MEMORANDUM AND ORDER
JOHN GLEESON, District Judge:This is an antitrust class action brought by merchants against Visa, MasterCard, and a number of banks, alleging that the defendants conspired to fix certain credit card fees and rules. In a December 13, 2013 memorandum and order, DE 6124, 986 F.Supp.2d 207, 2013 WL 6510737 (E.D.N.Y.2013) (“Approval Order”), I approved a settlement, see DE 2111. The settlement has two principal components: a fund of about $7.25 billion (before reductions for opt-outs, which reduced the fund to about $5.7 billion), against which merchants who did not opt out of a Rule 23(b)(3) class may make damages claims; and injunctive relief in the form of various credit card network rules changes, which apply to all members of a Rule 23(b)(2) class. The Approval Order deferred resolution of the Class Plaintiffs’1 simultaneous motion for attorneys’ fees and costs, see DE 2113, which I address now.
Although every case is unique, this case stands out in size, duration, complexity, and in the nature of the relief afforded to both the injunctive relief and damages classes. Class Counsel2 took on serious risks in prosecuting the case. They now represent that, taking together all of the hours that they and other plaintiffs’ counsel billed on this case, the lodestar figure for attorneys’ fees is approximately $160 million, reflecting almost 500,000 hours of attorney and paralegal work conducted through November 30, 2012. They request a fee of $570 million, equal to approximately ten percent of the fund after opt-out reductions.3
*440For the reasons given below, I grant attorneys’ fees in the amount of $544.8 million. I also approve Class Counsel’s request for expenses in the amount of $27,037,716.97. The request for incentive payments to the Class Plaintiffs is denied without prejudice to renewal.
DISCUSSION
A. Attorneys’Fees
I assume familiarity here with the facts and case history .set forth in the Approval Order.
Class action fee awards are evaluated based on the six-factor standard set forth in Goldberger v. Integrated Resources, Inc., 209 F.3d 43, 50 (2d Cir.2000). Under that standard, I must weigh “(1) the time and labor expended by counsel; (2) the magnitude and complexities of the litigation; (3) the risk of the litigation ...; (4) the quality of representation; (5) the requested fee in relation to the settlement; and (6) public policy considerations.” Id.
I may award attorneys’ fees using either a percentage of the fund or a lodestar calculation. Id.; see also Wal-Mart Stores, Inc. v. Visa U.S.A., Inc., 396 F.3d 96, 121 (2d Cir.2005). The trend in this Circuit, and the method I adopt here, is a percentage of the fund. The percentage method better aligns the incentives of plaintiffs’ counsel with those of the class members because it bases the attorneys’ fees on the results they achieve for their clients, rather than on the number of motions they file, documents they review, or hours they work. See Wal-Mart, 396 F.3d at 121 (“In contrast [to the percentage method], the lodestar creates an unanticipated disincentive to early settlements, tempts lawyers to run up their hours, and compels district courts to engage in a gimlet-eyed review of line-item fee audits.”) (internal quotation marks, citations, and alterations omitted). The percentage method also accords with the overwhelming prevalence of contingency fees in the market for plaintiffs’ counsel: when potential clients and lawyers bargain freely for representation, most contracts award the lawyer a percentage (commonly, about one third) of the client’s recovery. As Professor Charles Silver points out, the contingency fee model covers all sorts of plaintiffs’ litigation, including cases where sophisticated individual clients have high-stakes, complex claims worth hundreds of millions of dollars. See Declaration of Professor Charles Silver Concerning the Reasonableness of Class Counsel’s Request for an Award of Attorneys’ Fees 25-34 (“Silver Decl.”), DE 2113-5. Although I cannot hope to reconstruct what a hypothetical arm’s-length negotiation of fee rates between the class and Class Counsel might have yielded, it is essentially unheard of for sophisticated lawyers to take on a case of this magnitude and type on any basis other than a contingency fee, expressed as a percentage of the relief obtained.
