It's always going to be subjective, but there are plenty of ways to benchmark and get an acceptable range for valuation (and this is usually how it will be expressed, rather than a definitive number). In taxation, most countries have rules (transfer pricing) requiring transactions between connected entities to be at market value. You'd look at comparable transactions to get a view on value (either evidence that you sell to / buy from unconnected companies at similar values, or else you'd do industry wide research to get a market rate). So there's a whole industry based around doing this kind of work (usually accountancy firms), and their findings are usually expressed as a range.
For transfers, you'd look at other evidence where possible - i.e. before Saudi, did anyone else bid anything like the value the Saudis ended up paying, if so that's indicative of how sensible the valuation is. If you sold a player to the Saudi league for £50m and had previously had offers of £40m that you'd rejected, then you could probably argue £50m was OK - you rejected £40m because you thought the player was worth more. If the only other offers you'd had were £20m then the value looks off, unless there were other distinguishing factors between the offer and ultimate sale (e.g. contract length / age at each respective date).
You would probably also look at insurance valuation (usually split by player and notified to the insurer) / internal valuations for financial statements (prepared at each year end to assess whether write-downs are required), as these would give an indication of the value the club reasonably believed applied to each player and would be put together without being biased to justify an individual transfer. Insurance valuations would typically be re-done quite regularly (e.g. when a new player is acquired or another one sold).
