Cliff Lee struck out 10 batters, walked one, and didn’t allow a home run in 7.2 innings in last night’s start against the Tampa Bay Rays. Lee gave up six earned runs, taking the loss in the 6-4 contest.

Remarkably, this performance increased Lee’s ERA with Texas to 3.44, and his record with his new team fell to 2-3. The increase doesn’t seem too ridiculous, until you consider that Lee, in his 65.1 innings with Texas, has struck out 58 batters, unintentionally walked two batters, and allowed 4 home runs. Tonight’s outing brings Lee’s FIP ever closer to 2.00, a mark that becomes even more impressive given the higher degree of difficulty in attaining a 2.00 FIP as opposed to a 2.00 ERA.

And yet, Lee’s results with Texas are relatively underwhelming. Lee’s 3.44 ERA equals those of fellow veteran left-handers Ted Lilly and Barry Zito. His win% below .500 is hardly becoming of a staff ace designed to navigate the rough and tumble playoffs. Although those watching the game can clearly tell that Lee is an elite pitcher, right now, his effect on the team hasn’t been of one.

Naturally, poor luck is involved. This sequence against the Rays in the eighth inning tonight, in which Tampa scored the final four of their six runs, doesn’t exactly scream good contact.

[Click to enlarge]

This play log doesn’t even do the inning justice. The Rays mustered a total of two line drives in the inning – B.J. Upton‘s double (more of a bloop than a liner) and Carlos Pena’s single. Other than that, it was grounder after grounder. Jason Bartlett reached on an infield single. Carl Crawford reached on a fielder’s choice ground ball because shortstop Joaquin Arias made an ill-advised attempt to retire the lead runner instead of taking the out at first. Evan Longoria grounded to center, and after Pena’s line drive single, Ben Zobrist capped off the inning with a grounder to left.

The sequence is clearly a case where the mantra of “process over results” shines through, as any claim that Lee’s 10 strikeout, one walk start was anything short of masterful would be blind to the mitigating factors surrounding his pitching. He couldn’t control Upton’s bloop double, nor Arias’s misplay, nor, for the most part, the fact that grounders went to the holes instead of at fielders.

Starts such as the one last night are nothing for the Rangers to worry about. The Rangers are still 17 games above .500 and eight games clear of the second place Angels. They’re clearly the most talented team in the division. Lee has pitched like an ace during his time with Texas. It’s only a matter of time before the results fall in line.

On the surface, the Francisco Rodriguez incident seems utterly disastrous for the New York Mets franchise. After a season which started out with playoff possibilities has fallen to below .500 and 10 games out of the NL East in August, the Mets’ problems only appeared to be compounded by losing their closer Francisco Rodriguez, first to a suspension following the now-infamous father-in-law punch-out incident.

Despite the black mark it may put on the organization, this whole incident may turn out to be a major financial boon for the Mets. Thanks to the torn ligament in Rodriguez’s hand resulting from the fight, the Mets may attempt to void the remainder of Rodriguez’s contract, which calls for a guaranteed $15 million and another $14M if Rodriguez’s 2012 option were to vest. That’s quite the cost for a reliever whose FIP over the past three years barely ranks in the top 20 and hasn’t posted a 2.5 WAR season since 2006. That doesn’t mean that Rodriguez isn’t a good pitcher – he’s a strikeout machine and is projected to have a FIP under 3.00. It’s just very, very difficult for a reliever to justify that kind of paycheck, unless he’s Mariano Rivera.

Even if the Mets fail in voiding the entirety of the contract, they may dodge a bullet in that 2012 vesting option. The option vests if K-Rod finishes either 55 games in 2011 or 100 games between 2010 and 2011. As Rodriguez finished 46 games in 2010, that means that K-Rod’s option will vest if he finishes 54 games in 2011. He still may achieve that mark if he stays with the Mets – he has finished at least 56 games every season since 2005. However, if the Mets’ are intent on keeping Rodriguez’s option from vesting, they will have a much easier time of it now that Rodriguez is on the shelf for the rest of this season – he was on pace to finish 63 games this season, meaning that he would only need to finish 37 to vest the option, an easy task for any full-time closer.