Nonetheless, I will also use the lodestar figure as a “cross-check” to assure that the percentage-based fee is reasonable. See Goldberger, 209 F.3d at 50 (noting that “where used as a mere cross-check, the hours documented by counsel need not be exhaustively scrutinized by the district court,” and instead “the reasonableness of the claimed lodestar can be tested by the court’s familiarity with the case”).
Evaluation of the six Goldberger factors is not a mechanical process, and some of them present perplexing issues in this case, as discussed below.
1. Risk; Complexity of Litigation
The most important Goldberger factor is often the case’s risk. See, e.g., McDaniel v. Cnty. of Schenectady, 595 *441F.3d 411, 424 (2d Cir.2010); Beckman v. KeyBank, N.A., 293 F.R.D. 467, 479 (S.D.N.Y.2013); In re KeySpan Corp. Sec. Litig., 01 CV 5852(ARR), 2005 WL 3093399, at *5 (E.D.N.Y. Sept. 30, 2005). This case was unusually risky for a number of reasons:
• When the litigation began in 2005, only one court had ruled on an antitrust challenge to the manner in which interchange rates are set, and it had found in favor of the defendant. See National Bancard Corp. (NaBanco) v. VISA U.S.A., Inc., 779 F.2d 592 (11th Cir.1986).
• As in the first Visa/MasterCard antitrust case I presided over, the plaintiffs did not piggyback on previous government action — indeed, the government piggybacked on their efforts. See Walr-Mart, 396 F.3d at 122.
• Once the case was initiated, the plaintiffs’ legal theories faced many risks, as I discussed in the Approval Order. In brief, the plaintiffs: could have lost on antitrust standing grounds under Illinois Brick Co. v. Illinois, 431 U.S. 720, 736, 97 S.Ct. 2061, 52 L.Ed.2d 707 (1977); had to deal with the networks’ restructuring as independent companies, which occurred after the case had been filed; would have had to overcome the indisputable procompetitive effects of the challenged network rules; would have had serious obstacles in proving damages; and would have had to win class certification and maintain that status through the end of trial. See Approval Order, 986 F.Supp.2d at 224-29.
Those risks could have meant the end of the litigation with no recovery for class members and no fee for counsel. Counsel should be rewarded for undertaking them and for achieving substantial value for the class. If not for the attorneys’ willingness to endure for many years the risk that their extraordinary efforts would go uncompensated, the settlement would not exist.
In Goldberger, the Second Circuit — correctly, I believe — doubted that substantial contingency risk inheres in every common fund case. See 209 F.3d at 52 (citing Janet Cooper Alexander, Do the Merits Matter? A Study of Settlements in Securities Class Actions, 43 Stan. L.Rev. 497, 578 (1991)). When a court finds that, in fact, there was relatively little risk of failure, the fee award should reflect that finding. But given the existential threats to this litigation discussed in the Approval Order, I conclude that the risk in this case was enormous. My award of attorneys’ fees must recognize that, from an ex ante perspective, counsel no doubt had serious doubts about taking on such a risky and expensive litigation.
As for complexity, no one can reasonably dispute the fact that this case was enormously complex, both factually and legally.
2. Quality of Representation; Time Spent by Counsel
In light of that serious risk and the complexity of the case, the quality of representation in this case may be measured in large part by the results that counsel achieved for the classes. I discussed the merits and demerits of the settlement in detail in the Approval Order, but I reiterate here that the settlement constitutes a significant step toward remedying the merchants’ complaints about interchange rates in Visa and MasterCard credit card transactions. Even standing alone (that is, without considering the other rules changes created or locked in by the settlement), the merchants’ newly acquired ability to surcharge the use of credit cards at the product level has great value. The *442networks and the banks fiercely resisted such a change in the rules throughout the long and hard-fought settlement discussions. Class Plaintiffs’ expert estimates that it could save merchants between $26.4 and $62.8 billion over the next decade. Frankel Deck, ¶¶ 67-73, DE 2111-5. Plaintiffs’ counsel also worked toward the passage of the Durbin Amendment, which removed discounting restrictions at the network level. And this case also helped precipitate the networks’ consent decree with the Department of Justice after plaintiffs’ counsel shared their work with government attorneys several years into the litigation. For these and other reasons, the settlement cannot be reduced to the damages alone; it encompasses real programmatic reforms that enable merchants to stimulate network and bank competition on interchange rates by taking action at the point of sale. When the rules changes are combined with the massive damages fund, the settlement must be labeled a significant success. That assessment reinforces my judgment that plaintiffs’ counsel litigated the case with skill and tenacity, as would be expected to achieve such a result. See Goldberger, 209 F.3d at 55 (“[T]he quality of representation is best measured by results.”).
