Talk about long shots

Compared with Sunday night's battle against the hated Yankees, last night's game with Toronto was a day at the beach for Daisuke Matsuzaka. (JIM DAVIS/GLOBE STAFF)

The probability of four consecutive home runs? The unscientific answer is easy: You have a better chance of winning the lottery.

"Ain't no doubt about that," closer Jonathan Papelbon said yesterday.

The mathematicians are a bit more precise in their calculations. So we enlisted the help of three of them: Susan K. Reynolds, a Red Sox consultant; Dr. Nancy Rallis, a professor of mathematics at Boston College; and Jim Lackritz, associate dean for academic affairs at San Diego State, who was called upon to do similar calculations when the Dodgers hit four in a row against the Padres last September.

All were in agreement on how to calculate the odds of any team hitting four consecutive home runs.

"What is needed in finding the various probabilities that you are interested in is the following ratio: p=the total number of home runs hit in the major leagues, divided by the number of plate appearances," Rallis wrote in an e-mail. It would be reasonable, she said, to use the numbers from 2006 to come up with that number.

Last season, there were 5,386 home runs hit in 188,052 plate appearances. Thus p is equal to .02857.

The probability of four consecutive home runs is p to the fourth power, or p times p times p times p. That equals .000000673, which in this case means there is a 1 in 1.4 million chance.

J.D. Drew, who was one of the four Sox players to homer consecutively Sunday night, also was one of the four Dodgers who homered consecutively last September. On each occasion, Drew was the second in the sequence of batters.

To calculate the probability of that happening, Rallis wrote, you need Drew's ratio of home runs per at-bat, which is 1/19.6. You multiply four times p to the third power (p x p x p) times 1/19.6 x p to the third power (p x p x p) x 1/19.6.

That's 7 in 100 million.

Or 1 in 14.3 million.

It gives you some idea of how remarkable an event took place Sunday night.

"I was getting stretched by the trainer, Mike Reinold," Papelbon said. "He says, 'I'm calling J.D., back to back.' I'm like, 'No way, dude, you called it.' I'm sitting there, thinking surely they're not going to hit another one, and sure enough, bam, Mikey Lowell goes off.

"I jump off the table. I'm thinking, 'If this guy [Yankee rookie Chase Wright] throws another one . . .

"But you know, all he was thinking was, 'Don't give up a home run.' And dude, it almost never fails, he threw it again."

Papelbon said he felt some sympathy for Wright, who last season was pitching for Single A Tampa and yesterday was optioned back to the minors to make room for Hideki Matsui, who came off the DL.

"Of course you do," Papelbon said, "but that's the bitterness of it. It's not easy to pitch in the American League East."

Craig Shipley, the Sox international scouting supervisor who negotiated the signing of Hideki Okajima last winter, said the Sox didn't sign the lefthanded reliever just to caddie for Daisuke Matsuzaka.

"We were confident he would be able to handle pitching in Boston," Shipley wrote in an e-mail. "That confidence was based on his background and his stuff. He was drafted by and played for the [Yomiuri] Giants for 11 years, a team that gets as much attention as any in the US.

"Hideki pitched as a starter, closer, and short reliever in the NPB. He closed the final game of the Japan Series in 2001 and was an integral member of Nippon Ham's pen last year when they won the Japan Series.

"I have read several articles that state Hideki was brought here to help Daisuke's acclimation. That is totally false. We signed Hideki because of his ability to help our club. We would have signed him even if we didn't win the bid for Daisuke."

A Sox executive said this weekend that another club had offered Okajima more money; Okajima confirmed that last night but said through interpreter Sachi Sekiguchi that it wasn't an issue.

"The Red Sox were the first team to offer me a contract," Okajima said. "I always pictured myself in Boston. No matter what someone else offered, I was going to pitch in Boston."

Sox CEO Larry Lucchino was among those stunned by the death of author David Halberstam, a frequent visitor to Fenway Park. "Oh my God," wrote Lucchino in an e-mail. "What a gigantic loss." Johnny Pesky, one of the subjects of Halberstam's best-selling book, "The Teammates," along with Ted Williams, Bobby Doerr, and Dominic DiMaggio, also expressed sorrow. "I feel very badly about this," Pesky said. "He spent quite a bit of time with me on the phone and at my house while he was writing the book. A very nice man. He was a great orator and writer. He fell in love with Dominic, who was definitely the smartest of all of us."

Terry Francona said Coco Crisp could have played last night -- he entered Sunday night's game as a defensive replacement after being a late scratch with a tight oblique -- but the manager gave Crisp another day to heal. Wily Mo Peña had a hit in four trips in Crisp's place, but in addition to a couple of tumbles in the field, he also hit the bag awkwardly after his sixth-inning single . . . Portland center fielder Jacoby Ellsbury has reached safely in all 11 Sea Dogs games, hitting in 10 of them.

Nick Cafardo of the Globe staff contributed to this report; Gordon Edes can be reached at edes@globe.com.