Carlos Zambrano has been frugal toward opponents in building a 6-1 mark thus far in 2008 but some underlying stats suggest tough times could be ahead.

AP

Every year we suffer through stories of the hard luck starting pitcher who has a WHIP of 1.10 but an ERA of 4.50. We know those two numbers don't correlate together, but we're not exactly sure how one affects the other. A few years ago I played around with these ratios and found that they were linked by something called a pitcher's Strand Rate (S%), which is a measure of how many men that reach base he keeps from scoring. This is the flip side of an offensive player's left on base numbers. Strand Rate is calculated this way:

S% = (H + BB - ER)/(H + BB - HR)

What's interesting about the Strand Rate -- and makes it useful -- is that it stays relatively constant (of course the rate is slightly higher in the NL because pitchers are forced to hit, Micah Owings notwithstanding). The rate hovers around 70 percent, but I like to use a three-year average to determine the individual league rates. Based on the past three full seasons, we get:

NL: S% = .711
AL: S% = .704

Sure, that's not a huge difference, but I'd rather use those numbers than eyeball it and say S% is 70 percent (interleague play has caused the individual league rates to converge toward each other). So knowing these values, let's use some basic math on the formula for S% to create a relationship between ERA and WHIP:

S% = (H + BB - ER)/(H + BB - HR)
S%*H + S%*BB - S%*HR = H + BB - ER
ER = H*(1 - S%) + BB*(1 - S%) + S%*HR
ER = (1 - S%)*(H + BB)+ S%*HR
9*ER/IP = 9*(1 - S%)*(H + BB)/IP + 9*S%*HR/IP
ERA = 9*(1 - S%)*WHIP + 9*S%*HR/IP

Follow all that? Of course, you could just multiply S% by a pitcher's HR rate per nine innings for that last value, but I prefer keeping it in terms of HR and IP as they're easier values to get. Now let's plug in our three-year averages for S% in both leagues to create formulas for calculating a pitcher's expected ERA based on those averages:

NL: xERA(S%) = 2.601*WHIP + 6.399*HR/IP
AL: xERA(S%) = 2.664*WHIP + 6.336*HR/IP

Note that the formula relating the two ratios is not linear, and dependent on a pitcher's HRs, which intuitively makes sense. A pitcher who keeps the ball in the park likely strands more runners.

What we've learned about these formulas is that pitchers who are relatively close to their expected ERAs based on S% shouldn't see much change. But those that are significantly different from their expected ERA tend to improve or decline based on where they are. Thinking of it another way, if a pitcher had a very high S% compared to the league average (say 80 percent or higher), then he's due for some bad innings as karma sorts him out. Conversely, a hard-luck pitcher with a S% around 60 percent or lower is likely headed toward better times. Of course that may sound like a bad application of the mythical law of averages, and yes, WHIP can also be a moving target, but I've kept an eye on this phenomenon the past few years and it's mostly worked.

Use This Information Only for Good, Never for Evil

So now that we're armed with these formulas, we'll look at pitchers in each league and see who is most likely to head down or up based on the WHIP, ERA, and HRs. Note that my criterion for "significant difference" between expected and actual ERAs was 0.75 earned runs. So if the xERA was 0.75 or more higher than the actual ERA, the pitcher was listed as more likely to see rougher starts than usual ahead. If the xERA was 0.75 or more lower than the actual ERA, the pitcher was more likely to have better starts than usual ahead. If the xERA and actual ERA were within 0.75 earned runs of each other, than the pitcher was likely performing as expected. I have included each pitcher's innings pitched in my tables below as more innings mean more certainty that we'll see a course change in the pitcher.

Also note -- and here's the important part -- that expected performances are relative to the talent level of the pitcher and not relative to other pitchers.  For example, the data suggests Carlos Zambrano (1.80 ERA vs. 3.23 xERA) is more likely to see bad starts (for him) in the near future than Jeff Suppan (4.63 ERA vs. 4.89 xERA), but you'd still rather have Zambrano pitching for you than Suppan.  I beg you not to interpret this column as meaning to drop Zambrano and pick up Suppan, or that there's an urgency to unload Zambrano. Please.

Think of the difference between the pitcher's actual and expected ERAs as a "Surprise Meter." The bigger the gap between the two ERAs the more likely the pitcher will have a surprise performance where he will either blow up (if his xERA is much higher than his actual ERA) or dominate (you know, the other situation). I call these Negative and Positive Corrections, respectively, but not because of the silly stock market, but because I enjoyed the book by Jonathan Franzen.

NL WHIPs and ERAs

Most Likely to See a Negative Correction (NL):

Suddenly Edison Volquez has a big "Sell High" sticker on his back, doesn't he? The problem is that he's been a league leader in strikeouts, so even if (when) he gets rocked, he should still help you.  Just make sure you get a good return if you do trade him.  I know that John Smoltz is headed to the bullpen, but I wanted to point out that with Smoltz there are two other Braves on this list (three more if I had included Jo-Jo Reyes who has only 8.0 IP). The Braves are headed for trouble unless they stabilize their starters and relievers. The list also indicates Houston is headed for a big fall (as opposed to a big Fall).  And as non-dominant as Johan Santana has been, there's room for him to be worse.