Francisco Rodriguez is a very good closer, but it was hard to imagine his contract being worth the money when he signed it. The 2012 vesting option looked especially dangerous, but thanks to Rodriguez’s stupidity and rash actions, the Mets may be able to get out from under that financial burden. Remarkably, it’s possible that they may even wiggle their way out from under the guaranteed 2011 season. If the Mets manage to void Rodriguez’s contract, it would be a major coup for both the Wilpons and GM Omar Minaya.

The return of Bryan Bullington was covered by our own R.J. Anderson last week. Entering yesterday’s start against the New York Yankees, Bullington was 0-7 with a 5.02 ERA and similarly poor peripheral statistics. Now, Bullington has a major league victory.

Some major league victories are cheap. Surely Brad Thomas earned his fifth win of the season after throwing all of one scoreless inning in a 21 run game between the White Sox and the Tigers. Surely Tyler Clippard earned win number nine after throwing two innings immediately after Stephen Strasburg struck out seven batters in only five innings. And surely Kyle Kendrick earned his eighth victory of the 2010 season last night, a season in which he has a 5.03 FIP.

Bullington’s first major league victory was not cheap, by any means. In eight innings, Bullington struck out five Yankees, walked only one, and allowed only two hits. It’s not like the Yankees were scorching the ball either – according to our data, the Yankees did not hit a single line drive against Bullington. Instead, it was 10 ground balls at infielders and 10 weak fly balls which stayed in the yard. Bullington had a fantastic start by any measure, particularly WPA, which had Bullington at +.612 in the Royals’ 1-0 victory over the AL East and MLB leading New York Yankees.

As R.J. noted, Bullington was a first overall draft pick with “middle of the rotation potential.” Perhaps the fact that his peak was a Jake Westbrook type pitcher says it all as to why the Pirates should have avoided Bullington as a first overall pick. It’s certainly not as if this one good start suggests that Bullington will go on to have a successful major league career in Kansas City, either.

Bullington’s career stats only support the notion that he was a mistake as a number one pick. Entering last night’s start, Bullington had struck out fewer than six batters per nine innings and walked nearly four. Toss in some home run issues – 1.38 HR/9 in 52.0 career innings pitched – and you have a pitcher who flirts with replacement level with every trip to the mound.

Given that 5,889 people had done it entering Sunday’s games, it’s hard to call the club that Bullington has joined “elite.” Still, Bullington pitched an extremely good game against one of the best lineups in the league today, making his performance on Sunday even more impressive. Bryan Bullington turns 30 next month, and it’s difficult to imagine anything great coming out of Bullington’s major league career over the next few years. Despite the struggles, his first victory is out of the way. Now he’s one step closer to joining an even more exclusive club: those 5,066 pitchers with at least two major league victories.

Expanded Four Factors links:
Austin Jackson
Aaron Hill
Ryan Howard
Average Player
Math/Reference

Last time, we took a look at Austin Jackson, and in particular, his outlandish .422 BABIP. With the help of the Four Factors, we came to the conclusion without such fantastic success on balls in play, Jackson is not likely to be an impact hitter and, without his stellar center field defense, might have trouble reaching replacement level with his bat. Today, we’ll take a look at a hitter who is having similar success on balls in play, but is also succeeding in other aspects of the game as well.

That player would be Josh Hamilton of the Texas Rangers. Hamilton is putting together an utterly ridiculous .357/.405/.622 line this season, good for a .440 wOBA. After posting a meager 1.4 WAR up in an injury riddled season last season, Hamilton has already posted 6.0 WAR this season in only 470 plate appearances.

Unless you’re Barry Bonds, it’s difficult to put up a line like this without a giant BABIP, and Hamilton certainly has that. His .396 BABIP ranks second in the majors to only the aforementioned Jackson. However, Hamilton has also improved his contact this year, striking out in a career low 17.2% of plate appearances. Most important, however, is the fact that Hamilton is showing great power, with an ISO of .265 and a POWH (XB/H) of .742. It’s not like this power is anything particularly new, however – his career POWH is a nearly identical .743.

Hamilton is a line drive hitter (23% LD this year, 23% career) and avoids the fly ball (35% career), so a high BABIP is natural. However, we would expect something closer to his career BABIP of .343 as opposed to the near-.400 mark he is currently running. Let’s take a look at what would happen to Hamilton with a lower BABIP.

