
76 Wn. App. 507 (1995)
887 P.2d 449
JOSEPH K. MAILLOUX, ET AL, Respondents,
v.
STATE FARM MUTUAL AUTOMOBILE INSURANCE COMPANY, Appellant.
No. 15577-0-II.
The Court of Appeals of Washington, Division Two.
January 9, 1995.
David Allan Larson; William R. Hickman and Reed McClure, for appellant.
Hollis Herman Barnett and Campbell Dille & Barnett, for respondents.
MORGAN, J.
State Farm Mutual Automobile Insurance Company appeals a superior court judgment that confirmed *509 an underinsured motorist (UIM) arbitration award in favor of Joseph K. Mailloux. We affirm.
On November 23, 1989, Woods was driving his pickup across the Narrows Bridge. The bed of the pickup was covered by a canopy. According to Mailloux, "a particularly ferocious windstorm" was in progress. The wind "ripped" the canopy off the truck, and Woods stopped to retrieve it. He parked in the roadway, because the bridge has no shoulder on which to pull off. Stray stopped behind Woods, and Mailloux stopped behind Stray. Johnson then rear-ended Mailloux, who was injured as a result.
Mailloux had UIM coverage with State Farm. Johnson had liability insurance with limits of $50,000, and Woods had liability insurance with limits of $100,000.
Mailloux settled with Johnson for $50,000. Before releasing Johnson, he offered State Farm the opportunity to purchase his rights against Johnson for the amount of the settlement. See Hamilton v. Farmers Ins. Co., 107 Wn.2d 721, 733 P.2d 213 (1987). State Farm did not accept.
Mailloux elected not to claim against Woods.[1] However, he demanded UIM arbitration with State Farm, and an arbitration hearing ensued. Mailloux took the position that Johnson was at fault and Woods was not. State Farm took the position that both Johnson and Woods were at fault.
On April 11, 1991, the arbitrators found that Mailloux's total damages were $107,500.[2] They allocated fault 90 percent to Johnson, 10 percent to Woods, and none to Mailloux. They awarded Mailloux $96,750 (90 percent of $107,500), "less any offsets or credits allowed by law".[3]
*510 After the arbitrators' award, State Farm claimed it was entitled to offset the sum of Johnson's and Woods' liability limits, or $150,000. Mailloux sued for a judgment confirming the award and declaring the amount owed by State Farm. The Superior Court confirmed that Mailloux was entitled to recover 90 percent of his total damages ($96,750). It also ruled that State Farm could offset Johnson's liability limits of $50,000, but not Woods' liability limits of $100,000. It concluded that Mailloux was entitled to recover $46,750 pursuant to his UIM coverage.[4]
State Farm now appeals. The issues are whether State Farm was entitled to offset the sum of Johnson's and Woods' liability limits, and whether Mailloux is entitled to reasonable attorney fees.

I
Washington's UIM statute is RCW 48.22.030. It requires that UIM insurance be "provided ... for the protection of persons insured thereunder who are legally entitled to recover damages from owners or operators of underinsured motor vehicles". RCW 48.22.030(2). It defines an "underinsured motor vehicle" as
a motor vehicle ... with respect to which the sum of the limits of liability under all bodily injury or property damage liability bonds and insurance policies applicable to a covered person after an accident is less than the applicable damages which the covered person is legally entitled to recover.

RCW 48.22.030(1).
Essentially, this statutory language requires that a lower number, hereafter called the subtrahend, be subtracted from an upper number, hereafter called the minuend. The minuend is "the applicable damages which the covered person is legally entitled to recover". RCW 48.22.030(1). The subtrahend is "the sum of the limits of liability under all bodily injury or property damage liability bonds and insurance policies *511 applicable to a covered person after an accident".[5] RCW 48.22.030(1).
The minuend is not in issue here. It is apparent that the arbitrators calculated it in accordance with RCW 4.22.070(1),[6] and neither party disputes the result.
