By Andrew Mooney, Boston.com Correspondent

On the surface, the matchup looks awfully familiar. The Celtics, the league’s best defensive team, meet the explosive Miami Heat in the Eastern Conference playoffs. But with a year elapsed since Miami’s five-game series victory over Boston—and a year’s wear and tear added to the Celtics’ veteran odometers—why should we expect this installment of the rivalry to be any different?

As it stands now, however, history can’t tell us much. Injuries have distorted these teams’ makeups such that games from last season, or even earlier this season, are not particularly instructive for predicting what will unfold between the two teams starting tonight. Still, it’s worth examining the matchups we will see in this series to get a better sense of the task now facing the Celtics.

Miami’s offense all season has been predicated on the pick-and-roll penetration of LeBron James and Dwyane Wade. But without the deadly 15-foot jump shot of Chris Bosh, who accounted for 18 percent of the Heat’s scoring during the regular season, the Celtics can follow the Pacers' blueprint and clog the lane against that penetration. The Heat's other candidates to knock down the pick-and-pop jumper: Udonis Haslem (39 percent from midrange) and Joel Anthony (yikes).

For Boston, the primary difficulty will be finding adequate defenders to slow down James and Wade. Paul Pierce has done a so-so job defending James the last two seasons; in 11 games dating back to last year, LeBron has averaged about two points more per 36 minutes with Pierce on the court than when he’s on the bench.

But the biggest concern, with shoulder surgery ending Avery Bradley’s season, is finding anyone to stop Wade. By default, that role falls to a hampered Ray Allen, and if Wade keeps up the level of offensive production he displayed over the last three games against the Pacers (33.0 points per game on 61.5 percent shooting), Allen won’t be in any position to stop him.

Slowing these two down, then, will require a total team defensive effort, which means peripheral defenders coming off their men to help out and double team. Perimeter shooters Mike Miller (45.3 percent from three), James Jones (40.4 percent) and Shane Battier (33.9 percent) will get their open looks, and if they knock them down consistently, the Celtics are in trouble.

Of course, the Celtics do have Rajon Rondo as their trump card, but it’s unclear whether his superiority over Mario Chalmers will be enough to counterbalance the prolific play expected from James and Wade. Michael Wilbon wondered aloud on ESPN whether the Heat’s two “great, great” players could defeat Boston’s four “great” players, and, by at least one metric, it appears they can. A look at Win Shares—a measure of how much a player contributes to his team’s wins over a season, offensively and defensively—on basketball-reference.com shows the Heat’s top four remaining players (not including Bosh) enjoying a 30 to 23.5 advantage in Win Shares, with James and Wade alone contributing 22.2.

Yet, despite that bleak assessment, I still expect the Celtics to take the floor at AmericanAirlines Arena tonight, and the only information we can be sure of is what we see once the ball tips. Far be it from me to dismiss these Celtics, who have warded off the dark embrace of Father Time for another series with stifling defense and timely shooting. Unfortunately, the Atlanta Hawks and Philadelphia 76ers are not the Heat, and, as sad as it is to admit, the end of an era probably starts tonight.

By Andrew Mooney, Boston.com Correspondent

As ESPN’s John Hollinger artfully illustrated in April, the Celtics’ dramatic turnaround from has-been, elder statesmen of the East to dangerous veterans bent on one last title run can be attributed almost entirely to their defensive resurgence. The introduction of Avery Bradley into the starting lineup and the shift of Kevin Garnett from power forward to center transformed a .500 team into a dark horse Finals pick.

The numbers back up the wisdom of this lineup shift. With what was the team’s most common five-man unit of Rajon Rondo, Paul Pierce, Brandon Bass, Kevin Garnett, and Ray Allen, the Celtics’ defensive efficiency (number of points allowed per 100 possessions) was 98.9 during the regular season—solidly below the league average of around 102, but still unspectacular, given that the unit was only just above the league average for offensive efficiency (103.4 points per 100 possessions).

