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By the Numbers: What a relief!

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Every other week, we scan the majors' 30 rotations for pitchers who are poised to deliver value as well as heartaches. In this week's Lucky/Unlucky analysis, we turn our attention to relievers for the first time this season. After four months, we finally have some sample sizes that, while still small, can tell us something about the future value of Fantasy relievers. Seemingly random statistical fluctuations have shaped the seasons of starters like Trevor Cahill (for the better) and Kevin Slowey (for the worse), and the same is true for many of this year's more notable relievers.

A quick look inside the "Likely Lucky" boxes in the tool below reveals that Mariano Rivera and Luke Gregerson have probably benefitted from some good fortune. One could easily argue that, luck or no luck, they are the best closer and setup man in the game, respectively. What their crazy-low BABIP rates tell us is that we shouldn't expect their WHIPs to stay below 0.70 all season. Most owners can probably get over that sort of bad news. Likewise, Brian Wilson and Heath Bell have probably been unlucky, but even if their BABIPs don't come down, they could continue to be the two most commonly-owned relievers in Fantasy and rightfully so.

Even after excluding these non-findings from our Lucky/Unlucky analysis, there are still plenty of relievers whose stats portend meaningful changes ahead, including a few with new roles created out of player movement at the trade deadline. How will Chris Perez fare as a closer, now that he no longer has to look over his shoulder for Kerry Wood? Is Aaron Heilman the answer in Arizona? Check in just below the tool for the answers (and stop and try the tool out on the way).

Players' stats are for all games played through Sunday, August 1.

Who has probably been lucky?

Jose Valverde, Detroit: Valverde's value has been hurt by a lack of save opportunities, but he has made the most of them, converting 21 of 22 chances. Given his tendency towards wildness (23 walks in 46 innings), it's a bit surprising he has been this successful. He has helped himself by limiting opponents to a 16 percent line drive rate, but even if he keeps that up, his .200 BABIP is sure to rise over the season's remaining weeks. It might be a good time to test the market for the former NL saves leader, as his value could sink further as the season wears on.

Andrew Bailey, Oakland: His strikeout rate is only about two-thirds of what it was in his impressive rookie season, but Bailey's other Fantasy stats look as good as last year's. That would not likely be the case if not for a major league-lowest .522 BABIP on line drives. It's not clear when Bailey might return from an intercostal strain, but he won't be as trustworthy of an option as he appears, once he is back in the A's bullpen. If not for his health issues, he would be an ideal “sell” candidate right now.

Chris Perez, Cleveland: Perez is the new closer in Cleveland, but he has already had more save opportunities (15) than incumbent Kerry Wood (11). The 25-year-old acquitted himself nicely in his "tryout," but owners should not expect the same level of success now that the job is truly his. Perez has walked more than a batter every other inning but has covered up the damage to his WHIP with a .245 BABIP. That's not an outrageous rate for many relievers, but it is when hitters are smoking line drives off nearly every fourth ball hit off you. He will need to bring his line drive rate down if he is to succeed as the Indians' full-time closer.

Evan Meek, Pittsburgh: Few owners probably expect Meek to maintain a 1.23 ERA and 0.87 WHIP, but there may even more trouble lurking than what appears. Through the first two months of the season, Meek built a superb set of Fantasy stats through strong strikeout and walk ratios and with little help from favorable BABIP rates. That story has reversed itself since June 1, as his deteriorating strikeout and walk rates are being camouflaged by a sub-.200 BABIP. He will have to compete with Joel Hanrahan for scant save chances in Pittsburgh, and the lack of saves along with drooping skill trends give Meek limited appeal as a closer candidate.

Who has probably been unlucky?

Jonathan Broxton, L.A. Dodgers: Broxton has struggled so much since the All-Star break, blowing two of three save chances and allowing six earned runs in five innings, that Dodgers manager Joe Torre has expressed concerns about his closer's velocity. While Broxton's velocity is in fact down this year, he is still missing bats at his typical pace. His BABIP rates are usually higher than average, but his .379 rate this season just looks fluky all over. Because of his mediocre ERA and WHIP, Broxton has fallen to middle of the closer pack this year, but given his continued strong command of the strike zone, he could easily finish the season as strong as any closer in Fantasy.

Joba Chamberlain, N.Y. Yankees: Despite moving to a full-time relief role this year, Chamberlain is still owned in 23 percent of leagues on CBSSports.com. He is active in fewer than half of those leagues, and judging by his 5.60 ERA and 1.51 WHIP, perhaps he should be sitting on even more Fantasy benches. Those stats make it appear that Chamberlain has been a bust, posting back-to-back disappointing seasons, but his peripherals show reasons for hope. Unlike last year, Joba has compiled respectable walk and home run rates, and his K/9 ratio has skyrocketed from 7.6 to 10.0. It's only his .375 BABIP and 62 percent left-on-base rate that create the appearance of a bad season, and both of those stats look highly aberrant. Chamberlain is already fourth in the majors in holds, and he could add a low ERA and WHIP to his resume over the next two months, making him a useful arm to activate in deeper leagues.

