Two weeks ago, I wrote about using run differential as a tool for predicting a team’s success. Today, let’s advance to Sabermetrics 201 for a lesson on “cluster luck.”

Joe Peta, a former Wall Street trader, presented cluster luck in his book, Trading Bases. Essentially, the concept boils down to this: When a team’s batters cluster hits together to score more runs and a team’s pitchers spread hits apart to allow fewer runs, that’s cluster luck. Say a team tallies nine singles in one game. If all of those singles occur in the same inning, the team would likely score seven runs; if each single occurs in a different inning, however, it’d likely mean a shutout.

To gauge whether cluster luck might be affecting this year’s results, let’s turn to ThePowerRank.com, a site maintained by sports analyst and Grantland contributor Ed Feng. The Power Rank calculates cluster luck by using the Base Runs formula to compare actual runs scored and runs allowed to expected runs scored and runs allowed. Here’s a look at how all 30 teams ranked based on clustering through Monday’s games, from luckiest to unluckiest. The first figure in parentheses represents runs-scored luck, the second is runs-allowed luck; positive values indicate good fortune, while negative values point to poor luck.

1. Seattle: 24.88 (25.65, -0.77)

2. San Francisco: 22.43 (0.08, 22.35)

3. New York Mets: 21.23 (6.35, 14.89)

4. Toronto: 14.52 (-6.88, 21.40)

5. Oakland: 14.51 (8.27, 6.24)

6. Texas: 12.26 (0.96, 11.30)

7. Kansas City: 11.39 (9.96, 1.42)

8. Baltimore: 8.72 (-6.69, 15.41)

9. Boston: 6.49 (-8.15, 14.65)

10. Philadelphia: 4.99 (-4.07, 9.06)

11. Miami: 4.79 (-2.19, 6.98)

12. Milwaukee: 3.72 (-14.83, 18.55)

13. Detroit: 2.07 (-4.47, 6.55)

14. San Diego: 0.56 (-8.12, 8.69)

15. Washington: -0.23 (-6.37, 6.14)

16. New York Yankees: -0.97 (-2.06, 1.09)

17. Chicago White Sox: -1.45 (13.48, -14.94)

18. Minnesota: -1.74 (5.75, -7.49)

19. Colorado: -3.56 (-10.81, 7.26)

20. Atlanta: -6.39 (-18.80, 12.41)

21. St. Louis: -6.71 (-8.75, 2.03)

22. Pittsburgh: -8.29 (-13.84, 5.56)

23. Cincinnati: -8.29 (-16.68, 8.40)

24. Los Angeles Dodgers: -10.01 (-19.67, 9.66)

25. Chicago Cubs: -11.20 (5.26, -16.47)

26. Los Angeles Angels: -13.33 (6.43, -19.76)

27. Cleveland: -14.16 (-4.88, -9.28)

28. Tampa Bay: -15.48 (-10.29, -5.19)

29. Arizona: -19.76 (-8.41, -11.35)

30. Houston: -25.45 (-15.10, -10.35)

These results tend to regress over time, which is bad news for the Mariners, who’ve scored about 26 more runs than expected while allowing only about one run more than expected based on average hit-clustering patterns. At the other end of the spectrum, teams like the Diamondbacks and Astros have combined terrible luck with being just plain terrible. And while we’ll have to see how things play out over the course of the season, slightly poorer results for the A’s and Giants and slightly better results for the Cardinals and Dodgers look like pretty safe bets.

More broadly, the takeaway is that positive values indicate teams that have been fortunate, and thus are more likely to see some pullback in their run-clustering luck as the season progresses. Meanwhile, teams with negative values have been unlucky, and thus are potentially due for better cluster luck the rest of the way. It’s not bankable, but it’s something to watch as we jump into the final two-thirds of the season.

For now, avoid the head, wear a cup, and hope for the best.

And be sure not to flinch.

It’s Week 8 of The 30.

Bat Flip of the Week

Ladies and gentlemen, for the first time in this award’s short but prestigious history, Bat Flip of the Week honors are going to a pitcher: Cubs ace Jeff Samardzija, who is second in the majors in ERA, yet has just one win to show for it. Whether Shark’s flip was an F-you to the pointless wins stat or just a little styling, he deserves this prize for displaying such flair on a routine pop out.

Loathsome Fivesome

These five clubs continue to bring up the rear.