The amount of time and energy that counsel spent on the case is clear from the reported number of hours — nearly 500,-000 — and from even a cursory review of the docket sheet.
3. Fee in Relation to Fund; Public Policy Considerations
This brings me to the final two factors: the requested fee in relation to the size of the settlement fund, and public policy considerations. Class Counsel have requested a fee of $570 million, which represents about 10% of the fund (after reductions for opt-outs).4 Relying on counsel’s representation of a lodestar value of about $160 million, the requested fee would amount to a multiplier of 3.54.
Even with the aid of the Goldberger factors, I have struggled to find a strong normative basis by which to evaluate the requested fee or to generate my own figure. The law sets only minimal constraints on fee awards. Within the boundaries of those constraints, it offers no concrete guideposts. And this case is *443so large and complex that it has few comparators to guide my judgment. More precise guidance would be useful, not so much for the district judges making the fee awards, who generally welcome broad discretion, but for the lawyers who do this kind of work. Bearing the risk of failure on the merits comes with the territory, but it seems anomalous that counsel must also bear the additional financial risk that inheres in such broad discretion even when they succeed. In any event, I elaborate below on my thought process in awarding fees in this case for the benefit of the parties and any reviewing courts.
As mentioned above, unlike more routine class cases — for example, wage and hour settlements with values of about a million dollars, for which countless comparators could be found — comparison to similar cases is difficult here given the singular size and complexity of this case. And unlike (for example) securities cases under the PSLRA, I am afforded no guidance by the parties’ negotiations. In PSLRA litigation, a lead plaintiff may bargain with lead counsel over fees, though in this Circuit a district court need not defer to such a bargain when actually making the award at the end of litigation. See In re Nortel Networks Corp. Sec. Litig., 539 F.3d 129, 133 (2d Cir.2008) (reserving the question of whether a negotiated fee is presumptively reasonable, which is the rule under cases such as In re Cendant Corp. Litig., 264 F.3d 201, 282-83 (3d Cir.2001)). It would be helpful to have a negotiated benchmark from which to work, and in a future case, I will consider employing my authority under Rule 23(d) to require such negotiation — perhaps with court-appointed counsel to represent a cross-section of the plaintiffs for the purposes of the fee negotiation.5
In theory, even in the absence of a negotiated rate here, I could look to other, comparable cases in which counsel and class members bargained over fees. See In re Nortel Networks Corp. Sec. Litig., 539 F.3d at 134 (noting that fee awards should, where possible, approximate market rates, and citing cases). But there is little information about how sophisticated plaintiffs and lawyers behave in cases with recoveries this large, because there are very few cases of comparable size, and none include a fee arrived at through private bargaining.
For these reasons, my starting point for assessing the requested fee in relation to the settlement fund is large class cases with court-set fees. The closest comparator case I know is the Visa/MasterCard settlement I presided over ten years ago. In that case, I approved a fee award of about $220.3 million, about 6.5% of the value of the fund, for a multiplier of 3.5, see In re Visa Check/Mastermoney Antitrust Litig., 297 F.Supp.2d 503, 524 (E.D.N.Y.2003), which the Second Circuit upheld, see Wal-Mart, 396 F.3d at 121-23. The two cases are in some ways similar: both are antitrust cases involving the two largest networks and banks, with merchants as plaintiffs; both involve novel and complex legal questions; in their history, both encompassed many years of litigation involving many thousands of hours of law*444yering; and in their results, both ended in huge settlement funds accompanied by programmatic reforms of (possibly) even greater monetary value. In one meaningful respect, however, they are different: This case was more challenging. The impediments to the tying allegation in the Walr-Mart case were not as ominous as the obstacles faced by the plaintiffs here, which are discussed in the Approval Order. The more progress the merchants make— through private lawsuits, government cases, and legislation — the more difficult it becomes to establish an antitrust violation.
