By Andrew Mooney, Boston.com Correspondent

In the death throes of the Bobby Valentine era, it was laughable to imagine the Red Sox as anything even close to resembling a feel-good story. Yet here we are at the end of April, with the Red Sox leading the AL East by three games while producing moments like this. And were those cheers from the Fenway faithful for John Lackey? It’s all too much to contemplate.

For a team not expected to do much of anything this year, Boston’s hot start comes as even more of a surprise. Let’s break down how they’re doing it, compared to their ho-hum start to the 2012 season.

The difference hasn’t come from the offense; in fact, the Sox have scored a nearly identical number of runs as they did last April. Daniel Nava and Shane Victorino have been pleasant offensive surprises, picking up the slack for the struggling bats of Will Middlebrooks and Stephen Drew. Still, on paper, this team shouldn’t produce nearly as much as last year’s lineup. One of the big question marks going forward is if the Sox will be able to sustain this level of run production—their team BAbip of .340 suggests a bit of a drop-off may be coming soon.

The transformation from a .500 team in April to a division leader has come about through improved performance on the mound. Resurgent stuff from Clay Buchholz and Jon Lester, as well as offseason pickup Ryan Dempster, has made Boston’s pitching staff into the American League’s second-best unit, behind only Texas. The bullpen has been on par with the starters; instead of comically blowing leads as they did last April, the relief staff, led by a healthy Andrew Bailey, has been dependable in locking up wins. As a whole, Boston hurlers have struck out nearly 100 more batters than they did through the first month of 2012, a big reason for their success.

Apparently that’s the formula for morphing from the city’s most scorned team into perhaps its most inspirational: a new cast of characters, solid bats, and lockdown pitching. Still, the team has yet to play even a sixth of its full schedule, so if you’ve been saving up some vitriol to spew at John Henry and crew, stay tuned.

By Andrew Mooney, Boston.com Correspondent

In 2013, it seems safe to say that by almost any measure—viewership, ticket sales, merchandising—America considers football to be its national pastime. Gone are the days when youngsters snuck into the Polo Grounds or Fenway Park to catch the matinee performance of their favorite ballplayers; now is the era of Friday Night Lights and Madden.

Of course, only the thinnest slice of those kids who grow up dreaming of gridiron glory actually achieve it at the highest professional level; over a million U.S. teenagers play high school football, and only 1,696 roster spots exist in the NFL. Yet despite this miniscule success rate, nearly two thousand successful cases is certainly a large enough sample on which to perform some analysis. In this case, I’ll look at how that NFL talent is distributed across the country.

I examined the birth states of all active NFL players from the records kept on pro-football-reference.com and combined this with state population estimates from 2012 U.S. Census data. There were quite a few players that PFR listed as having “Unknown” birthplaces, but I assumed for the purposes of this post that the distribution of this group’s birthplaces was similar to the data I was able to gather. Armed with this dataset, I determined the most prolific football talent-producing states, both on an absolute and per capita basis.

The first state north of the Mason-Dixon line to appear on the per capita list is Nebraska, at number eight. Though the state contains less than two million people, 14 Nebraskans are on NFL rosters at present.

It’s not surprising that the South, the holy land of football, leads the way in NFL players per capita with seven of the top ten states. But the top individual states aren’t the ones you might expect. The triangle of Louisiana, Mississippi, and Alabama comprise three of the top seven states, all of which lie ahead of traditional football sanctuaries Texas and Florida.

Of course, these latter two are penalized by this method of measurement for their sheer size. In absolute numbers, Texas and Florida rank second and third in number of active pros with 130 and 107, respectively. The only other state to surmount the century mark for active players is the behemoth of this list, California, which boasts 143 current NFL players. Though it has by far the largest population of any state in the country (nearly 50 percent larger than second place Texas), California still comes in around the middle of the pack (18th) in the per capita rankings, a testament to the football prowess of the Golden State.