[1] The subtrahend cannot be understood without first understanding RCW 4.22.070(1).[7] Under that statute, any party to a proceeding can assert that another person is at fault. Adcox v. Children's Orthopedic Hosp. & Med. Ctr., 123 Wn.2d 15, 25, 864 P.2d 921 (1993). Only the plaintiff, however, can assert that another person is liable to the plaintiff. If no one proves fault, the other person is neither at fault nor liable to the plaintiff. Adcox, 123 Wn.2d at 25-26. If the plaintiff proves fault that is a proximate cause of the plaintiff's *512 damages, the person at fault is also liable to the plaintiff, and judgment is entered as set forth in the statute. If a party other than the plaintiff proves fault that is a proximate cause of the plaintiff's damages, the person at fault is not liable to the plaintiff  the plaintiff has made no claim against him or her  but his or her fault nevertheless operates to reduce the "proportionate share" of damages that the plaintiff can recover from those against whom the plaintiff has claimed.
Because of these provisions, the subtrahend involves at least two distinct questions.[8] (1) Should the subtrahend include the liability limits of a liability insured when the plaintiff claims that the liability insured's fault is a proximate cause of the plaintiff's legally recoverable damages? (2) Should the subtrahend include the liability limits of a liability insured when the plaintiff does not claim that the liability insured's fault is a proximate cause of the plaintiff's legally recoverable damages, but the UIM carrier does? The second question involves what we hereafter call an "empty chair liability insured".
The second question is the one in issue here. Mailloux claimed against Johnson, but declined to claim against Woods. State Farm injected Woods into the arbitration proceeding, and successfully proved that he was 10 percent at fault. Under RCW 4.22.070(1), Woods' fault operated to reduce the percentage of damages that Mailloux could recover from Johnson, but it did not make Woods liable to Mailloux. Thus, Woods was an empty chair liability insured, and the question presented is whether the subtrahend should include the liability limits of an empty chair liability insured.
*513 [2] Although the second question is the one in issue, most of the parties' argument bears on the first question or is immaterial to the case. State Farm argues that Johnson and Woods are jointly and severally liable, and that the subtrahend therefore includes the sum of their liability limits. See Allstate Ins. Co. v. Dejbod, 63 Wn. App. 278, 292, 818 P.2d 608 (1991). A person is not liable to the plaintiff at all, much less jointly and severally, if he or she has not been named by the plaintiff. Thus, State Farm's argument rests on the presupposition that Mailloux made UIM claims based on the conduct of both Johnson and Woods.
That presupposition is incorrect. As shown above, Mailloux claimed against Johnson, but never against Woods. When Mailloux proved his claim against Johnson, Johnson became liable for purposes of arbitration; but when State Farm proved its claim against Woods, Woods became merely an empty chair liability insured  i.e., a person whose fault reduced the percentage of damages Mailloux was entitled to recover from Johnson, but whose fault did not make him liable to Mailloux, jointly, severally, or in any other way. We hold that Johnson and Woods are not jointly and severally liable for purposes of this UIM arbitration, and that State Farm is not entitled to cumulate their liability limits on that basis.
Mailloux argues that Johnson and Woods cannot be jointly and severally liable because he settled with Johnson before the UIM arbitration took place. For the reasons already stated, however, Johnson and Woods would not be jointly and severally liable to Mailloux even if Mailloux had not settled with Johnson. Thus, this argument is immaterial to the case.
State Farm relies on Allstate Ins. Co. v. Dejbod, supra, but that case does not help with the question at hand. In Dejbod, there were two potential tortfeasors, Gilven and Church, and the plaintiff, Dejbod, was actively claiming against both. There was no person against whom Dejbod was not claiming, but whose fault nonetheless was a proximate cause of Dejbod's legally recoverable damages. Thus, the question we considered was whether the subtrahend should include the limits of a liability insured against whom the UIM plaintiff *514 was claiming.[9] We did not consider the question of whether the subtrahend should include the liability limits of an empty chair liability insured.
State Farm makes only one argument that bears on whether the subtrahend should include the limits of an empty chair liability insured. Pointing out that RCW 48.22.030 allows a UIM carrier to offset "the sum of the limits of liability under all bodily injury or property damage liability bonds and insurance policies applicable to a covered person after an accident", and assuming that the liability policy of an empty chair insured is "applicable" to a UIM plaintiff, State Farm asserts that Woods' policy should have been included in the subtrahend.
We disagree. We think that the test for "applicable" liability insurance is whether the liability insured has been found liable to the plaintiff in the UIM proceeding. See Allstate Ins. Co. v. Dejbod, 63 Wn. App. at 286 (whether to include liability limits in subtrahend is tested by tortfeasor's liability, not by fact of settlement). As explained above, the mere fact that arbitrators assign fault to an empty chair insured does not make that person liable to the plaintiff for purposes of the UIM proceeding. Thus, the mere fact that arbitrators assign fault to an empty chair liability insured does not, by itself, cause that person's liability limits to be includable in the subtrahend.