30. Houston Astros (20-32 record, -49 run differential, no. 30 last week)

29. Arizona Diamondbacks (21-32, -66, LW: 29)

28. Chicago Cubs (19-30, -2, LW: 28)

27. San Diego Padres (23-29, -23, LW: 26)

26. Philadelphia Phillies (22-26, -27, LW: 27)

While Josh Beckett’s no-hitter Sunday afternoon in Philadelphia was a tremendous accomplishment for a pitcher returning from thoracic outlet syndrome, it was also a lowlight in what’s shaping up to be a lost season for the Phillies, who had an uncharacteristic offensive outburst Monday but have been shut out six times in their last 19 games.

Amid that kind of futility, a team will look for silver linings wherever it can find them, and Phillies pitcher David Buchanan offered one of those rare happy moments in his major league debut Saturday: With a 4-2 lead and speedster Dee Gordon dancing off third base in the fifth inning, Buchanan got ahead of Justin Turner 1-2, reared back, fired, and snuck a pitch right by the Dodgers third baseman. As the rookie walked off the mound, he received a rousing ovation from the crowd, including his dozen-plus friends and family in attendance. Amid the celebration, no one seemed too concerned about the particulars of the pitch, a navel-high, 82 mph changeup that many hitters would’ve launched to New Jersey.

Though we’re only through Memorial Day, the Phillies’ season has already been reduced to celebrating these small victories. After what seemed like a worst-case scenario 73-win season last year, the Phils are on a nearly identical pace this season, which means they’re probably going to start throwing some prospect spaghetti against the wall to see what sticks. Buchanan, who just turned 25, is a bit old to be making his MLB debut and isn’t an elite prospect. And while the Phillies’ farm system is improving and has some promising minor league bats, there are few exciting arms beyond Double-A left-hander Jesse Biddle. Still, it’s once again time to see if general manager Ruben Amaro Jr. will try to accelerate a youth movement that’s pushed twentysomething players like Domonic Brown, Cody Asche, and Ben Revere into the lineup.

If Amaro chooses that path, the most obvious approach would be to trade Cliff Lee for prospects. The 35-year-old southpaw was having another excellent season before hitting the DL, ranking fifth in the National League in Fielding Independent Pitching (2.61) and carrying the second-best strikeout-to-walk rate (6.8-to-1). This success is nothing new for Lee, who since 2008 leads all major league starting pitchers in FIP and K/BB rate and ranks fifth in innings pitched. He’s also found other ways to keep spirits high:

Buchanan’s debut gave the Phillies a glimpse into the Lee-for-prospects world, as the rookie’s start came in Lee’s usual spot in the order, with the lefty missing a start because of an arm injury for the first time in his career. The Phillies hope Lee’s DL stint will end in the minimum 15 days, but fans might want to bet the over. Lee said he’d been feeling sore since throwing a career-high 128 pitches in the aforementioned 13-strikeout loss against the Braves, and he’ll wait until later this week to have the flexor tendon strain in his pitching elbow reevaluated.

For those rooting for the Phils to expedite their “don’t call it a rebuilding” rebuilding process, Lee’s health will be the dominant story line for the next two months. He’s owed about $43 million through the end of next season, with a $27.5 million club option (or $12.5 million buyout) for 2016. Those numbers might look huge at a glance, but if this injury isn’t serious, Lee will remain one of the most (only?) reliable pitchers in the game at a time when injuries are destroying rotations. Combine that usual reliable excellence with a much shorter contract commitment than a pitcher of his caliber would fetch on the open market, and Lee could tempt numerous suitors. To name just a few, every AL East team except the Rays looks like a logical match, while a reunion with his former Seattle club could also be in the cards. The longer the Phillies wait, the less they’re likely to get in return. Stay tuned.

Mired in Mediocrity

Treading water, all.

25. New York Mets (22-28, -15, LW: 23)

24. Boston Red Sox (21-29, -25, LW: 14)

23. Pittsburgh Pirates (23-27, -21, LW: 25)

22. Tampa Bay Rays (23-29, -23, LW: 24)

21. Chicago White Sox (26-27, -12, LW: 21)

20. Cleveland Indians (24-28, -23, LW: 22)

19. Kansas City Royals (24-26, -7, LW: 19)

18. Minnesota Twins (23-25, -26, LW: 18)

17. Texas Rangers (26-25, -11, LW: 17)

16. Miami Marlins (27-25, +21, LW: 15)

15. Cincinnati Reds (22-27, -13, LW: 16)

14. Seattle Mariners (25-25, +13, LW: 20)

The Kansas City Royals have many of the characteristics of a winning team: They have an ace in James Shields; their bullpen once again ranks among baseball’s best behind lights-out closer Greg Holland and strikeout machine Wade Davis; and their defense is still among the league’s best by Ultimate Zone Rating, Baseball Info Solutions’ Defensive Runs Saved, and any other advanced metric.