Bringing up the rear is New England. Despite a near-dynastic pro franchise in close proximity, the Northeast produces almost no native NFL players of its own. Maine, New Hampshire, and Rhode Island have a combined two players currently in the NFL. Massachusetts, the home state of the Patriots, has a slightly less embarrassing total of seven active players, and Connecticut, a state of a little over three million people, has a respectable 11. Still, just two in a million people from all of Patriots territory have reached the highest level of the sport.

If you'd like to see the complete lists, click on the Full Entry button.

By Andrew Mooney, Boston.com Correspondent

After closing the season out on a 37-2 tear and finishing with a league-high 66 wins, the Miami Heat are generally considered the presumptive favorite for the NBA Championship. Vegas certainly agrees with this sentiment; vegasinsider.com currently has Miami at 1-to-2 odds to repeat, with the Oklahoma City Thunder a distant second at 5-to-1 odds. But is it fair to so preemptively crown LeBron James and crew for the second year in a row? When digging into the numbers a little more, the supremacy of the Heat is not nearly so obvious.

When one witnesses Russell Westbrook jacking a long pull-up two in transition, the first word to come to mind is not “efficiency.” Yet the Thunder offense was nearly as efficient as Miami’s in 2012-13, scoring 112.3 points per 100 possessions compared to 112.4 for the Heat, according to Basketball Reference. One reason for this is the Thunder’s ability to both get to the free throw line and convert attempts there; OKC was second in the league in free throw attempts and first by a significant margin in free throw percentage at 82.8.

The Thunder are also a vastly underrated defensive team, allowing 102.6 points per 100 possessions this season, good for fourth-best in the NBA and 1.1 points fewer than the Heat. In choosing to keep Serge Ibaka over James Harden this past offseason, Oklahoma City retained one of the league’s most formidable defensive front lines in Ibaka and Kendrick Perkins. Ibaka blocks 7.4 percent of opponents’ two-point shots while on the court, leading the league in that category among power forwards.

In the regular season, the Thunder owned the NBA’s top point differential, outscoring opponents by 9.2 points per game, over a point better than the Heat’s 7.9 per-game differential. So how is it that Miami finished six games better in the standings than Oklahoma City? Part of the reason is the teams’ respective records in close games; the Thunder were 4-5 in games decided by one possession, while the Heat were 9-3. If a few more bounces go OKC’s way late in some of those games, the gap between the teams begins to look much slimmer.

I see a bet on Oklahoma City at the present odds having significant positive expected value; certainly their odds at a title aren’t 50 percent lower than the Heat’s, which is how the teams’ chances are currently priced. The Thunder must travel a much more difficult road through the Western Conference to get back to the Finals, but once there, they should perhaps be considered the favorite over anyone they might meet—and that includes Miami.

By Andrew Mooney, Boston.com Correspondent

Cue Jim Nantz and the tinkling piano: the Masters is officially under way. The field of 93 will attempt to duplicate the legendary green jacket-winning performances of years past, including a “who’s who” of golfing royalty: Tiger Woods, Jack Nickalus, Arnold Palmer, Phil Mickelson, Seve Ballesteros.

Though the competitors always play the same course, Augusta National has undergone many significant changes since it hosted the first Masters tournament in 1934. As a result, it’s difficult to compare performances at the Masters across the years. Simply tabulating raw scores is not the most accurate way to do it; in different years, the field faces different temperatures, winds, and moisture, not to mention the alterations to the course itself and the equipment in players’ bags.

In a piece written in 2011, Grantland’s Bill Barnwell proposed another method for evaluating golf scores using a statistical measure called a Z-score. Barnwell’s argument was that a golfer’s actual raw score was less important than how that score compared to the rest of the field.

Take two victories by Golfer A and Golfer B, each of whom shoot 11-under-par, while the runners-up each shoot 6-under-par. They look equal, but the rest of the field's performance matters. Let's say the third-place finisher in Golfer A's tournament shoots 5-under-par, but the third-placed duffer in Golfer B's tourney shoots 1-over-par. Player B has clearly outperformed the rest of the field to a greater level than Player A, but raw margin of victory fails to capture that detail.

