Your points relating to the hash function are correct, but the output length of SHA1 is not related, since the secret seed itself is not necessarily the result of a SHA1 hash. It could be longer or shorter than 160 bits.
True, however since we know nothing about the size of the secret seed, we are left with assuming that it could potentially be larger than 160 bits.
I rushed into answering this, and I'll admit that I may have overlooked an important point, but since the secret seed (concatenated with the userID) is passed through the digest function SHA1, it means that there are an infinite number of secret seeds that will all result in the exact same SHA1 value for all the current userIDs. It is only necessary to find 1 of these infinite number of secret seeds to reliably predict when someone will achieve legendary status. As such, the length of the output of SHA1 would seem to be relevant?
I would not be surprised if this was an unsolved cryptographic problem. If SHA1 were a
random oracle (the ideal "perfect" hash function), then the output length is completely irrelevant, since each bit is completely independent of the other output bits and at the same time dependent on every bit of the input.
But the SHA1 algorithm is certainly not perfect, and internally uses 80 rounds of hashing, each round using 128 of every 512-bit chunk of the input. It's designed so that this is as difficult to exploit as possible, but I would not be surprised if 128, 160, or 512 bits were somehow "critical numbers" that subtly affected how the hash works. I suspect that there would be, but finding them is certainly not trivial.