West Derby Castle is more like 120 yards from end to end.
No-one actually knows how big West Derby Castle was, all records of its plans have been lost over the last almost a thousand years. We do know that when it was in use ~150 soldiers were quartered there, we know where the main motte was centered (there’s a monument), and it’s about 900 feet from there to “Castlegate Grove” and “The Armoury” as the crow flies. 400 yards (1200 ft) seemed about reasonable on that basis (there’s the other side of the motte, after all).
Whether there’s any historical accuracy in the road naming is up for debate of course. It was a motte and bailey castle, so it’s going to be of a reasonable size, just because the bailey part is separate from the motte. It was described as “dominating the landscape for miles around”, which also lends itself to the thing being reasonably big.
There were around 600 of these motte and bailey castles dotted around the UK, mainly as point-to-point contact and troops barracks. Liverpool also had another castle (
a stone one) down by the river for coastal defence.
My point, castle-size notwithstanding, is that it’s not going to be a “real” castle, it’ll be one of those towers-that-someone-called-a-castle-because-it-sounds-better. There was a strange inversion in naming when real actual castles were named towers (eg: the Tower of London), leading to actual towers being then named castles as the meaning of the word was confused. Etymology is odd.