Unfortunately, the Royals can’t hit. Again.

They rank last in the American League in park-adjusted offense, batting a punchless .255/.309/.352 as a team. They’re also last in the majors in home runs with 20 — just four more than Nelson Cruz has by himself. They’re walking less often than any AL team except the Orioles.

Even more unfortunately, this is nothing new for K.C. The Royals ranked 12th in the AL in park-adjusted offense last year, finished last in the league in homers, and were third to last in walk rate. The team’s objection to bases on balls in particular goes back decades. I asked Grantland’s resident Royals historian Rany Jazayerli for some background on this. As a fan of the team with the longest playoff drought in the majors (29 years), Rany fired back an answer within seconds: “They’ve finished in the bottom half of the league in walks for 24 straight years, and 33 of the last 34, with 1989 the only outlier. That was the year Kevin Seitzer drew 102 walks; he’s the last Royal to draw even 90 walks in a season. He was fired as the hitting coach after the 2012 season, after which the Royals’ offense went on to great success and everyone lived happily ever after.”

Despite those deeply ingrained tendencies, some of the Royals’ failings should improve at some point this season. A look at the player performance checklist reveals no notable reasons for 28-year-old Billy Butler to start hitting like he’s Lorde. He’s swinging at and making contact with a few more pitches out of the strike zone than usual, and striking out a bit more than he has in the past, but not enough to turn him into one of the worst hitters in the league. Butler’s seeing lots of fly balls die a bit short of doing damage, and mostly just seems to be fighting one of the worst slumps of his pretty good career. There’s also hope for teammate Eric Hosmer, who has just one home run this season, but has experienced similarly ugly stretches in the past. In fact, Hosmer ended last May with just one homer, then went on a big tear.

Still, the Royals’ prospects haven’t developed as hoped, with the recently demoted Mike Moustakas the most glaring example of that failure.

Moustakas set the world on fire this spring, leading to much optimism that he’d finally start hitting consistently during the regular season, when the games actually matter. It didn’t happen. Moustakas looked completely lost at the plate this year before finally getting sent down to Triple-A on Thursday. Call this a case of fool-me-twice, because the same disappointment surfaced last year, when Moustakas delivered a torrid spring, then a terrible .233/.287/.364 regular season.

Suddenly, the Royals also have another concern, as electric starter Yordano Ventura left Monday’s game early with lateral elbow discomfort. After blazing onto the scene to start the season, the 22-year-old righty had stumbled in May, posting a 5.60 ERA. That the Royals pulled Ventura right after his usually blistering fastball dropped to 91 mph is a real cause for concern, especially amid the rash of pitching injuries this year.

With Ventura hurt, the presumed big bats failing to deliver, and supporting figures like Norichika Aoki struggling, the Royals are in a quandary. For most teams, the dilemma would boil down to deciding whether to become buyers or sellers. In the Royals’ case, however, it’s not as simple as choosing whether to chase the elite Tigers and fellow wild-card hopefuls or give up on guys like Shields and Holland sooner than they’d like to, because selling now would essentially mean admitting that the last eight years of rebuilding were a waste.

Given that wrinkle, the team’s string of disappointing results since 1985, and the long tenures for GM Dayton Moore and manager Ned Yost, few teams have more at stake over the next two months than K.C.

The Aspirants

They’re not quite elite, but they have the potential to get there.

13. Washington Nationals (25-26, +4, LW: 10)

12. Baltimore Orioles (26-23, -5, LW: 12)

11. New York Yankees (27-23, -4, LW: 9)

10. Los Angeles Dodgers (28-24, +8, LW: 11)

9. Colorado Rockies (27-24, +33, LW: 6)

8. Toronto Blue Jays (30-22, +28, LW: 13)

7. Atlanta Braves (28-22, +12, LW: 8)

6. St. Louis Cardinals (28-23, +22, LW: 7)

When Oakland visited Toronto over the weekend, the A’s broadcasters did a good job of chronicling moments from Blue Jays history. They discussed old Exhibition Stadium and all of its … ummm … quirks. They talked about some of the great players in franchise history. They made the requisite mention of Joe Carter’s home run for the ages.

