EASTERBROOK, Circuit Judge.

While off duty from his job as a police officer, Darrin Macon argued with Andrew Richardson about Macon's former girlfriend. Macon fired his gun at Richardson but missed. When on-duty police officers arrived, Macon said that Richardson had struck him with a baseball bat. Richardson was arrested and charged with assault and battery. After the charges were dismissed, Richardson filed this suit making 39 claims under 42 U.S.C. § 1983 and state law against Chicago, Macon, the arresting officers, and others.

Chicago prevailed before trial because municipalities are not vicariously liable under § 1983, and the district judge found that none of the City's own policies (including its training regimens) is constitutionally deficient. See Monell v. New York City Department of Social Services, 436 U.S. 658, 98 S.Ct. 2018, 56 L.Ed.2d 611 (1978). The other claims went to trial, and all defendants other than Macon won. The jury decided in Richardson's favor on one claim, concerning the shot Macon fired, and awarded $1 in nominal damages plus $3,000 in punitive damages. Macon did not appeal — nor did Chicago, which under Illinois law must indemnify Macon for the $1 but not the punitive award — but the main event of the case lay ahead: a request for attorneys' fees under 42 U.S.C. § 1988.

Richardson asked for more than $675,000 in fees. The district judge ultimately awarded about $123,000. 2013 U.S. Dist. LEXIS 78677 (N.D. Ill. June 5, 2013). First she excluded time that counsel had devoted to unsuccessful motions (or the unsuccessful response to Chicago's motion for summary judgment under Monell). The judge then observed that Richardson's lawyers had not kept time sheets in away that allow the identification of hours spent pursuing claims against the defendants who won at trial, or indeed to unsuccessful claims against Macon. Because non-compensable time could not be separated out, the district judge decided that the lodestar (the number of hours times the market rate for each hour) should be cut across the board. But what was the right reduction? The judge noted that Richardson had asked for $500,000 in settlement and rejected a generous offer, then asked the jury for $200,000, yet recovered only $3,001. That result was a flop, the judge reckoned, even though it technically makes Richardson a "prevailing" party. See Farrar v. Hobby, 506 U.S. 103, 113 S.Ct. 566, 121 L.Ed.2d 494 (1992).

If the jury had stopped with the $1 in nominal damages, then under Farrar an award of attorneys' fees would be un-warranted. But the $3,000 in punitive damages was enough, in the judge's view, to justify some attorneys' fees. The judge thought that a roughly 80% reduction from the lodestar appropriate in light of the modest success counsel had achieved for Richardson. The district court ordered Macon personally — but not the City of Chicago — to pay Richardson $123,165.24 under § 1988. The court also ordered Richardson to reimburse Chicago's costs under Fed.R.Civ.P. 54(d)(1).

Macon did not file a notice of appeal. But in response to Richardson's appeal, Macon (in his role as appellee) maintains that the award should have been against Chicago rather than against him personally. His decision not to appeal means, however, that we cannot alter the judgment to make it more favorable to him. See, e.g., Greenlaw v. United States, 554 U.S. 237, 128 S.Ct. 2559, 171 L.Ed.2d 399 (2008); El Paso Natural Gas Co. v. Neztsosie, 526 U.S. 473, 119 S.Ct. 1430, 143 L.Ed.2d 635 (1999).

Richardson, like Macon, wants Chicago added as a judgment debtor on the award of attorneys' fees (though Richardson does not want Macon's liability ended). Yet Chicago's only substantive obligation is to indemnify Macon for the nominal award. That obligation rests on state law, but we put to one side the fact that § 1988 deals with parties who have prevailed on federal claims. Cf. Graham v. Sauk Prairie Police Commission, 915 F.2d 1085 (7th Cir.1990) (discussing the possibility, not raised by Richardson's briefs, that a state indemnification statute may include attorneys' fees independent of § 1988). We also bypass Richardson's failure to object to a magistrate judge's recommendation that Macon alone be liable for attorneys' fees. See Thomas v. Arn, 474 U.S. 140, 106 S.Ct. 466, 88 L.Ed.2d 435 (1985); Video Views, Inc. v. Studio 21, Ltd., 797 F.2d 538 (7th Cir. 1986). It is enough to rely on Farrar, which holds that establishing an entitlement to nominal damages does not justify an award of attorneys' fees under § 1988. So even if we assume that Chicago's obligation runs directly to Richardson (to whom Chicago wrote a check for $1), rather than to Macon, Richardson is not entitled to anything from Chicago under § 1988.

Quite the contrary, Richardson must pay the City's costs under Rule 54(d)(1), just as the district court held. Rule 54 entitles prevailing parties to recover their costs. Chicago prevailed against Richardson under § 1983 when the district court granted its motion for summary judgment under Monell, and it prevailed at trial on all state-law claims. State law requires Chicago to cover the $1 award, given the jury's special verdict that Macon acted under color of state law because he had a City-issued weapon, which the Police Department requires its officers to carry when off duty. That verdict was not a victory by Richardson against Chicago, however; it was a victory by Richardson against Macon, and by Macon against Chicago.