But, after Allen’s nagging ankle injury caused Bradley to be inserted into the lineup, the Celtics have been a far more productive team, on both ends of the court. The unit of Rondo, Pierce, Bass, Garnett, and Bradley allowed just 89.8 points per 100 possessions, almost a full six points better than the team’s overall average (95.5). They have also been a superior offensive unit, averaging 109.4 points per 100 possessions, powered by a highly efficient shooting percentage (50.6 percent) from the field.

However, though this lineup is capable of locking down an opposing offense, it remains plagued by the one aspect of defense in which the Celtics have been notably deficient all year: rebounding. This is not a problem unique to this five-man unit, but rather due to the team’s construction; the Celtics' relative lack of size in the frontcourt makes them susceptible to getting pounded on the offensive glass, an issue that has increasingly come to light this postseason.

Friday’s Game 4 against the 76ers was particularly representative of this phenomenon. Though the Celtics held Philadelphia to 37.8 percent shooting from the field, the 76ers attempted 11 more shots from the field, in large part because of their 17-5 edge in offensive rebounds. As the Celtics discovered, stingy defense becomes less of a weapon when allowing more possessions each trip down the court.

In fact, the Celtics’ fortunes during the playoffs have closely followed their performance in the rebounding battle. In their series with the Hawks and now the 76ers, the Celtics have won every time they have outrebounded their opponent (5-0). When they have trailed their opponent in rebounding margin, however, the Celtics are just 1-4, with the only victory coming in the Game 4 blowout of Atlanta. In those four losses, the Celtics have been outrebounded 190-148, and in only two of these 10 contests have the Celtics held the advantage in offensive rebounding margin.

So far, the Celtics have been able to get by despite their futility on the boards due to their otherwise outstanding team defense; in ten postseason games, Boston opponents are shooting, on average, just 40.51 percent from the field. But, as happened Friday, much of that advantage is nullified when giving up a significant edge in offensive rebounding, and thus, additional attempts at the basket. Tied at two, the series looks to be a toss-up heading into Monday’s pivotal Game 5. The result may hinge not on the offensive production of Kevin Garnett and Brandon Bass, but on the ability of the frontcourt to clean the glass and prevent second chance points.

Boston Dirt Dogs photo illustration

By Andrew Mooney, Boston.com Correspondent

Ah, May 15. That day of universal celebration across Red Sox Nation: Josh Beckett's birthday. On this merry occasion, Beckett's mailbox will surely be stuffed with the most fervent wishes of well-being from his legions of adoring fans. And he'll even be returning the favor, toeing the rubber this afternoon against the Seattle Mariners and doubtless delivering a gift of a performance to his supporters -- all 15 of them.

Sarcasm aside, Red Sox fans have unfortunately been led to expect next to nothing from Beckett, given his last few months in the spotlight. He has supplemented subpar performances on the mound by being at the center of nearly all the negative PR currently surrounding the team. For some reason, an ERA hovering around six doesn't put people in a forgiving mood.

But Beckett's struggles on the field shouldn't be attributed to the deteriorating clubhouse environment he has helped to create; plenty of malcontents have been consistently great players, and his attitude doesn't affect the jump on his fastball. What should be more alarming for the Sox is the fading strength of Beckett's 32-year-old right arm.

Beckett's velocity topped out in 2006, his first season with the Red Sox. His fastball averaged 94.7 mph, and he relied on the pitch heavily, throwing it 69 percent of the time. Between '06 and '09, his velocity remained relatively constant, but he began utilizing his peripheral pitches more frequently, throwing his curveball and changeup more often and even mixing in a cut fastball. He was one of the most productive pitchers in baseball over this period, ranking 12th among all hurlers in Wins Above Replacement.