Then things turned grim. Glen Kuiper and Ray Fosse picked over the past two decades of Jays baseball, starting with the 21-year playoff drought since Carter’s homer. They noted the seven managerial changes in the past 14 years; the 10th-ranked payrolls of the past two seasons, including the team’s $137.2 million in salaries on Opening Day this year; the six consecutive last or second-to-last AL East finishes.

The Jays didn’t figure to fare much better over the weekend with the big, bad A’s bringing baseball’s best record to town after winning 11 of their past 13 games. When the A’s left town three days later, however, they did so with three more losses on their ledger after getting swept by a Toronto team that has now won 12 out of 14 in its own right. The Blue Jays are now the hottest team in the majors, alone in first place atop the AL East. It’s been a while:

Last time Blue Jays were alone in 1st place after May 25 was July 6, 2000. — Richard Justice (@richardjustice) May 26, 2014

That turnaround has stemmed first and foremost from Toronto’s murderers’ row of a lineup, as the Jays currently field the best offense in either league. They lead the majors with 73 home runs, 16 more than the second-ranked AL club, the A’s. It’s been a team effort, with six Toronto players cranking eight homers or more:

Juan Francisco (eight homers): With Ryan Goins struggling to hit .150, the Jays got creative, pushing Brett Lawrie to second base and awarding Francisco the bigger half of a third-base platoon. I talked a bit about the 26-year-old, lefty-swinging Dominican last month in a feature on the Brewers, noting that Francisco’s ample power wasn’t enough to keep him in Milwaukee, where his tire-fire defense and high strikeout totals proved toxic. Not much has changed: Francisco still strikes out way too much and he’s still a lousy defender, and while power is the one true skill in his arsenal, he’s probably not going to blast better than one homer every 12 at-bats all season long. Even so, he’s serviceable as a cheap, part-time option while the Jays work out other issues.

Brett Lawrie, (eight homers): When Jays GM Alex Anthopoulos appeared on the season premiere of my podcast, he offered numerous tidbits, including this one: While Lawrie looked poised to become a fine all-around player, he probably wasn’t going to develop into a big home run hitter. Well, Lawrie has struggled in multiple ways this year, striking out more, walking less, and sitting on a .230 batting average with a .278 on-base percentage. He’s been very good in three areas, however: He’s playing his usual sharp defense, he’s running the bases well … and he’s on pace to smash 25 homers. Go figure.

Melky Cabrera (eight homers): Cabrera dealt with multiple injuries that crushed his performance last year. If we throw out his 2013 numbers and focus only on his 2012 performance and his 2014 numbers to date, we get the following aggregate line: .336/.379/.527. Not bad for a guy making $8 million in the second and final year of a $16 million deal.

Colby Rasmus (nine homers): Anthopoulos also talked about the Jays’ desire to sign Rasmus to a contract extension, since he’s eligible to become a free agent at season’s end. Good luck finding an obvious purchase price, though. If Lawrie’s been somewhat erratic this year, Rasmus has been infuriating, following his excellent .276/.338/.501 campaign last year by hitting just .222 with a .266 OBP this year, albeit with the best power numbers of his career.

Jose Bautista (12 homers): I highly recommend this Bautista piece by The Score’s Drew Fairservice. Until you get to it, here’s the short version: Bautista has been phenomenal this year, and he kept the Jays in the race while they struggled out of the gate and waited for the cavalry to finally arrive.

Edwin Encarnacion, (15 homers): With a team-record 13 bombs in May alone, Encarnacion helped that cavalry arrive almost by himself. His season has really taken wing.

There are other elements clicking for the Jays right now, from unlikely solid starts from J.A. Happ and Liam Hendriks to Jose Reyes looking like his vintage self, scoring from second on a routine groundout Saturday and swiping three bases Sunday. Neither Reyes’s health nor consistently strong pitching from a suspect starting five should be considered a given from here on out. Even Mark Buehrle, who appears to be having a banner season, owes his shiny superficial stats to a career-low home run–per–fly ball rate, a career-high strand rate, and some off-the-charts defensive support, none of which is likely to last much longer.

Still, you have to love that every member of the organization seems to be giving it his all:

The enthusiasm is there. To match that with sustained results, the Jays will need to come up with contingency plans should injuries strike again this year and, more important, find starting pitching help between now and July 31. Regardless, don’t underestimate what a team full of mashers can do. Four of the past six teams to lead the majors in home runs won their division. Hopefully for Toronto, the fact that the Jays were one of the two that didn’t is merely a nasty coincidence.