The essential premise underlying this holding is that the plaintiff has not improperly prejudiced or impaired the *515 carrier's right to later prove, in a lawsuit brought in the plaintiff's name pursuant to its right of subrogation, that the empty chair insured really is liable to the plaintiff. So long as the carrier retains that right, it can pursue the empty chair insured to judgment and, if judgment is obtained, the rights of the plaintiff and carrier can then be adjusted accordingly. This places the burden of pursuing the empty chair insured where it should be  on the one who asserts that the empty chair insured is liable to the plaintiff. It also allows for the rights of the plaintiff and the carrier to be determined as they should be  on the basis of actual legal liability, determined in a way that binds the empty chair insured. If the plaintiff has improperly prejudiced or impaired the carrier's right to later prove in litigation that the empty chair insured is liable to the plaintiff, it may be that the empty chair insured's liability limits should be included in the subtrahend, but we need not decide that today.
In this case, the arbitrators did not find that Woods was liable to Mailloux; they only found that a percentage of Mailloux's damages should be attributed to Woods.[10] Moreover, Mailloux never prejudiced or impaired State Farm's right to pursue Woods in a way that State Farm is entitled to complain about.[11] Therefore, we hold that the trial court did not err in declining to include Woods' liability limits in the subtrahend.


*516 II
Mailloux claims reasonable attorney fees on the grounds that this appeal is frivolous. We hold, however, that this appeal is not frivolous.
Mailloux also claims reasonable attorney fees on the authority of Olympic S.S. Co. v. Centennial Ins. Co., 117 Wn.2d 37, 811 P.2d 673 (1991).[12] We hold, however, that Olympic Steamship does not authorize such fees in this case.
[3] In Olympic Steamship, the Washington Supreme Court held that reasonable attorney fees were authorized in cases in which an insurer unsuccessfully denies coverage to its insured.[13] 117 Wn.2d at 53. In Dayton v. Farmers Ins. *517 Group, 124 Wn.2d 277, 876 P.2d 896 (1994), however, the Washington Supreme Court distinguished cases in which an insurer denies a claim but not coverage. The court said:
Washington follows the American rule in awarding attorney fees. Under that rule, a court has no power to award attorney fees as a cost of litigation in the absence of contract, statute, or recognized ground of equity providing for fee recovery.... We have recognized a narrow exception to this rule where specific facts and circumstances warrant. Olympic Steamship presented such a situation.
This case presents an entirely different set of circumstances. Coverage is not an issue; Farmers accepted coverage. Unlike the insured in Olympic Steamship, Mr. Dayton has not compelled Farmers to honor its commitment to provide coverage. Instead, this case presents a dispute over the value of the claim presented under the policy. Such disputes are not properly governed by the rule in Olympic Steamship.

Dayton, 124 Wn.2d at 280. Thus, Olympic Steamship does not authorize reasonable attorney fees when an insurer denies a claim but not coverage.[14]
[4] For present purposes, whether an insurer denies coverage depends on whether the insurer denies a contractual duty to pay regardless of whether the facts needed to support the insured's claim against a third party are proved. More specifically, whether a UIM insurer denies UIM coverage depends on whether the UIM insurer denies a contractual duty to pay regardless of whether the UIM insured's damages are shown to exceed the limits of applicable liability insurance. In other words, UIM coverage is denied when a UIM insurer says it has no contractual duty to pay even if the UIM insured's total damages are shown to exceed the limits of applicable liability insurance. But UIM coverage is not denied if, while not denying a contractual duty to pay if its insured's damages exceed the limits of applicable liability insurance, a UIM insurer denies that its insured's damages *518 do in fact exceed such limits. In the latter instance, the UIM insurer denies the UIM claim, but not UIM coverage. See Kraus v. Grange Ins. Ass'n, 48 Wn. App. 883, 886, 740 P.2d 918 (1987) (differentiating between coverage and claim).
Throughout this case, State Farm's position has been that Mailloux's damages do not exceed the limits of applicable liability insurance. State Farm has never denied its contractual obligation to pay if in fact Mailloux's damages exceed the limits of applicable liability insurance. Thus, State Farm has not denied UIM coverage, even though it has denied the UIM claim, and Olympic Steamship does not authorize reasonable attorney fees.[15]
The parties' remaining arguments lack merit or need not be reached.
