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A benchmark of linear predictability of sea surface height (SSH) globally is presented, complementing more complicated studies of SSH predictability. Twenty years of the Estimating the Circulation and Climate of the Ocean (ECCOv4) state estimate (1992-2011) are used, fitting autoregressive moving average [ARMA(n, m)] models where the order of the coefficients is chosen by the Akaike information criteria (AIC). Up to 50% of the ocean SSH variability is dominated by the seasonal signal. The variance accounted for by the nonseasonal SSH is particularly distinct in the Southern and Pacific Oceans, containing >95% of the total SSH variance, and the expected prediction error growth takes a few months to reach a threshold of 1 cm. Isolated regions take 12 months or more to cross an accuracy threshold of 1 cm. Including the trend significantly increases the time taken to reach the threshold, particularly in the South Pacific. Annual averaging has expected prediction error growth of a few years to reach a threshold of 1 cm. Including the trend mainly increases the time taken to reach the threshold, but the time series is short and noisy.