Fearsome Fivesome

These five clubs have held up best through a tumultuous quarter.

5. Milwaukee Brewers (30-22, +11, LW: 4)

4. Los Angeles Angels (28-22, +43, LW: 5)

3. Detroit Tigers (28-19, +19, LW: 1)

2. Oakland A’s (31-20, +100, LW: 2)

1. San Francisco Giants (32-19, +38, LW: 3)

The Giants’ starting rotation is weird and wonderful. One pitcher is a shadow of his former self; one suddenly isn’t what he used to be; one has found the fountain of youth; one looked bound for extinction before turning his season around this month; and one has established himself as the only rock-solid commodity this team can truly trust. Let’s tackle them in order:

Tim Lincecum still occasionally pulls out the kind of start that led him to consecutive Cy Young awards and NL domination — just ask the Braves, who managed only three hits in an 11-strikeout whitewash on May 12. For the most part, though, Lincecum has the same lithe physique and the same Freak-like pitching motion, but none of the knockout stuff that once made him terrifying to face. He’s made four quality starts in his past five outings, but he’s also averaging just less than six innings per start. He’s also skating by with some luck, as he did when he walked six Twins and uncorked two wild pitches on May 23, but escaped with a win and just two runs allowed in six innings pitched. He’s still striking out batters at a better-than-average rate, but he’s also getting hit harder than ever before.

Matt Cain spent seasons defying the odds, posting low ERAs year after year with numbers one might be tempted to call lucky, but might in fact have stemmed from Cain being a big outlier in the otherwise orderly world of pitching. Cain’s magic act stopped working last year, however, when he posted a 4.00 ERA following a four-year stretch in which he averaged less than 3.00. Several metrics that started to swell last year — most notably HR/FB rate and walks — have grown worse this year. In Cain, the Giants have something more like a no. 4 starter rather than an ace, and that’s assuming the hamstring injury that caused him to miss Monday’s start doesn’t turn into something more serious.

Tim Hudson is the active wins leader and a three-time All-Star who’s finished in the top 10 in Cy Young voting four times. Yet somehow, at age 38, he’s putting up the best numbers of his career: a 2.13 ERA, with his lowest walk rate and his highest strikeout-to-walk rate. Ever the expert worm killer, Hudson’s inducing ground balls at a 61.5 percent rate, the highest mark in four years and a byproduct of throwing more splitters than ever before. He’s been lucky, too. As this ESPN Insider article by Scott Spratt notes, Hudson has been one of the luckiest pitchers in baseball, getting extraordinary defensive support even above and beyond what his fellow Giants pitchers have received.

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Ryan Vogelsong’s season was a raging disaster through his first four starts. He’d rolled up a 7.71 ERA, with five homers and 24 hits allowed in 16⅓ innings pitched. He’s been a different pitcher since, changing his pitch mix significantly and reaping masterful results. In his past six starts, he’s given up just six earned runs, good for a 1.35 ERA and an opponents’ batting line of .191/.253/.234. Some of that is thanks to an easier schedule that has included two starts against a Braves team that’s second to last in baseball in runs scored and one at AT&T Park against a Marlins team that’s hit poorly on the road. Still, let’s give credit where credit’s due: Vogelsong was out of the majors entirely for half a decade before improbably resurrecting his career, and while last season appeared to burst his bubble, his numbers this year are almost identical to what he did in 2011 and 2012. This might not be a fluke.

Finally, there’s Madison Bumgarner, whose story is the dullest of the bunch because of his amazing reliability over the past three-plus seasons. Since the start of the 2011 season, he ranks seventh among NL starters in ERA, seventh in FIP, and fourth in innings pitched. Bumgarner has now surpassed Lincecum and Cain to become the Giants’ true ace, and he’s the biggest reason San Francisco has maintained a top rotation despite its former leaders fading in effectiveness.

Much like the A’s and Tigers, the Giants will run into regression at some point. But they’ve also dodged their share of bullets. Buster Posey and Angel Pagan have shaken off injuries. Brandon Hicks has emerged as a bizarro version of Marco Scutaro, hitting below the Mendoza Line but ranking among the team leaders in homers while filling in for the injured veteran second baseman. Pablo Sandoval has recovered from his slow start to catch fire over the past 15 games. Brandon Belt should return in about a month. And 13 of the next 17 games come against teams that are currently .500 or worse.

The Giants are currently the best team in baseball, and their even-year magic just might be real.

This article has been updated to remove an incorrect reference to the year Melky Cabrera was suspended for PED use.