Since the thing is inside of conditioned space, in Chicago the standby losses from the jacket insulation are only "real" losses 3-4 months out of the year. The rest of the year those losses are supporting the heating load of the house.
OTOH, if it's a atmospheric drafted unit a good portion of the total standby losses are going straight up the flue, convecting heat out through the center-flue heat exchanger to be vacuumed out at the draft hood. Even worse, the open flue is also sucking conditioned air out 24/365, driving infiltration of outdoor air inward whether the thing is firing or not. From a water heating efficiency perspective you can guage it by the relative EF numbers, but the whole-house picture is more complicated. Going with an electronic-ignition forced-draft model has true whole-house fuel & AC electricity savings, factors well beyond what is measured in an EF test, and which will vary a lot from one house to another. A sealed-combusion/direct vented version is even one better, since it draws it's combustion air from the great outdoors rather that using conditioned space air, but direct-vent tank HW heaters aren't too common. (Many tankless versions get combustion air from the outdoors, or can be converted to do so.)