The fraction of time the miner does not know whether the most recent block was valid is clearly τ / T, which means the fraction of the time the miner does know is 1 - τ / T = (T - τ) / T.
You are attempting to develop an equation on orphan rate relative to the propagation delay (which includes verification delay), but this can't be done without context of the distribution of computation in the network, which some argue is modeled by a Poisson distribution.
... miners will be motivated to improve how quickly their nodes can perform the ECDSA operations needed to verify blocks.
I had argued upthread that bandwidth limitation (propagation delay) is the only justification for not expending more resources on verification instead of forming 0 txn blocks (when blocks are mostly funded by txn fees, which may not be the case now):
This delay is a form of propagation delay and thus drives up the orphan rate for miners with less resources. Afaik proportional increases in orphan rate are more costly than proportional decreases in hashrate, because
the math is compounded (but diminishing) on each subsequent block of the orphaned chain. Thus this action doesn't appear to make economic sense unless it is explained as a lack of bandwidth and not a lack of desire to apply more of their resources to processing the txns than to hashrate. If it is bandwidth that is culprit, then it argues against larger block sizes.
Peter R posts nonsense, then the Yes votes go bonkers and they can't change their vote after Peter R has been thoroughly refuted.