A Z-score measures the number of standard deviations a particular observation is from the mean of those observations. When applied to golf scores, a Z-score can tell us how different a player’s score was from the average, in addition to incorporating the range of those scores. Barnwell applied this method to the four major tournaments and recorded the top-20 performances since 1960, three of which came at the Masters, which you can read here.

As the first round kicks off today, I decided to examine the greatest performances in the history of the Masters more in-depth. I gathered the 72-hole scores for every Masters tournament, pulling the data from golfobserver.com all the way back to 1934. I then converted each year’s raw scores into Z-scores so I would have a uniform standard for comparison across years. Since a low score in golf is good, a more negative Z-score reflects a better performance. The 20 best scores are in the table below.

Many people point to Tiger Woods’ 1997 Masters as the most impressive 72 holes Augusta has ever seen, significant not only for his otherworldly display of golf, but for the fact that it came at age 21, it was his first major win, and it was the first time a non-white player had won the tournament.

Though Woods’ score of 270 remains a tournament record, his performance was slightly less superior relative to the rest of the field than Jack Nicklaus’ 271 in 1965. Woods defeated second-place Tom Kite by 12 strokes in 1997, three more than Nicklaus bested Arnold Palmer by. But only eight other players were under par in the 1965 tournament, compared to 15 in 1997. Nicklaus’ lower Z-score suggests that his total of 17-under came in a more difficult overall course environment and thus exhibited more dominance than Tiger’s 18-under.

A couple of other takeaways from this list:

• Woods, Nicklaus, Raymond Floyd, and Nick Faldo are the only golfers to appear on this list more than once.
• In 2005, Chris DiMarco submitted one of the best-ever Masters performances and finished second, falling to Woods in a playoff, much to the relief of the Nike marketing department.
• Doug Ford tied with Tommy Aaron for the worst to-par score on this list at five-under, but in Ford’s case, only two other players in the tournament finished under par.
• In gathering this data, I was also able to uncover the worst performances in Masters history (for players that made the 36-hole cut). The most shameful 72-hole score at Augusta came in 1940, when Chick Evans posted a 43-over, shooting 82-84-86-79 for a total of 331 (Z-score: 3.627). In second-to-last place is the aforementioned Tommy Aaron’s 2000 Masters, which came 27 years after he donned the green jacket. A score of 25-over can be forgiven for a man of 63, but it still yielded a ghastly Z-score of 3.346.

By Ray Charbonneau, Boston.com Correspondent

The saying "Everybody complains about the weather, but nobody does anything about it," probably wasn't coined by a runner, but it should have been. Part of every runner's preparation for the Boston Marathon is a prayer to the weather gods, asking for favorable conditions. The weather has a major impact on the results of any road race, and Boston weather always presents a multitude of possibilities to marathoners on Patriots' Day, many of them unpleasant.

The right weather can help speed runners on their way along the 26.2 mile course from Hopkinton to Boston. But no matter how fast you are or how hard you've trained, when Mother Nature tosses out a day like she did last year -- the sun was bright, the air was still, and temperatures were near 90 -- everybody's performance suffers significantly.

Historically, Boston’s typical April weather is actually pretty good for marathon running. According to one study, elite runners run fastest when the temperature is about 39 degrees Fahrenheit, while the slowest runners in the study performed best at about 50 degrees. Another way of looking at the effect of temperature is to examine the frequency at which runners drop out of races. The fewest runners drop out when the temperature is about 53 degrees.

The average temperature in Boston in mid-April is not too far from that ideal, ranging from about 47 degrees at 9 am, when the first runners leave Hopkinton, to a high of 53 degrees by 4 pm, when the last runners are crossing the line on Boylston St.