Most Likely to See a Positive Correction (NL):

With his injury, Esteban Loaiza likely has lost his rotation spot, but he could have better numbers. However, Loaiza also illustrates a good point about this data: even if a pitcher should have a 5.00 ERA instead of an 7.00, we still likely don't want him (let's call that the Barry Zito Rule). Jack Cassel makes for an interesting play, but he's back in the minors. Watch for his return.  Johnny Cueto has been roughed up while Volquez has shined, but the numbers indicate we could see a reversal of fortune.

Pitchers Right on Target (NL):

Since the majority of pitchers are on this list, and the numbers are, well, boring, I'll list some significant starters with the difference between their xERA and actual ERAs in parentheses:

Ben Sheets (0.55), Mike Pelfrey (0.48), Brandon Webb (0.42), Ryan Dempster (0.39), Aaron Harang (0.36), Todd Wellemeyer (0.33), Jeff Suppan (0.26), Jair Jurrjens (0.12), Mark Hendrickson (0.09), Shawn Hill (0.08), Oliver Perez (0.07), Cole Hamels (0.07), Greg Maddux (0.06), Dan Haren (0.05), Matt Cain (-0.02), Roy Oswalt (-0.02), Tim Redding (-0.03), Ian Snell (-0.04), Joel Pineiro (-0.04), Tim Hudson (-0.05), Derek Lowe (-0.13), Brandon Looper (-0.21), Micah Owings (-0.33), Max Scherzer (-0.34), Jonathan Sanchez (-0.39), Randy Johnson (-0.39), Randy Wolf (-0.56), Brad Penny (-0.70).

AL WHIPs and ERAs

Most Likely to See a Negative Correction (AL):

I was down on Kason Gabbard at the beginning of the season and have been surprised by his numbers.  Time for me to surprise him.  Despite Monday afternoon's results, Fausto Carmona can't walk that many batters and get away with it.  Duck and cover may be your best bet.  And that goes for Daisuke Matsuzaka, but he seems better poised to absorb the free passes. As I thought, Cliff Lee is due for, um, wait, that correction would still make him awesome. Nevermind.

Most Likely to See a Positive Correction (AL):

I only included Francisco Liriano to show there was light at the end of his tunnel. His numbers are worse than they should be.  But don't look for him before the All Star Break.  The worst thing about this list is that besides Boof Bonser and Andy Sonnanstine, nobody has numbers good enough to make you want them. Of course, CC Sabathia (who has apparently made it his season-long mission to prove me wrong) has been great in his last few starts and may make us forget the first few.

Pitchers Right on Target (AL):

And again, the guys that are least likely to surprise you in the AL:

Jon Lester (0.71), Jeremy Bonderman (0.63), Greg Smith (0.55), Paul Byrd (0.50), Aaron Laffey (0.47), Shaun Marcum (0.47), Gavin Floyd (0.42), Daniel Cabrera (0.37), Dana Eveland (0.36), Ervin Santana (0.30), Joe Blanton (0.23), Armando Galarraga (0.21), Tim Wakefield (0.20), Jon Garland (0.19), John Danks (0.09), Jeremy Guthrie (0.05), Chien-Ming Wang (0.02), Javier Vazquez (-0.04), Clay Buchholz (-0.07), Brian Bannister (-0.10), Roy Halladay (-0.14), Mike Mussina (-0.14), Dustin McGowan (-0.21), Miguel Batista (-0.25), AJ Burnett (-0.29), Josh Beckett (-0.57), Kenny Rogers (-0.69), Jered Weaver (-0.70).

Note that there were more AL pitchers with an ERA difference between 0.75 and -0.75 than in the NL.  Perhaps that means there are more waiver wire and trade opportunities in the NL than in the AL.

Mound Minutes

• While the lowly Rangers are running away with the unearned runs crown and are one of the AL's worst, but the team in second is one of the NL's best: the Diamondbacks. The D-backs are middle of the road in errors, but when they do make one, it opens the flood gates. Unless the Snakes can show more concentration and plug this leak, they may head south with the Rangers.

• And speaking of Arizona pitching problems, their bullpen completely came apart against the Cubs. The starters only gave up four earned runs (yes, plus one unearned run) in 18.0 IP, while the bullpen threw underhand in giving up 11 ER in 6.0 IP. This could have been a blip on the radar screen for a closed park team playing in the wind and rain, but it does bear watching (although if they play like that again, I may not be able to watch).

• Two guys I was luke warm about that have made it onto my teams are Armando Galarraga and Aaron Laffey. I jumped on the Laffey bandwagon earlier, but I still have a general aversion in fantasy baseball to guys that are light in strikeouts (hence my reason for never drafting Chien-Ming Wang or Kirk Rueter). As for Galarraga, I just couldn't shake my memory of him in Texas. Both should be taken in all leagues.

• So what does it mean if your team leads the Majors in errors and is second to last in the NL in pitching strikeouts? If you're the Florida Marlins, it means you're skating on thin ice. I've stayed away from Florida pitchers despite the wins because of the lack of strikeouts. Unless the defense fields the ball better, the team with the best record in the NL (man, I still can't get used to that) is heading for a rough patch, especially when they play against the big AL offenses.

When he's not conducting sabremetric analyses of the players from his 10-year-old Pony League baseball team, David Young is a fantasy baseball expert who has written weekly columns for, among others, ESPN and Sports Illustrated's web sites. He also won KFFL's Expert League in 2007. Send him a comment or question at davebaseball29@yahoo.com.