The judgment is affirmed.
HOUGHTON, A.C.J., and ALEXANDER, J. Pro Tem., concur.
NOTES
[1]  Mailloux asserts in his brief on appeal that Woods had testified, in deposition, that Woods "had no reason to believe the canopy was not secured properly". Br. of Resp't, at 2. However, this testimony is not in the record.
[2]  A small portion of these damages were suffered by Mailloux's wife, but for convenience we refer to all of the damages as being suffered by Mailloux.
[3]  Clerk's Papers, at 13.
[4]  The court also made certain rulings related to Mailloux's personal injury protection (PIP) coverage, but those rulings are not in issue on this appeal.
[5]  It is necessary to calculate more than one minuend and more than one subtrahend when more than one liability insured is severally but not jointly liable to the plaintiff. See Allstate Ins. Co. v. Dejbod, 63 Wn. App. 278, 291-92, 818 P.2d 608 (1991). However, no one contends that is necessary in this case.
[6]  RCW 4.22.070(1) provides in pertinent part:

"(1) In all actions involving fault of more than one entity, the trier of fact shall determine the percentage of the total fault which is attributable to every entity which caused the claimant's damages.... Judgment shall be entered against each defendant except those who have been released by the claimant or are immune from liability to the claimant or have prevailed on any other individual defense against the claimant in an amount which represents that party's proportionate share of the claimant's total damages. The liability of each defendant shall be several only and shall not be joint except:
"....
"(b) If the trier of fact determines that the claimant ... was not at fault, the defendants against whom judgment is entered shall be jointly and severally liable for the sum of their proportionate shares of the claimants [sic] total damages."
Here, Mailloux claimed only against Johnson. State Farm claimed against Woods, using what would have been called an "empty chair" defense if the proceeding had been in court. Mailloux successfully proved that Johnson was at fault, and State Farm successfully proved that Woods was at fault. The arbitrators allocated 90 percent of the fault to Johnson, 10 percent to Woods, and set Mailloux's total damages at $107,500. Based on that allocation, and in accordance with RCW 4.22.070(1), they awarded Mailloux an amount representing Johnson's proportionate share of the total damages, or $96,750.
[7]  State Farm argues that RCW 4.22.070 does not apply in a UIM arbitration proceeding. We reject that argument as meritless.
[8]  State Farm also argues a third question: That the subtrahend is not an arbitrable issue, and that only the superior court can calculate it. Cf. Hartford Accident & Indem. Co. v. Novak, 83 Wn.2d 576, 586, 520 P.2d 1368 (1974); Kraus v. Grange Ins. Ass'n, 48 Wn. App. 883, 885-86, 740 P.2d 918 (1987); A.S. Klein, Annotation, What Issues Are Arbitrable Under Arbitration Provision of Uninsured Motorist Insurance, 29 A.L.R.3d 328 (1970). However, this question makes no difference to this case, because the arbitrators and the Superior Court calculated the subtrahend in the same way. We assume we are reviewing the calculation of the Superior Court, but our analysis and result would not differ even if we were reviewing the calculation of the arbitrators.
[9]  We held that the subtrahend should not include the limits of a liability insured if, according to the arbitrators' award, the plaintiff has made but not proved a UIM claim based on that liability insured's fault. 63 Wn. App. at 285. We held that the subtrahend should include the limits of a liability insured if, according to the arbitrators' award, the plaintiff has both made and proved a UIM claim based on that liability insured's fault. 63 Wn. App. at 285. We held that UIM insurance should take up where liability insurance leaves off, 63 Wn. App. 286-92; that when the liability of two or more tortfeasors is several only, liability insurance leaves off at a point represented by each tortfeasor's legally available liability limits, 63 Wn. App. at 292; and that when the liability of two or more tortfeasors is joint and several, liability insurance leaves off at a point represented by the sum of the tortfeasors' available liability limits. 63 Wn. App. at 292.
[10]  This is apparent because the arbitrators' award was only for Johnson's proportionate share of Mailloux's damages. If the arbitrators had found both Johnson and Woods liable to the Plaintiff, their award would have been for Mailloux's total damages.