Despite the absence of concrete guideposts, there are some legal principles that help me evaluate the requested fee in relation to the fund. One is that the percentage of the fund awarded should scale back as the size of the fund increases. I recently observed that “[t]o avoid routine windfalls where the recovered fund runs into the multi-millions, courts typically decrease the percentage of the fee as the size of the fund increases.” Precision Associates, Inc. v. Panalpina World Transp. (Holding) Ltd., 08-CV-42 JG WP, 2013 WL 4525323, at *16 (E.D.N.Y. Aug. 27, 2013) (internal quotation marks and citation omitted). That seems to be the practice of judges nationwide. For example, a recent study found that for federal class action settlements in the years 2006 and 2007, the percentage awarded “tended to drift lower at a fairly slow pace until a settlement size of $100 million was reached, at which point the fee percentages plunged well below 20 percent, and by the time $500 million was reached, they plunged well below 15 percent, with most awards at that level under even 10 percent,” though that last category covered only eleven settlements. Brian T. Fitzpatrick, An Empirical Study of Class Action Settlements and Their Fee Awards, 7 J. Empirical L. Stud. 811, 838 (2010). Another study, by Theodore Eisenberg and Geoffrey P. Miller, also showed decreasing percentages as the size of the fund increased. See Theodore Eisenberg and Geoffrey P. Miller, Attorney Fees and Expenses in Class Action Settlements: 1998-2008, 7 J. Empirical L. Stud. 248, 265 (2010).
As my formulation in Precision Associates makes clear, I believe the main reason courts adopt the downward-scaling percentage method is to prevent a windfall for class counsel. But what is a windfall? Lawyers for a class receive a windfall only if their compensation exceeds the value of their services.6 Comparison to private fee arrangements shows that sophisticated clients often require counsel to accept a smaller percentage of a recovery as the size of the recovery increases. Thus, some scaling back seems appropriate here as well.
*4454. Graduated Schedule and Fee Award
I have employed a percentage calculation, but as many large individual clients in high-stakes patent cases or institutional investors in securities cases under the PSLRA do, I have scaled the marginal percentage down as the amount of the recovery increased. See, e.g., In re Inter-public Sec. Litig., 02 CIV.6527(DLC), 2004 WL 2397190, at *12 n. 4 (S.D.N.Y. Oct. 26, 2004) (discussing graduated fee schedule for In re WorldCom Securities Litigation ). Other courts have adopted graduated schedules in class cases. See In re Oracle Sec. Litig., 132 F.R.D. 538 (N.D.Cal.1990) (holding an auction for counsel in securities case, and accepting a winning fee with a graduated, declining schedule). Obviously, the same resulting fee could be reached by picking a single percentage (noted as the average in the table set forth below) and applying it to the entire fund. But the graduated fee schedule has a number of advantages.
First, a graduated schedule permits a more reasoned and transparent calculation of the lawyers’ fee based on comparison to other cases. For example, it is very common to see 33% contingency fees in cases with funds of less than $10 million, and 30% contingency fees in cases with funds between $10 million and $50 million. As mentioned above, it is also common to see a graduated schedule in cases where sophisticated clients negotiate fees in advance.
Second, a graduated schedule implicitly acknowledges and addresses a worry that many courts, including the Goldberger court, have expressed, i.e., that “it is not ten times as difficult to prepare, and try or settle a 10 million dollar case as it is to try a 1 million dollar case.” Goldberger, 209 F.3d at 52 (quoting In re Union Carbide Corp. Consumer Products Bus. Sec. Litig., 724 F.Supp. 160, 166 (S.D.N.Y.1989)).
