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tokens: overly optimistic. 9 In addition to uncertainties in the most representative noise model, even choosing an accurate number of pulsars is non-trivial. PTA continue to expand by adding new systems, which are a very important part of detection forecasts (e.g. Taylor et al. 2016b ), but have different frequency sensitivities and thus different leverages on SNR. Finally, the GWF detection statistics we use are suboptimal in at least two respects. First, the statistics in Rosado et al. ( 2015 ) do not account for eccentric effects, and we treat the GW energy from single sources that is split across multiple frequency bins as entirely independent. Secondly, the excess power statistics may not perform as well on data where noise processes are harder to distinguish from single GW sources. The presence of line-like noise, due to uncertainties in planetary ephemerides (and their harmonics) for example; or instrumental effects, could introduce significant interference. At the very least, it is likely that foreground sources with periods comparable to the observing duration will be hard to distinguish from red noise when using single pulsar searches. This may necessitate correlated searches with lower recovery efficiencies. 4.2 Conclusions Single GW sources resolvable above the background, which we refer to as GWF sources, tend to be most detectable at frequencies near ∼0.1–0.3 yr −1 . At higher frequencies there are fewer sources which also tend to be less loud. At lower frequencies the GWB from all other sources is more likely to drown out the singles. According to most of our models, we would expect there to be a foreground source with a characteristic strain of about 10 −15 (or timing residual of ∼30 ns) after 10 yr of observations. These values are roughly a factor of 2 higher than those predicted by Sesana et al. ( 2009 , e.g. Fig. 3 ) and Ravi et al. ( 2014 , e.g. Fig. 4 ). When taking eccentricity into account, the primary effect of non-circular evolution is to shift GW energy from lower to higher frequencies. Thus, increasing eccentricity decreases the occurrence rate of GWF sources, especially at lower frequencies, both by increasing the GWB amplitude and by diffusing the single-source strains themselves. Changes in the effectiveness of stellar scattering, and more generally the rate of environmental hardening, has a small effect on the properties and occurrence rates of the GWF. Measurements of the number of GWF sources can thus provide strong constraints on the eccentricity distribution of the underlying MBHB population. Even in the absence of foreground detections, measuring the number of sources contributing to the background could provide the same information. This could be done either by directly resolving numerous loud sources in particular frequency bins (i.e. in frequency space), or indirectly by inference from the degree of anisotropy of the GWB (i.e. in angular space). DPs are usually higher for the GWF than for the GWB – indicating