[11]  We base this statement on three propositions. First, State Farm is not entitled to complain that Mailloux prejudiced its right to pursue Johnson, because Mailloux complied with Hamilton v. Farmers Ins. Co., supra. Second, Mailloux never did anything to prejudice State Farm's right to pursue Woods on a several basis. Third, we do not believe that State Farm is entitled to complain that its right to subrogate against Johnson and Woods on a joint and several basis was prejudiced or impaired by Mailloux's settlement with Johnson. Although Mailloux's settlement with Johnson destroyed State Farm's ability to subrogate against Johnson and Woods on a joint and several basis, Washburn v. Beatt Equip. Co., 120 Wn.2d 246, 840 P.2d 860 (1992), State Farm had a fair opportunity to avoid that result. The burden of identifying an empty chair liability insured should rest on the carrier, for the plaintiff may not know whom the carrier considers an empty chair insured. When Mailloux offered his cause of action to State Farm in exchange for $50,000, State Farm had the opportunity to identify Woods as an empty chair insured, and to propose that Mailloux transfer his cause of action against Woods, as well as his cause of action against Johnson. If Mailloux had accepted  and a fair interpretation of the record is that he would have, given that he was not claiming against Woods  State Farm would have received unimpaired causes of action against both Johnson and Woods, and it thereafter could have subrogated against both on a joint and several basis.
[12]  Olympic Steamship was not discussed in our initial opinion, because it was not cited in Mailloux's brief on appeal. After we filed our opinion, however, Mailloux filed a motion for reconsideration in which he pointed out that he had cited and relied on Olympic Steamship in a statement of additional authorities submitted months before oral argument. See RAP 10.8. State Farm sought leave to file a supplemental brief, and we granted leave to both parties. Having received and reviewed those briefs, we have decided to consider whether Mailloux is entitled to reasonable attorney fees on the authority of Olympic Steamship.
[13]  After Olympic Steamship, there was confusion as to its breadth. At least two cases said it was limited to situations in which the insurance contract contained a supplementary payments clause. McMahan & Baker, Inc. v. Continental Cas. Co., 68 Wn. App. 573, 581, 843 P.2d 1133 (1993) ("We do not construe the language in Olympic Steamship to allow attorney fees in the absence of a supplementary payment clause."); Hess v. North Pac. Ins. Co., 67 Wn. App. 783, 789, 841 P.2d 767 (1992), rev'd on other grounds, 122 Wn.2d 180, 859 P.2d 586 (1993). In Estate of Jordan v. Hartford Accident & Indem. Co., 120 Wn.2d 490, 508, 844 P.2d 403 (1993), however, the Supreme Court granted reasonable attorney fees without referring to or relying on a supplementary payments clause. Thus, cases since Jordan have said that Olympic Steamship is "specific and without limitation", and does not require a supplementary payments clause. State Farm Mut. Auto. Ins. Co. v. Johnson, 72 Wn. App. 580, 594, 871 P.2d 1066 (McMahan & Baker "appears to have rejected this requirement in Estate of Jordan"), review denied, 124 Wn.2d 1018 (1994); see also McGreevy v. Oregon Mut. Ins. Co., 74 Wn. App. 858, 873-74, 876 P.2d 463 (1994); Gerken v. Mutual of Enumclaw Ins. Co., 74 Wn. App. 220, 229-30, 872 P.2d 1108, review denied, 125 Wn.2d 1005 (1994).
[14]  We refer only to claims denied in good faith. Claims denied in bad faith are subject to rules that we do not here consider.
[15]  Nothing said herein is inconsistent with Barney v. Safeco Ins. Co. of Am., 73 Wn. App. 426, 869 P.2d 1093 (1994), a case cited and relied on by Mailloux. There, Barney had UIM limits of $500,000. The value of his UIM claim was $329,127.67. Safeco reasoned that it was required to pay only $324,127.67, because it had already paid $5,000 pursuant to Barney's PIP coverage. Thus, it was not disputing that Barney had proved the facts necessary to support recovery in the amount of $329,167; rather, it was asserting that even though Barney had proved the facts necessary to support a claim in the amount of $329,167, it was contractually obligated to pay only $324,167. This raised a coverage question within the meaning of Olympic Steamship, and we awarded reasonable attorney fees for the litigation in which the amount of coverage had been decided. We did not, however, award fees for the arbitration in which the amount of the claim had been decided. See 73 Wn. App. at 433.