The average temperature may be conducive to fast running, but as Mark Twain once said, "There is a sumptuous variety about the New England weather that compels the stranger's admiration -- and regret." The link between higher temperatures and slower finish times is very strong. Over the last ten years, the correlation coefficient is 0.8, which represents a very strong positive correlation. A mid-pack runner's time slows about 18 percent when race temperatures go up 20 degrees. Someone capable of running a 3:28 under “ideal” conditions would be projected to run about 4:05 when the temperature on race day hits 70 degrees.

Slower runners are affected more by an increase in temperature, perhaps in part because they're out on the course longer. Since most races start in the morning, temperatures are usually lowest for the start and then rise during the race. Thus, the average race temperature for most races is higher for slower runners than for faster runners. This is especially true for Boston, where the slower runners start well after the elites.

The wind can also have a major effect on marathon runners. Wind matters more in Boston than at other races. If a course loops around so the finish is near the start, the effect of the wind is more likely to even out, pushing runners ahead at some points and back at others. But since Boston is a point-to-point course, the wind can blow at runners from one direction for the entire race.

All else being equal, the drag on a runner created by air resistance varies according to the square of the runner's velocity through the air. That means that the performance hit from a 10 mph headwind is four times greater than that from a 5 mph wind.

A tailwind helps runners, but not quite as much as a headwind hurts them. One estimate says that, when running at a six minute-per-mile pace, a 10 mph tailwind would increase one’s performance by about 6 seconds per mile, while the equivalent headwind (six-minute miles into a 10 mph wind) slows one down by about 12 seconds per mile. That's a possible swing of almost eight minutes over the course of a marathon.

According to Windfinder.com, April is Boston's windiest month, averaging about 14 mph. The chance that the wind is 13 mph or more is 55 percent. Most often, April's wind is from a little south of east -- a headwind for the race -- but tailwinds are also fairly common.

Unlike heat, the wind affects faster runners more than slower runners. The additional resistance from running into a steady wind at a 5:40 mile pace is twice that encountered when running into the same wind at a 8:00 mile pace. Unfortunately, that's not much of a consolation for the slower runner, who still has to spend an extra hour fighting against the wind.

Runners can counteract much of the negative effect of a headwind by "drafting." A marathoner can reduce wind resistance by as much as 80 percent by running one meter behind another runner. The benefits of drafting drop off quickly as the distance between runners increases, so a marathoner needs to choose carefully when picking a runner to follow.

Wind isn't always bad. A stiff breeze on a hot day can help counteract the negative effect of the temperature. On the other hand, on a cold day the wind can make the last few miles miserable for tired, sweaty runners. In 2007, when the race was held during a nor'easter, 20-30 mph headwinds combined with temperatures in the 40's left a number of runners in the medical tent getting treatment for hypothermia.

Temperature and wind have the greatest effect on runners, but precipitation also makes a difference. In April, there's almost a 50 percent chance of some form of precipitation at some point during the day in Boston. The last time there was any snow on Patriot's Day was in 1961, but rain is common. Rain on a hot day helps runners stay cool enough to keep going, but there are few hot, rainy days in April. Marathoners have to use more energy when running in weather that is cold and wet.

It's true that "if you don't like the weather in New England now, just wait a few minutes." Unfortunately, marathoners standing at the line in Hopkinton can't wait for perfect weather. They hope for the best but have to ready to deal with the worst. For their sake, let's hope that in 2013, Zeus, Amadioha, Feng Po, Zephyrus, Amm, and all the other weather gods cooperate and bring cool breezes on Patriots’ Day to help speed all runners on their way to Boston.

This year, Ray Charbonneau is running the Boston Marathon (his fifth) as a sighted guide for a vision-impaired runner. 50 percent of the proceeds from sales of his latest book, Overthinking the Marathon, go to benefit the Mass. Association for the Blind. Ray's articles on running have appeared in the Boston Globe, Ultrarunning, Marathon & Beyond, Level Renner, Cool Running and other publications. Find out more at y42k.com.