The following table lays out the fee schedule I have chosen to adopt.
Bracket_Fee percentage Marginal fee
0-$10 million_33%_$3.3 million
$10 million-$50 million 30%_$12 million
$50 million-$100 million 25% $12.5 million
$100 million-$500 million 20%_$80 million
$500 million-$l billion_15%_$75 million
$1 billion-$2 billion 10%_$100 million
$2 biIlion-$4 billion_8%_$160 million
$4 biIlion-$5.7 billion_6%_$102 million
TOTALS_(average) 9.56% $544.8 million
Thus, counsel are awarded 33% of the fund up to $10 million, or $3.3 million, which reflects a common contingency fee arrangement in less complex class cases; 30% of the next $40 million (reaching $50 million); 25% of the next $50 million (reaching $100 million); 20% of the next $400 million; 15% of the following $500 million; 10% of the following $1 billion; 8% of the following $2 billion; and 6% of the remainder, up to the final value of $5.7 billion.7 The result is a total fee of $544.8 million, or 9.56% of the total fund.
I acknowledge an irreducible minimum of arbitrariness in the cutoff amounts and *446the percentages in any such schedule, including this one, but I take some inspiration from the empirical studies cited above.8 I have also examined the Silver Declaration, which catalogs fee awards in many “megafund” cases with values exceeding $100 million. And I have also tried to adhere to what I believe to be norms of the profession.
In picking these specific brackets and percentages, I am especially mindful of two facts. First, this case settled only after many years of hard-fought litigation. Privately negotiated fees in complex cases (including PSLRA cases) often include a higher fee for cases that proceed past a motion to dismiss, discovery, summary judgment, or other benchmarks;9 the Goldberger factors also dictate a smaller fee for less work. An earlier settlement reached through less work would surely warrant a smaller fee. Second, as I mentioned in footnote 4, although it is impossible to know with certainty the ultimate value of the injunctive relief, it may very likely exceed the value of the monetary relief in the long run. The injunctive relief is therefore a “relevant circumstance,” to say the least. See Staton, 327 F.3d at 974.
A final reason to employ the schedule methodology advanced here is for the benefit of counsel in future cases. If plaintiffs’ lawyers know in advance (that is, at the start of a case) that such a schedule will be used, it will alter their thinking for the better. A graduated schedule ensures that the greater the settlement, the greater the fee, and it therefore avoids certain incentive problems that come from simply scaling an overall percentage down as the size of the fund increases.10 See In re Synthroid Mktg. Litig., 264 F.3d 712, 721 (7th Cir.2001) (citing eases, and noting that the graduated schedule ensures that “attorneys’ fees never [go] down for securing a larger kitty, and counsel always [have] an incentive to seek more for their clients”). Using such a schedule as a guideline for future cases — from which departures based on case-specific circumstances may of course be warranted — will permit counsel to make reasonable decisions ex ante in those future cases.
In my view, a guidepost is sorely needed. We know from other contexts that the conferral of broad discretion on district judges without providing sufficient guidance for the exercise of that discretion produces unwarranted disparities in outcomes, which undermine justice and the appearance of justice. Broad discretion in *447this context is certainly appropriate; as Goldberger acknowledges, each case is unique, and district judges should be empowered to set a fee that recognizes those unique circumstances.11
Still, a starting point, from which explained departures in either direction would be permissible, and perhaps even frequent, might reduce both those unwarranted disparities and the extent to which class counsel, ex ante, regard future attorneys’ fee proceedings as a crapshoot in large cases. I expect no deference to the particular schedule I have found useful here; I have tailored it to the unique facts and circumstances of the settlement I have approved here, which combine to produce a generous but well-deserved fee. I believe that the adoption of something like this schedule — or indeed a different sort of benchmarking mechanism, such as a PSLRA-like mechanism for a negotiated rate — by a higher court or a coordinate branch would be beneficial. In any event, it is my considered judgment that, in this ease, the cutoff amounts and percentages I have used above result in a fair overall figure.