In 2010, Beckett turned 30 -- bad news for any athlete, pitchers included. A study on peak age for pitchers conducted by Tom Tango found that, on average, the number of innings pitched for all pitchers tops out at age 27. Pitchers' value (measured in WAR per game) continues to increase until it crests at age 30, due to the inability of below-average pitchers to remain in the league beyond their mid-20s physical peaks; in other words, only good pitchers are able to stay in the majors into their 30s. Even so, as Tango writes, pitchers "are definitely on the down slope starting at age 30."

Beckett appears to be no exception to this trend. Since turning 30 in May of 2010, he has lost about three MPH off both his fastball and curveball, suggesting his arm just doesn't have the life it once did (all data courtesy of Fangraphs).

Things have only gotten worse in 2012. Beckett has thrown his fastball at 91.5 mph, on average, and he seems to have recognized the relative weakness of the pitch; he has thrown it at a career-low rate of 49.7 percent during the young season. To compensate, Beckett has added a much higher proportion of cutters and changeups, which seems to be a sensible adjustment for an older pitcher -- except that, so far, it hasn't really worked, as evidenced by the results he's gotten on the field.

Within this context, his mostly exceptional 2011 begins to look more like an aberration. He was the beneficiary of luck and good timing for much of last year; he allowed a career-low .245 BABIP -- which may have had something to do with his new, more deception-based approach -- and stranded a career-best 80 percent of runners he allowed on base.

But it's still too early to pass any definitive judgment. We'll need to see more of a healthy Beckett in 2012 to determine whether the sudden drop in velocity is due to a pesky lat or a significant decrease in ability. Perhaps he can recapture some of the 2011 magic by pitching smarter, not harder.

The bottom line? Beckett will have to reinvent himself a lot more successfully than he's done early in 2012 if he hopes to be in Boston for much longer -- which is itself a pretty big question mark. If he continues to struggle, expect the Red Sox to try to unload him sooner rather than later; Beckett is owed more than $47 million through 2014, and the Sox' books are already bloated with aging, underperforming (or not-at-all performing) pitchers. The party might be over before he knows it.

By Andrew Mooney, Boston.com Correspondent

The Red Sox front office did everything they could this offseason to make 2012 a fresh start. Out went general manager Theo Epstein and manager Terry Francona, veterans of two World Series-winning teams. The new power structure included additions from inside and out, with Ben Cherington ascending to the role of GM and wild card Bobby Valentine brought in as manager.

So much for shaking things up. The team’s uneven performance in April did little to dispel the discontent surrounding last September’s collapse. In fact, you could be forgiven for confusing the two months; the Sox’ numbers during these two periods were eerily similar.

In September 2011, the Sox ranked among the top five in the majors in batting average, slugging, on-base percentage, hits, and runs scored, scoring ten runs or more five different times. They were well ahead of the Rays, with whom they were competing for the final playoff spot in the AL, in all these categories.

Boston’s bats were again hot this April. Paced by the near-.400 hitting of David Ortiz and pleasant surprises Ryan Sweeney and Mike Aviles, the Sox led the major leagues in runs scored and were second in hits, batting average, and slugging.

The problem, to no one’s surprise, was pitching. As has been well documented, the Red Sox staff sported a league-worst 5.84 ERA last September, highlighted by the starting rotation’s 7.08 ERA. In April, the Sox ranked second-to-last with a 5.54 ERA, slightly ahead of the hapless Minnesota Twins.

This time, the bullpen was the weak link. Led by new acquisition Mark Melancon’s rancid 49.50 ERA, Red Sox relief pitchers set the standard for futility in the young season with a collective 6.10 ERA, worst in the majors.

Obviously, the team has struggled to deal with the loss of new closer Andrew Bailey, and he’ll presumably bring some stability to the unit when he returns around the All-Star break.

But, if April is any indication, the Sox face an even more daunting divisional battle than last season. In case you didn’t notice, Boston currently sits last in the AL East, despite finishing April with seven wins in eight games. Now, whether Baltimore and Toronto can continue to mount serious playoff bids is questionable, but they can no longer be considered doormats. If the Red Sox hope to seriously contend this year, they will need a major improvement in the contributions of…well, just about every pitcher on the staff.