With a drop in BABIP back to .340, Hamilton’s looking like a .383 wOBA hitter, which is still quite good. Even if it drops all the way back to .300, Hamilton’s still a comfortably above average hitter, at .346. Any BABIP above .360 projects Hamilton as a .400+ wOBA hitter. To be exact, every 10 points of BABIP is worth just over 9 points of wOBA.

What does this tell us? Not much that we didn’t already know, really. First, Hamilton’s having an insanely good year, even though there’s very little chance that he maintains his .440 wOBA. Second, Hamilton’s power and contact skills make him an above average hitter regardless of his BABIP, and even with some regression he should remain on of the better hitting outfielders in the league. Third, it would take some very poor luck to push Hamilton to anywhere near or below average. Hamilton is a very good hitter having a tremendous season, and right now, he certainly looks like a candidate, if not the front runner, for the Most Valuable Player award in the American League.

Things are not looking good for the Los Angeles Dodgers. The Dodgers entered last night’s game eight games behind San Diego in the NL West and five and a half games behind the Giants. Baseball Prospectus had their playoff odds at a mere 1.9%. The trades the Dodgers made clearly show that they felt that they were in the race. With San Diego and San Francisco both winning last night, yesterday’s game against the Philadelphia Phillies was utterly key for the Dodgers.

After a three run rally in the top of the eighth inning that put the Dodgers ahead 9-2, the team had to feel good. With a mere 1% chance to win at this point, the Phillies chipped away in the eighth against Ronald Belisario, Kenley Jansen, and George Sherrill, putting up four runs on four singles as well as a Ben Francisco double.

Of course, the rally still meant that the Phillies would need to put up at least three runs in the ninth to make any of it matter, and they would have to do that against Jonathan Broxton– the same Johnathan Broxton who has the lowest FIP (2.35) among qualified relievers over the past three years. Even though Broxton hasn’t had the same kind of shutdown track record as, say,Mariano Rivera, or taking a step down, Joakim Soria, Broxton is clearly an excellent pitcher. With an average pitcher on the mound, the Phillies win expectancy was still tiny, at 4.6%. Against Broxton, that number comes down even farther.

When it comes down to it, though, odds between 1 and 20 and 1 in 30 aren’t that terrible, particularly compared to the 1 in 100 odds facing the Phillies entering the eighth. Broxton isn’t exactly a control artist, as his career and season walk rates are both above three. But one wouldn’t exactly predict that Broxton would load the bases via a HBP and two walks.

What happened next can hardly be attributed to Broxton, who did his job in inducing a Ben Francisco ground ball to third base. If it wasn’t for Casey Blake letting what should’ve been an easy play go five-hole, the Dodgers could either have gotten an out at home or possibly turned a 5-4-3 double play. Instead of either bases loaded, one out, and a three run lead or the ideal runner on third, two out, and a two run lead. Blake’s error resulted in two runs scoring and runners on first and second.

The result of the play was a 47.8% win expectancy for the Dodgers. Were the Dodgers to record the out at home, their win expectancy would’ve been 88.6%; a double play would have left them with a 93.7% win expectancy. These totals are increased somewhat by the presence of Broxton on the mound, but the error was clearly extremely costly for LA, much moreso than Broxton’s loading of the bases, which brought the team’s win expectancy down from 96.4% to 66.9%.

Still, the Dodgers were up by a run, and even with runners on and nobody out, the game was essentially a coin flip. Carlos Ruiz tipped the coin in the Phillies favor with a deep double to left field, plating both Francisco and Jayson Werth, and the Phillies won the game. As much as the Dodgers needed to win this game to really have any hope whatsoever of making the playoffs, this game was probably more important for Philadelphia. The victory allowed the Phillies to keep within two games of the Braves in the NL East race and within one of the Giants in the Wild Card, with each team winning last night.

[Click to enlarge]

As we can see in the Game Graph above, this one looked like it was over in the late innings. But there’s a reason that the Phillies’ win expectancy never read “0.00%” and the Dodgers’ never read “100.00%.” After 8.5 innings with only one play with a leverage index about 2.0, the 9th inning provided two of the most exciting possible plays in baseball, with leverage indexes above 5.0. It just shows that, as the legendary Yogi Berra said, “it ain’t over until it’s over.”

