I think you're right mate.
May seem a bit of an abstract analogy, but many years ago, when we first got married, we were desperately looking to buy our first house together. We'd been looking for over a year, seen several that we really liked, bid for them, but got gazumped every bleedin' time. It was very frustrating and my wife was 6 months pregnant with our first child. Then, this house came up for sale. It was on fairly cheap for the area. I thought it must need a lot of work on it. But, on inspection, it was immaculate, with a huge garden too. I said to my wife, "this is a must-have", it was easily the best of any we'd seen and it wasn't out of our range budget wise. Then, the bidding started...
The price went up, and up, and up. At one point we were told there were 15 people bidding on it. Eventually the estate agents informed that there would be a sealed bid on a certain date. The price had already gone up about £25,000 over the asking price. I said to my wife, "what do you think it's actually worth?" and "what more on top of that would we be prepared to pay in order to get it?". These are two very different questions. We thought it was worth, maybe, another £10k on top of the price it was at. But we bid another £25k, i.e. £15k more than what it was probably worth, just to have the chance to get it.
We succeeded. Just. I think we came in a couple of grand above the nearest bidder. What we'd done there was to pay over the top - and we knew that. But it got us what we wanted and fended the other bids off. 22 years later the extra that we paid is an irrelevance now - it's value has more than trebled in that time.
I know footballers aren't houses. But there are some principles here which I think may be applicable to both. Sometimes you have to weigh up what something is worth, not just today, but in the future, and take that into account when you are making your valuation. Sometimes it's easy to walk away, especially if you think that someone is taking the piss a bit on the price (exactly how we felt with the house). But if you really are so close to getting what you really want and need, it might not necessarily be a bad thing to just push the boat out a little bit further to ensure you get it, especially if the future value of it is going to be worth far more than you're paying for it.