5. Lodestar Cross-Check
There are at least two reasons that judges are comfortable assessing hourly rates when awarding fees. First, the billable hour is common in our profession, especially in certain types of cases and for certain types of clients. Second, many federal fee-shifting civil rights statutes that permit court-awarded attorneys’ fees incorporate a lodestar value or a close cousin. See generally. Arbor Hill Concerned Citizens Neighborhood Ass’n v. Cnty. of Albany & Albany Cnty. Bd. of Elections, 522 F.3d 182, 186-90 (2d Cir.2008). However, the fact that statutes dictate such a measure for some cases does not mean that the billable hour represents the “true” value of attorney time in general. Nor does the fact that many firms bill by the hour for many types of cases' compel that conclusion. Many defense firms are now facing pressure to change their billing models to flat fees or to incorporate incentives to avoid inflation of hours. Their clients evidently do not believe that the value of a firm’s services is necessarily related to the number of hours billed. On the plaintiffs’ side, where it is often easier to measure the value that lawyers produce for their clients, the contingency fee — that is, a cut of the proceeds — rules. That fact would be unremarkable to bankers, real estate brokers, sports agents, and other professionals who are used to being paid based on the value they obtain for their clients rather on the number of hours they have worked.
These concerns diminish the value of the lodestar crosscheck, but they do not eliminate it. Critically, the lodestar multiplier is one metric that permits, comparison across a wide range of case types and fund sizes. Here, with a fee award of $544.8 *448million, and a lodestar of about $160 million, the multiplier is about 3.41. That multiplier is comparable to (indeed, nearly identical to) the one I awarded in the WalMart case ten years ago, and it is also comparable to multipliers in other large, complex cases. Without engaging in a “gimlet-eyed review” of the fee application, I am nonetheless confident that this is a reasonable multiplier and a reasonable overall fee. See, e.g., In re WorldCom, Inc. Sec. Litig., 388 F.Supp.2d 319, 354-59 (S.D.N.Y.2005) (approving $194.6 million fee award, for multiplier of 4.0, or 5.5% of the fund, in complex securities case with value of approximately $3.5 billion, and citing cases).
B. Expenses
Counsel have also sought reimbursement of expenses slightly in excess of $27 million. As a general rule, counsel are entitled to reimbursement for reasonable out-of-pocket expenses incurred over the course of litigating the case. See, e.g., In re Vitamin C Antitrust Litig., 06-MD-1738 BMC JO, 2012 WL 5289514, at *11 (E.D.N.Y. Oct. 23, 2012) (“Courts in the Second Circuit normally grant expense requests in common fund cases as a matter of course.”); In re Global Crossing Sec. & ERISA Litig., 225 F.R.D. 436, 468 (S.D.NY.2004). Finding these expenses reasonable, I approve them here in the full amount requested: $27,037,716.97.
C. Incentive Payments
Finally, Class Counsel have also sought incentive payments totaling $1.8 million for the nine Class Plaintiffs. Along with their motion for attorneys’ fees, Class Counsel submitted declarations of corporate officers for each of the nine Class Plaintiffs. In various levels of detail, these declarations document the work that the named plaintiffs undertook to support the case, as well as the expenses they incurred in doing so.
It is true that $1.8 million constitutes only about .03% of the $5.7 billion fund. Nonetheless, the average incentive award proposed — $200,000 for each plaintiff — will no doubt dwarf the average monetary recovery per class member.12
Class representatives will certainly be permitted to recover their (properly documented) expenses. Just as the lawyers worked on behalf of the entire class, so too did the class representatives in producing documents, attending depositions, and so on. It is thus only fair for the absent class members to reimburse the named plaintiffs’ reasonable expenses. See, e.g., In re Marsh & McLennan Companies, Inc. Sec. Litig., 04 CIV. 8144(CM), 2009 WL 5178546, at *21 (S.D.N.Y. Dec. 23, 2009). To this point, however, only some of the Class Plaintiffs have even attempted to document those expenses. Before I approve any reimbursements, counsel for those representatives will need to provide better evidence of the amount of each named plaintiffs expenses.