On the surface, Johan Santana has had a solid season, putting up a 3.06 ERA supported by a 3.47 FIP and a 3.75 tERA. However, that masks a miniscule HR/FB rate of 4.6% and an xFIP of 4.53. If his HR/FB were to return to its normal levels – around 9% – Santana’s new inability to miss bats would likely be exposed. His swinging strike rate, never below 11% since 2002, has dropped to 8.9%, dangerously close to average for such a previously dominant pitcher as Santana. Unsurprisingly, his strikeout rate has dropped in tandem from 7.9 to 6.2, resulting in the higher xFIP.

Santana looked more like the Johan of old today against the Colorado Rockies, racking up 10 strikeouts against only two walks in a complete game shutout against one of the better offensive clubs in the National League. It was Johan’s old standby, the changeup, which made fools out of Rockies hitters. Santana pulled the string 40 times on opposing batters today, with 30 of them going for strikes. Rockies batters swung and missed a whopping 11 times, a 27.5% rate. That’s nearly double the 14.3 whiff (misses per pitch thrown) rate on Santana’s changeup this season to date.

Santana’s fastball didn’t show any more life, mixing around 86-90 mph and only drawing one swinging strike in 27 pitches. That’s right, Santana threw 13 more changeups than fastballs in this outing, a striking deviation from his average distribution of 58% fastballs to 27% changeups, with the remaining portion fitting in as sliders. It’s possible that a key to continued success for Santana will be a steady diet of changeups to opposing batters.

For the Mets and their fans, some of whom have compared Santana to the slightly less impressive Jarrod Washburn (and quite aptly, looking at Washburn ’09 vs. Santana ’10 here), this has to be encouraging. The fastball velocity is still down, but the changeup was working its former magic today. For the Mets brass in particular, who will pay Santana at least $77.5 million through 2014, this start has to bring some smiles.

Expanded Four Factors links:
Aaron Hill
Ryan Howard
Average Player
Math/Reference

Yesterday afternoon, I took a look at Aaron Hill and his abnormally low BABIP. Naturally, today we will be taking a look at Austin Jackson, who leads all qualified hitters with a .422 BABIP. That’s 29 points above the second highest BABIP, Josh Hamilton’s .393, and 123 points above the MLB average of .299.

As with Hill, Jackson’s profile does suggest that he should have an above average BABIP. He has a line drive rate of 25.8% and a ground ball rate above 50%, and both serve his speed quite well. As such, an above average BABIP should be expected.

But there are limits. First of all, Jackson’s high line drive rate is second in the league and ripe for some amount of regression to the mean. Second of all, Jackson’s BABIP on ground balls in particular is .333, and bound to come down. Jackson’s excellent 10.1% infield hit rate is about 4% above the league average, meaning that he accrues an extra 5.5 hits among his 148 ground balls, which only accounts for about 30 points of BABIP on grounders – that .333 GB BABIP is over 100 points above the league average rate, and can’t simply be explained by speed.

His BABIP on fly balls is also above the league average, by just under 70 points, and I don’t think the abnormality on fly ball BABIP can be explained as simply as his speed. Simply put, Jackson’s BABIP is going to come down. He has a .342 wOBA this season, which, after taking out the SB/CS component (16 SB, 4 CS), comes closer to his Four Factors-projected .335 wOBA. Right now, Jackson is below average in the other three non-BABIP components, with a 6.2% BB%, a 26.1% K% (K/PA), and a .334 POWH (XB/H) to go along with that .422 BABIP. Let’s take a look at what happens when that BABIP starts moving down toward the mean.

To account for the fact that Jackson is 23 and could easily improve, I have included a forecast for a 4% decrease in K% (in blue), along with a forecast for the same K% as this season (red). In the optimistic projection, a drop to a more realistic .350 BABIP (think Ichiro level) has Jackson as a .300 wOBA player – as well as Aaron Hill has hit with his .199 BABIP. In the pessimistic projection, that same drop would make Jackson a .287 wOBA player – think Carlos Gomez. In fact, given both players’ fantastic defensive abilities, they make decent comps. The depressing part here is that any BABIP below .380 – something I think is a mortal lock for the future – leaves Jackson as a below average hitter in either scenario, which isn’t necessarily a bad thing.

Even if Jackson isn’t a terrific, or average, or even competent hitter, he has fantastic defense in center field to fall back on, which could easily make him a league average player. His minor league numbers don’t particularly suggest an incoming increase in contact skills, walk rates, or power, however, so Tigers fans will likely have to be content with a light hitting, slick fielding center fielder under team control for a long time. And really, that’s not so bad.