Matt Lindstrom, Houston: Bouncing back from a difficult stint as the Marlins closer in 2009, Lindstrom has performed the way the Fish hoped he would, but in an Astros uniform, in 2010. He has made substantial improvements in his walk and homer rates and has done a much better job of stranding runners. Despite all of these successes, Lindstrom still sports a 1.45 WHIP, as he has been battered by a .352 BABIP. While he has never posted a rate lower than .331 in any of his four major league seasons, only once before has he put together a line drive rate below the major league average. He has a lower-than-average 18 percent rate this season, so as long as he can maintain that, his WHIP should recede over the coming weeks.

Chad Qualls, Tampa Bay: Leaving his awful stint as the Diamondbacks' closer behind, Qualls moves on to a middle and setup relief role with the Rays. Owners may think that Qualls has lost the last shred of value he had, moving to a team that has no need for a new closer, but he may still be able to help in Fantasy formats that utilize middle relievers. Qualls' skill ratios (strikeout, walk and homer rates) were not as good as his recent norms, but they weren't anywhere near as bad as an 8.15 ERA and 1.97 WHIP would suggest that they were. With a .431 BABIP, one would think that Qualls was getting scorched frequently, but he has not been very prone to giving up line drives (17 percent rate). He could be a surprisingly helpful free agent pickup in AL-only leagues that reward holds.

Who has been neither lucky nor unlucky (based on current batted ball rates)?

Jonathan Papelbon, Boston: Even with a reduced strikeout rate, Papelbon has been one of the top dozen relievers in Rotisserie. He's clearly not what he was two years ago, but the question for his current owners is whether he will decline even more. A .231 BABIP has helped the Red Sox closer to keep his WHIP under 1.10, but neither stat may increase much if he can maintain a lofty 46 percent flyball rate. Papelbon has paid a price for those flies, as he has yielded six homers in 44 1/3 innings, but even so, his ERA is just bubbling over the 3.00 mark. It is unrealistic to expect that he'll be one of Fantasy's best closers this season, but it's equally unrealistic to think he is bound for disaster.

Hong-Chih Kuo, L.A. Dodgers: Kuo has just three fewer holds than Fernando Rodney, and his ERA and WHIP are a fraction of the Angels' setup man's, yet he is owned in only about two-thirds as many leagues. Maybe owners don't believe that Kuo can maintain his current ERA and WHIP, both of which are below 1.00, but his .203 BABIP isn't too far from where we should expect it to be, given his sterling line drive and flyball rates. While those batted ball rates could creep northward, owners unsure of whether they can rely on him for ERA, WHIP and holds just might get the status quo from Kuo.

Bobby Jenks, Chicago White Sox: You don't have to look hard for affirmation if you want to believe that Jenks has been undeservedly saddled with a 4.70 ERA and 1.49 WHIP. His 11.5 K/9 ratio is his highest ever and he has only allowed two homers all season. It would be easy to blame his major-league worst .421 flyball BABIP as a fluke that is ruining his season. The fluke part is correct, but it doesn't get all of the blame for his subpar performance. Jenks doesn't allow many flyballs, which helps him to avoid home runs, but it is a trend that is conducive to a high overall BABIP. Jenks' overall .386 rate is bound to shrink somewhat, but given his high line drive and ground ball rates, he is not a candidate for dramatic improvement. With manager Ozzie Guillen's on-again, off-again threats to use other relievers in the ninth inning, Jenks could still be at risk of losing the closer's role.

Aaron Heilman, Arizona: The Snakes' new closer has made only mild progress on his control issues, while his strikeout rate has dropped for a second straight year, yet he is being rewarded with a respectable 3.38 ERA. Heilman's .280 BABIP rate looks normal and harmless enough, but it's a rate he will be hard pressed to keep, unless he cuts back on a 24 percent line drive rate. This is no one-time aberration, as Heilman has allowed 184 liners out of 848 hit balls (22 percent rate) over 282 1/3 innings since 2007. He simply does not have the command to be a successful closer long term.

Glossary
Runs Created per 27 Outs (RC/27) -- An estimate of how many runs a lineup would produce per 27 outs if a particular player occupied each spot in the order; ex. the RC/27 for Miguel Cabrera would predict the productivity of a lineup where Cabrera (or his statistical equal) batted in all nine spots; created by Bill James
Component ERA (ERC) -- An estimate of a what a pitcher's ERA would be if it were based solely on actual pitching performance; created by Bill James
GO/AO -- Ground out-fly out ratio
GB/FB -- Ground ball-fly ball ratio
Batting Average per Balls in Play (BABIP) -- The percentage of balls in play (at bats minus strikeouts and home runs) that are base hits; research by Voros McCracken and others has established that this rate is largely random and has a norm of approximately 30%
Left-on-base rate (LOB) -- Also known as strand rate. The percentage of baserunners that a pitcher allows that does not result in an earned run scoring. The research that established LOB norms and benchmarks was conducted by Ron Shandler. His research established that a certain level of variation in LOB can reflect differences in pitchers' abilities to prevent baserunners from scoring.
Isolated Power -- The difference between slugging percentage and batting average; created by Branch Rickey and Allan Roth
Walk Rate -- Walks / (at bats + walks)
Whiff Rate -- Strikeouts / at bats

Stay in touch with the most passionate Fantasy staff in the business by following us via Twitter . You can e-mail us your Fantasy Baseball questions to DMFantasyBaseball@cbs.com . Be sure to put By the Numbers in the subject field. Please include your full name, hometown and state.

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