As to the incentive awards, while I am mindful of the risks that the named plaintiffs may have undertaken, to this point, Class Counsel have not come close to justifying such large awards. In an admittedly much smaller case, I declined to approve a settlement in which the proposed incentive payments were four times the mean anticipated payment and over thirteen times the median anticipated payment. Gulino v. Symbol Technologies, Inc., 06 CV *4492810(JG)(AKT), 2007 WL 3036890, at *3 (E.D.N.Y. Oct. 17, 2007). Here, the ratio of the average incentive award to the average payment is much higher. Class Counsel are expected to provide, at a minimum, documentation setting forth the approximate value of each Class Plaintiffs claim and each one’s proposed incentive award. They are also expected to provide any relevant authority, factual and legal, for the requested awards.
CONCLUSION
For the reasons stated above, I award Class Counsel fees of $544.8 million and costs and expenses of $27,037,716.97. The application for incentive payments to class representatives is denied without prejudice to renewal in a properly-supported motion.
So ordered.
. "Class Plaintiffs” refers to proposed class representative merchants Photos Etc. Corp.; Traditions, Ltd.; Capital Audio Electronics, Inc.; CHS Inc.; Crystal Rock LLC; Discount Optics, Inc.; Leon’s Transmission Service, Inc.; Parkway Corp.; and Payless Shoe-Source, Inc.
. "Class Counsel” refers to the three firms appointed co-lead counsel for Class Plaintiffs: Robbins Geller Rudman & Dowd LLP; Robins, Kaplan, Miller & Ciresi L.L.P; and Berger & Montague, P.C.
.Class Counsel initially requested $720 million, which represented 10% of the fund before reductions for opt-outs, but in their reply they revised the request to equal 10% of the fund net of those reductions. Though they reserve the right to seek additional fees from opt-outs on the theory that they benefited from Class Counsel’s efforts, see, e.g., In re Diet Drugs, 582 F.3d 524, 546 (3d Cir.2009) (approving district court’s award of fees from opt-outs), that issue is not before me now.
. Although I have little doubt that the injunctive relief in this case will eventually have great value to the merchants, I have not relied on its value in a strict mathematical sense— that is, I will not award a percentage of that additional value as fees. (I should note that, in contrast to the first Visa/MasterCard case, Class Counsel here make no such request.) As the Ninth Circuit wrote in Staton v. Boeing Co.,
Precisely because the value of injunctive relief is difficult to quantify, its value is also easily manipulable by overreaching lawyers seeking to increase the value assigned to a common fund. We hold, therefore, that only in the unusual instance where the value to individual class members of benefits deriving from injunctive relief can be accurately ascertained may courts include such relief as part of the value of a common fund for purposes of applying the percentage method of determining fees. When this is not the case, courts should consider the value of the injunctive relief obtained as a "relevant circumstance” in determining what percentage of the common fund class counsel should receive as attorneys’ fees, rather than as part of the fund itself.
327 F.3d 938, 974 (9th Cir.2003) (internal citation and footnote omitted). The value of the rules changes accomplished by the settlement (which may be enhanced by the recent, not-yet-approved settlement in separate litigation against American Express, see Hilary Stout, "An Easing of Rules on Charges by Amex,” The New York Times, December 20, 2013, at B1 (also available at http://www. nytimes.com/2013/12/20/business/an-easingof-rules-on-charges-by-amex.html)), is too uncertain at this point to be anything other than the kind of "relevant circumstance” described by the court in Staton.
. The need for representation of a cross-section of the putative class is important. In the Wal-Mart case, class counsel had negotiated with five merchants a fee arrangement that, they claimed, would produce attorneys’ fees far in excess of the amount awarded by the district judge. They urged the Second Circuit to hold that the negotiated fee had been improperly ignored below. The court rejected the argument. The five merchants were among "the nation’s largest merchants,” and the Second Circuit found no abuse of discretion in disregarding a fee negotiated with those five merchants “when settlement payments to approximately five million merchants are at stake.” 396 F.3d at 123.