Expanded Four Factors links:
Ryan Howard
Average Player
Math/Reference

Aaron Hill has a .199 BABIP in 406 plate appearances in 2010. That is, unsurprisingly, the worst among qualified players, coming in 11 points below Carlos Quentin‘s mark and a staggering 34 points below Carlos Pena’s .233, second worst among players with at least 400 plate appearances. Naturally, this is a huge reason why Hill’s wOBA this season is all the way down to .300, 57 points down from his breakout 2009 season and 31 points below his career average.

This drop in BABIP isn’t completely unexplainable. Hill’s LD% is all the way down to 10.2% from 18.8%, and those missing line drives have all turned into fly balls. Some around the Jays have noted that Hill has had more loft to his swing, which would explain this change. Given that LDs are the most likely to fall in for hits (.722 BABIP) and FBs are the least likely (.140 BABIP), that explains a lot. That’s roughly 27 line drives turned into fly balls, or 15 fewer hits. In 296 balls in play, those 15 hits account for 50 points of BABIP. Still, that would leave Hill’s BABIP at .249, in the bottom ten of the league.

That provides us with a fantastic opportunity to use our new favorite tool, Four Factors Equivalent wOBA (ffwOBA). Check the links at the top if you’re interested in the methodology. The following graph shows how Hill’s wOBA should change as his BABIP increases.

The fact that Hill’s wOBA is still at .300 (estimated at .292 by the method) is encouraging. The 50 point difference in BABIP mentioned above would bring Hill’s ffwOBA up 55 points to .347 from .292. If he were to get back to .288, his mark from last year, his current peripherals would have him as a .389 wOBA player due to his high power and contact rate. Hill, especially now, certainly doesn’t profile as the kind of hitter who could post above average BABIPs. For something really extreme, if Hill’s BABIP were to reach .360, with the amount of power and contact Hill makes, the Four Factors method would estimate a .464 wOBA. That’s not likely to happen, but it’s interesting to see.

ZiPS projects Hill’s BABIP at .258, and I’d expect it to come up to the .270-.280 range, as he has shown the ability to do so in the past. Either way, Aaron Hill should, as long as he can turn a few of FBs into LDs, become an above average hitter once again, and soon.

Expanded Four Factors links:
Average Player
Math/Reference

For our first use of the expanded four factors with a real, live Major League Baseball player, let’s take a look at Ryan Howard. Howard has had an interesting season this year, posting a solid .377 wOBA despite a pretty severe drop in both power and walk rate. His ISO is down from .292 to .236 and his POWH (XB/H) is down from 1.05 to 0.81. His walk rate has dropped from 10.7% to 7.5%, but the strikeout rate (in K/PA) has also dipped, from 26.5% to 23.7%.

Basically, we see two bad signs combined with one excellent sign for Howard. Some in Philadelphia are excited to see what Howard can do making more contact, especially if the power and discipline were to return to their normal rates. Let’s take a look at what would happen for Howard if his K-rate were to decrease from its career mark of 27.4% to his current mark of 23.7%, if his power and walk rates were to return to their typical levels. For his career, Howard has posted a .393 wOBA, which the Four Factors method overshoots by 5 points, even after his career 2B/HR and 3B/HR rates are input.

Here we see why Phillies fans would be so excited about a new, relatively contact happy Howard. Howard was truly an elite hitter in 2006, putting up a .436 wOBA, thanks in large part to 58 homers as well as a 15% walk rate. If Howard were to hold his strikeout rate as low as it has been in 2010 while returning to the power and discipline numbers that he’s shown over his career, his ffwOBA jumps up to .418 from .398 – not as high as his 2006 season nor Pujols’s crazy numbers from the last 3 calendar years, but still elite and likely top-5 type material.

That said, there are legitimate reasons to worry about Howard. He has been a second half hitter by the numbers, but stranger things have happened than a player losing a significant amount of his power in his age 30 season. What if instead of the K-rate staying down, it’s the power numbers that decline. Let his career BABIP remain at .329, slightly below his rate from this season. Finally, let’s look at this decline both if the walk rate stays at 7.5%, its current rate, his career low, or if it rebounds to 12.2%, his career average. The low walk rate is in blue; the high in red.

