good Halladay has been in his career against the Yankees, but let's come up with five ways in which we can try, prior to his start against them Tuesday night.

1. Let's start with the most basic piece of information: wins and losses. Halladay is 18-6 all-time against the Yankees, good for a .750 winning percentage against them.

Only two pitchers who have more than 20 decisions against the Yankees have better win-loss records: You've heard of the all-time leader, Babe Ruth (17-5, .773). No. 2 is early 20th-century Hall of Famer Addie Joss (28-9, .757).

2. Wins and losses rarely tell the whole story. Let's go one step further. Halladay's career ERA against the Yankees is 2.84. Let's look strictly at this time period -- the wild-card era (since 1994) -- before venturing further.

Halladay's 2.84 is not just the best among the 19 pitchers who have thrown 100 innings. It's the best by an overwhelming margin. Here are the only pitchers among that group with ERAs under 4.00.

Halladay, 2.84; Pedro Martinez, 3.20; David Wells, 3.47. The other 16 pitchers all have ERAs over 4.

3. Let's broaden the scope to cover all time periods, which we can do, thanks to the Elias Sports Bureau. Rob Tracy at Elias looked at pitchers' ERAs against the Yankees and compared them to the ERAs of other pitchers of the time specifically against the Yankees.

Halladay stacks up about as well as can be historically. In the time in which he pitched, the average pitcher had an ERA against the Yankees of 5.15. He's nearly 81 percent better than the average pitcher (giving him an ERA+ of 181). And look who Halladay ranks ahead of historically (among those with 200 innings against the Yankees) -- only the guy many consider the best pitcher ever, Walter Johnson.

The only pitcher listed who is better: Hoyt Wilhelm, made only 13 starts. The knuckleball specialist dominated the Yankees primarily from the bullpen.

4. Halladay has seven complete games in 35 starts against the Yankees. No other pitcher in the wild-card era has more than four. In fact, to find another pitcher with seven complete games against the Yankees, you have to stretch the span back to measure from 1987 to 2010.

If you do that, Roger Clemens has seven as well. But his mark against the Yankees in that span pales in comparison, 16-12 with a 3.70 ERA.

For those who say it's easy for Halladay to rack up that many complete games given the number of starts he's made, consider this: Halladay has completed seven of 35 starts, which equates to 20 percent.

Of the 72 pitchers to have made at least 10 starts against the Yankees since 1994, only a dozen have multiple complete games against the Yankees. And of those 12, only Chris Carpenter has completed 20 percent of his starts against the Yankees (two out of 10)

For the record, Tom Candiotti, Omar Olivares, Steve Ontiveros and Todd Stottlemyre all have had two complete games in fewer than 10 starts against the Yankees within this time period. None dominated the Yankees though. The lowest ERA from that group is Ontiveros's 3.48.

5. Let's close by looking at the performance of the Yankees' captain against Halladay.

Derek Jeter career: .242 BA, no home runs, 100 plate appearances.

There is a group of 16 pitchers with which Jeter is most familiar, having faced them 50 times or more. He shreds most of those on the list, with a couple of exceptions.

Within that group, there's no one he dreads more than Halladay. Jeter's .296 on-base percentage against Halladay is his worst against anyone in that group by 21 points. And his .582 OPS is 65 points worse than against any other.

So if he's good enough to embarrass Jeter, that (and our other four points) should be enough to declare him among the best Yankee-killers there is.

Mark Simon is a researcher for Baseball Tonight. Follow him on Twitter at @msimonespn or e-mail him at webgemscoreboard@gmail.com.

##### CC Sabathia
 WINS ERA SO IP 14 4.78 175 211
BAR. Cano .314
HRR. Cano 27
RBIR. Cano 107
RR. Cano 81
OPSR. Cano .899
ERAH. Kuroda 3.31
SOC. Sabathia 175