Richardson asks us to treat the "state actor" verdict as at least a moral victory vis-à-vis Chicago, which may lead it to take greater care in the future when selecting and supervising police officers. Costs (and fees) do not follow moral victories, however; they depend on concrete judgments that alter legal relations. See Buckhannon Board & Care Home, Inc. v. West Virginia Department of Health & Human Resources, 532 U.S. 598, 121 S.Ct. 1835, 149 L.Ed.2d 855 (2001). Chicago won a judgment against Richardson, not the other way around, so the award of costs to Chicago was proper. See also First Commodity Traders, Inc. v. Heinold Commodities, Inc., 766 F.2d 1007, 1015 (7th Cir.1985).

The principal remaining question is whether a district court may reduce attorneys' fees across the board to reflect limited success, when the lawyers' records do not permit the court to decide which hours were devoted to winning claims and which to losing ones. Richardson contends that percentage reductions are never allowed. He relies principally on Riverside v. Rivera, 477 U.S. 561, 106 S.Ct. 2686, 91 L.Ed.2d 466 (1986), which held that a district judge may not routinely limit attorneys' fees under § 1988 to a fixed percentage of the recovery (such as 1/3 of the damages, along the lines of a contingent-fee contract). Yet a rule that fees may not be capped at a percentage of the plaintiff's recovery differs from a rule that a district judge never can award fees based on a percentage of the lawyer's bill.

The appropriate fee under § 1988 is the market rate for the legal services reasonably devoted to the successful portion of the litigation. See, e.g., Pennsylvania v. Delaware Valley Citizens' Council for Clean Air, 483 U.S. 711, 107 S.Ct. 3078, 97 L.Ed.2d 585 (1987); Hensley v. Eckerhart, 461 U.S. 424, 103 S.Ct. 1933, 76 L.Ed.2d 40 (1983). If an attorney's billing records permit the calculation of the hours devoted to the claims on which the plaintiff prevailed, then all a judge need do is determine the market rate for an hour of the lawyer's time and whether the fee generated by multiplying the hours by the rate is reasonable in relation to the value of the case (which can include precedential value as well as the plaintiff's monetary recovery). See Hensley, 461 U.S. at 440, 103 S.Ct. 1933. But when the lawyer's billing records do not permit time to be allocated between winning and losing claims, estimation is inevitable.

No algorithm is available. Some legal time will be a joint cost of winning and losing claims alike; it is compensable despite the losses. If the winning and losing claims are just different legal theories in support of the same relief, again full compensation is proper. But losing claims seeking different or additional relief, or damages against different defendants, usually add some marginal expenses to the litigation. A judge could try to estimate how much time would reasonably have been devoted to the winning claims, had no clunkers been presented. But if that attempt would be futile (the district judge here permissibly reached that conclusion), there is nothing to do but make an across-the-board reduction that seems appropriate in light of the ratio between winning and losing claims. As Hensley put it, a court may "identify specific hours that should be eliminated, or it may simply reduce the award to account for the limited success." Id. at 436-37, 103 S.Ct. 1933. Just as a percentage increase may be added to a lodestar to reflect exceptionally good results, see Perdue v. Kenny A., 559 U.S. 542, 130 S.Ct. 1662, 176 L.Ed.2d 494 (2010), so a percentage decrease may be applied to reflect poor results. See, e.g., Cooke v. Stefani Management Services, Inc., 250 F.3d 564, 570 (7th Cir.2001) (50% across-the-board reduction was within district judge's discretion); Spegon v. Catholic Bishop of Chicago, 175 F.3d 544, 558-59 (7th Cir.1999) (same).

The jury gave Richardson 1.5% of what he sought at trial. This was a dismal outcome; Richardson rued rejecting defendants' settlement offers. He prevailed against only one of nine defendants. He lost 38 of his 39 claims. The district judge concluded that chunks of the litigation had been overstaffed, with multiple lawyers doing tasks that a single lawyer could have accomplished more economically. Despite all of this, the judge awarded Richardson approximately 18% of the fees his legal team requested (or about 20% after reductions for time that confidently could be traced to losing claims). An award of some $123,000 is generous in relation to Richardson's recovery. It cannot be condemned as too low under the deferential standard applicable to appellate review. See Pickett v. Sheridan Health Care Center, 664 F.3d 632, 639 (7th Cir.2011); cf. Pierce v. Underwood, 487 U.S. 552, 571, 108 S.Ct. 2541, 101 L.Ed.2d 490 (1988).

In Estate of Enoch v. Tienor, 570 F.3d 821 (7th Cir.2009), we held that a district court could not take a meat cleaver to the requested attorneys' fees when the recovery ($635,000) was "spectacular ... in the realm of prison-related litigation" (id. at 822) just because plaintiff had asked the jury for an absurd award of $5 million. No one could think that Richardson's award of $3,001 is spectacularly high or that a verdict well below what he could have had in settlement reflects a significant victory.

Richardson's other arguments have been considered but do not require discussion.

AFFIRMED.