  The global gravitational-wave detector network achieves higher detection
rates, better parameter estimates, and more accurate sky localisation, as the
number of detectors, $\mathcal{I}$ increases. This paper quantifies network
performance as a function of $\mathcal{I}$ for BayesWave, a source-agnostic,
wavelet-based, Bayesian algorithm which distinguishes between true
astrophysical signals and instrumental glitches. Detection confidence is
quantified using the signal-to-glitch Bayes factor,
$\mathcal{B}_{\mathcal{S},\mathcal{G}}$. An analytic scaling is derived for
$\mathcal{B}_{\mathcal{S},\mathcal{G}}$ versus $\mathcal{I}$, the number of
wavelets, and the network signal-to-noise ratio, SNR$_\text{net}$, which is
confirmed empirically via injections into detector noise of the
Hanford-Livingston (HL), Hanford-Livingston-Virgo (HLV), and
Hanford-Livingston-KAGRA-Virgo (HLKV) networks at projected sensitivities for
the fourth observing run (O4). The empirical and analytic scalings are
consistent; $\mathcal{B}_{\mathcal{S},\mathcal{G}}$ increases with
$\mathcal{I}$. The accuracy of waveform reconstruction is quantified using the
overlap between injected and recovered waveform, $\mathcal{O}_\text{net}$. The
HLV and HLKV network recovers $87\%$ and $86\%$ of the injected waveforms with
$\mathcal{O}_\text{net}>0.8$ respectively, compared to $81\%$ with the HL
network. The accuracy of BayesWave sky localisation is $\approx 10$ times
better for the HLV network than the HL network, as measured by the search area,
$\mathcal{A}$, and the sky areas contained within $50\%$ and $90\%$ confidence
intervals. Marginal improvement in sky localisation is also observed with the
addition of KAGRA.