. Imagine, for example, a case in which a $500 million settlement fund was achieved against considerable ex ante odds of success (due to novel legal issues, intense opposition, difficult discovery, appeals, and so forth), so that the settlement required not only superior legal skill but massive investment of lawyers’ time, and the lodestar value of counsel's time was $150 million. In that circumstance, would it be a "windfall” to award class counsel 30% of the fund, i.e., the lodestar value? Or would a 10% award be required by the value of the fund alone? In analogous circumstances, at least one judge did not think strict adherence to the diminishing percentage principle was appropriate. In In re Initial Pub. Offering Sec. Litig., 671 F.Supp.2d 467, 505 (S.D.N.Y.2009), counsel claimed a lodestar of $278 million; after reducing the hourly rate in order to account for factors such as the economic downturn and the heavy use of paralegal time, reaching a figure of about $200 million, the court awarded one third of the $510 million settlement as fees. The settlement was huge, but so was the lawyers’ effort, justifying a high-percentage fee that, in that court's judgment, was not a windfall.
. Because the value of this case is "only” $5.7 billion, I have not filled in the chart past that value, though there will eventually be settlements that exceed that amount. One approach would be to create additional brackets with even lower marginal percentages. It *446would also be possible, and probably wiser, to index the bracket values to inflation.
. For the twelve settlements in 2006 and 2007 between $72.5 and $100 million, the median fee was 24.3%; for the 14 settlements between $100 and $250 million, the median was 16.9%; for the eight settlements between $250 and $500 million, the median was 19.5%; for the two settlements between $500 million and $1 billion, the median was 12.9%; and for the nine settlements between $1 and $6.6 billion, it was 9.5%. See Fitzpatrick, Empirical Study, at 839.
. See, e.g., In re Oracle Sec. Litig., 132 F.R.D. at 540-41 (proposed fee schedules from three bidders in securities case tied both to amount of recovery and to stage at which litigation settles or duration of litigation).
.Imagine, for example, how counsel will behave if a court adopts the following non-graduated rule instead: 30% of the (total) fund if it's up to $100 million, or 20% of the (total) fund if it's between $100 million and $500 million. Counsel will prefer to settle a case for $100 million, yielding a $30 million fee, than for $140 million, yielding a fee of $28 million. See also In re Synthroid Mktg. Litig., 264 F.3d 712, 718 (7th Cir.2001) (describing similar problem in actual case). That incentive is contrary to the best interests of the class.
. Even in large-value cases, courts have sometimes awarded contingency fees exceeding 30% of the overall fund. In addition to In re Initial Pub. Offering Sec. Litig., 671 F.Supp.2d 467 (S.D.N.Y.2009), awarding one third of a fund that slightly exceeded $500 million, there is In re Checking Account Overdraft Litig., 830 F.Supp.2d 1330, 1367 (S.D.Fla.2011), which awarded 30% of $410 settlement in consumer litigation, and cases it cites: In re Vitamins Antitrust Litig., 2001 WL 34312839 (D.D.C. July 16, 2001) (34.6% of $365 million) and Allapattah Servs. Inc. v. Exxon Corp., 454 F.Supp.2d 1185 (S.D.Fla.2006) (31.33% of $1,075 billion). Likewise, even in mega-fund cases, courts have sometimes awarded contingency fees of under 6% of the total fund. E.g. In re AOL Time Warner, Inc. Sec., 02 CIV. 5575(SWK), 2006 WL 3057232 (S.D.N.Y. Oct. 25, 2006) (5.9% of $2.65 billion); In re WorldCom, Inc. Sec. Litig., 388 F.Supp.2d 319, 353, 360 (S.D.N.Y.2005) (5.6% of $3.5 billion).
. In their brief in support of the motion for settlement approval, Class Counsel estimated that the class contains at least 12 million members. See DE 2111 at 33 n. 36. The history of the Wal-Mart settlement suggests that the number of actual claims filed will be lower.