By Andrew Mooney, Boston.com Correspondent

Chicago White Sox lefthander Philip Humber briefly seized the national sporting spotlight on Saturday, throwing the 21st perfect game in Major League Baseball history in a 4-0 victory over the Seattle Mariners.

As of Sunday, there have been 200,304 MLB contests played and the league has seen just about every feat accomplished dozens, if not hundreds of times, making the perfect game that much more of a special achievement. It’s also something that seems to happen at random; most of the greatest pitchers in baseball history have never thrown one, and two of the last three players to do so had fewer than 20 career wins at the time.

According to the MLB rule book, a perfect game is defined as “when a pitcher (or pitchers) retires each batter on the opposing team during the entire course of a game, which consists of at least nine innings. In a perfect game, no batter reaches any base during the course of the game.” Assuming a typical nine inning game, how difficult is it to prevent 27 consecutive batters from reaching base?

Using records from baseball-reference.com, I obtained the average on-base percentage in major league history, which, dating back to the 1876 season, is .326. However, on-base percentage doesn’t factor in another way a perfect game can be broken up: an error committed by a fielder.

From the historical record, I found that, all time, there have been 497,649 errors recorded in major league play, in 15,341,862 total plate appearances. However, of that error total, some fraction includes errors committed following a hit, when runners are already on base, such as an overthrow of the cutoff man that allows a runner to advance a base. These errors could not occur in a perfect game, as there cannot be any baserunners to begin with. I estimate the proportion of such errors to be one-third.

So, if two-thirds of errors result in a baserunner instead of a routine out, I should also multiply the complete error total by two-thirds to determine the number that might disrupt a perfect game. This amounts to an error rate of 2.16 per 100 plate appearances (.0216).

When I add this modified error rate to on-base percentage, the resulting number—.348—is the probability that the average hitter reaches base, or in other words, breaks up a perfect game. Conversely, the probability that a player does not reach base is 1 - .348 = .652. As an aside, I am treating the number of dropped third strikes and catcher’s interference calls as negligible, having no noticeable effect on the aforementioned probability.

Now, to find the likelihood of a perfect game, given a historically average pitcher facing a lineup of nine historically average hitters, I multiply .652 by itself 27 times. This gives me the probability that 27 consecutive hitters will not reach base against an average pitcher.

(.652)^27 = 0.00000983

As mentioned, there have been 200,304 games played in major league history, at the start of which two pitchers each have a chance to throw a perfect game. This brings us to 400,608 perfect game opportunities. Multiplying this number by the probability of the average perfect game gives me the number of perfect games that we would expect to have been thrown in history, based simply on the odds of their occurrence.

0.00000983 x 400,608 = 3.94 ≈ 4.00 perfect games, or one every 34 seasons

From these calculations, we can see that there have actually been more than five times as many perfect games (21) as the probabilities dictate. In fact, for the expected number of perfect games to equal 21, the historical average on-base percentage would have to be 0.284, or roughly the rate at which hitters reached base in 1883, that noted year of offensive explosion. If you need any more context, that’s lower than what we’d expect hitters to post against a league in which every pitcher was Greg Maddux or Randy Johnson.

Curiously, there has been a relative eruption of perfect games in the last decade. In the last four years alone, four pitchers—Mark Buerhle, Dallas Braden, Roy Halladay, and Humber—have achieved perfection, and one other pitcher, Armando Galarraga of the Tigers, was one blown call at first base from making it five. Given the odds listed above, the chances of four perfect games occurring in this four-year span (15,046 games) are 1.77 in 100,000.

Suffice it to say, they're pretty rare. A major league baseball pitcher has better of odds of dying in a lightning strike than tossing a perfect game. That’s all the more reason to appreciate Humber’s big day, though I don’t anticipate we’ll hear of him striking twice anytime soon.