Here we see cause for concern. If the walk rate returns but the power stays as low as it has, Howard will be around a .360 wOBA hitter, which is right around the level of David DeJesus and Vernon Wells, and it would be exceptionally difficult for Howard to justify his 5 year, 125 million dollar contract providing such little pop at the plate. If the walks and power both are gone, than Howard’s wOBA slips to .350, right in line with Daric Barton – a good first baseman, particularly with the glove, in a pitcher’s park, but that’s hardly the all-star level performance expected out of Ryan Howard.

Of course, we come now to the question of what we actually think will happen with Howard. ZiPS projects a .398 wOBA due to a spike in BB% and a jump in power to just below previous levels, along with a rise in K rate back to previous levels. CHONE doesn’t project that Howard’s walk rate will rise above 10% again. Along with a rise in K% back to previous norms and a rise in power that doesn’t quite reach its old heights, CHONE projects a .273/.344/.537 line.

Interestingly, power is the one aspect that takes the longest to stabilize. To me, that suggests that the power could easily return to 2009 levels, but the walk rates and strikeout rates may not. Howard’s ability to reach the base via the walk is extremely important, and his 2010 BB rate is merely half of what it was in that fantastic 2006 campaign. Still, the numbers here suggest that even a drop in XB/H from 1.05 to 0.95, as CHONE projects would cause nearly a 20 point drop in wOBA.

So, in summary, yes, Howard’s drop in power will be of concern unless he has another monster August/September, which, given his 153/175 career wRC+’s in those months, isn’t exactly unlikely. At the same time, Howard’s drop in strikeouts is great to see, but the projection systems don’t appear to be convinced in the slightest. Howard would likely be the best non-Pujols hitter in the league if both the drop in strikeouts persists and his power fully returns. The flip side, however, would see Ryan Howard and Daric Barton fighting it out on a yearly basis, and that would be disastrous for the Phillies. The most likely scenario, however, is the simplest: Howard returns to his old form with a slight drop in power, which would leave him as still one of the better hitters in the National League, although not quite a top-5 or necessarily even a top-10 hitter.

In case you missed it, this morning I went over the mathematics necessary to take the four factors of hitting to the next level. Now, it’s time to put it to good use.

As Eric pointed out in the comments section, the way that the math is done, we could figure out how much a change in one of the factors changes a player’s wOBA by taking the derivative of the new formula for wOBA derived from the four factors equations. However, that’s a lot of work, so instead, as he suggests, I’m going to do this analysis numerically using a little program called Microsoft Excel.

Let’s test run this method on the simplest of targets: the league average player. In this case, we’ll use the league average player from 2009 MLB. In 2009, the league average BB% was 8.9%, the league average K% (K/PA) was 17.9%, the league average POWH (XB/H) was .595, and the league average BABIP was .299. The following chart shows how changes in each variable changes the player’s Four Factors Equivalent wOBA (ffwOBA).

In order to more easily visualize these on the same scale, I looked how changing each statistic by one standard deviation impacts ffwOBA. In this case, one standard deviation for BB% is 3.7%, for K% it’s 7.3%, for POWH it’s .257, and for BABIP it’s .049 points.

The slope of these lines tells us how sensitive wOBA is, at least as predicted by the four factors, to changes in each stat. BABIP is the steepest, as changing BABIP by one standard deviation changes wOBA by 41 points. Next is POWH, which although it isn’t perfectly linear, it’s close enough that we can treat it as such. Changing POWH by one standard deviation changes wOBA by 33 points. One standard deviation change in K rate changes wOBA by 26 points. A player’s wOBA is by far least sensitive to BB%, as a one standard deviation change in BB rate only changes wOBA by 13 points.

My explanation for the small changes in wOBA brought upon by BB rate changes is that increasing BBs, at least in this model, reduce all favorable outcomes (all hits) as well as reducing outs. The reduction in outs is enough to mean that an increase in BB% is a good thing. However, decreasing K% only means decreasing outs, increasing POWH means increasing 2B, 3B, and HR at the expense of 1B, which is a high net increase, and increasing BABIP means increasing all hits at the expense of outs, which is clearly the best of all results.

Through the rest of the week, I’ll be taking a look at some interesting players, hopefully examining how this method performs at the extremes.