Applying Game Theory to transfers and why it is best to wait before signing
The League One fixture list was released this morning to a sigh of disappointment by Bradford City supporters. Swindon Town away. A long way, a bad roundabout and a difficult game. The League Cup draw at York City cushions the blow but City will be two games into the season before the season starts at Valley Parade.
In most quarters this was met with a gentle ho-hum but in some corners every season the fixture list seems to act like a tipping point for the disgruntled. With the start of the season now in sight then improvements should have been made and the failure to make them is a concern.
The day that fixtures are released seems to release a pressure valve on a meaningless fury and – albeit in a small section of the Bradford City community – there is concern. The concern is only of note because of its fundamental belief that the best time to sign players in a summer transfer window is early.
The wrong sort of data
When it comes to transfer deals we have but one statistic. The day that the deal was registered. There is no record of the first time a team made contact over signing a player from a club or recruiting him as a free agent. That data simply is not available and so a common assumption is that there is a correlation between an approach and a signing in the same way that there is between sowing seeds and reaping harvests.
And so if a player joins a club in the first week of August it is assume that the club got in touch a month before, or two weeks before, or so on. We probably have Championship Manager to thank for this. Everything takes a steady amount of time, and everyone behaves rationally.
Yet we know from Bryan Caplan‘s work that people do not behave rationally a good deal of the time when considering options which involve game theory as player recruitment does.
Let us consider the signings of Stuart McCall for his second spell at the clubs, and of Guy Branston. In both cases the player was highly motivated to the point where he would not have considered other offers with the assumption that no other offer would be significantly better. If Everton had asked McCall to rejoin following his exit from Rangers, or had someone in League One wanted Branston, then they may not have made the choices they did but in both cases the player had decided that they wanted to join the club and entertained no other offers.
Both deals were done early in the close season because the player was not interested in generating competition. Likewise the club wanted both players as marquee signings and so they had no other transfer priorities.
Both club and player made rational decisions because there was no competition in which to create a model of game theory. This is why I continue to raise the point that City made a poor deal when selling Nahki Wells. They allowed the buyer to “own” the rational decision rather than forcing them to be irrational.
The game’s afoot
When a second club becomes interested in a player or a club is interested in more than a single player there is a context for game theory – and Caplan’s thoughts on irrationality – to apply.
Let us consider two other signings from around the era of Branston’s arrival: Andrew Davies, and first Richie Jones.
Richie Jones was signed by Peter Jackson after he missed out on signing Gary Jones who stayed with Rochdale for another season. Richie Jones was not a player Jackson knew nor had seen but he signed him because he had failed to sign a player he wanted who was similar. In this way the club was the irrational operator. The manager decided to sign a (good) player he had not heard of because he had failed to sign a (also good) player he had and having failed in that there was an apparent need to succeed in another signing.
The irrationality is in Peter Jackson signing a player sight unseen to play in his midfield because he had not secured another target. The objective of the game was not to sign any player, it was to sign a specific player, and Jackson got that wrong but it is not an uncommon mistake to make.
City made a bad decision cause by Jackson’s out of date knowledge of the transfer market. Players were not scarce, they were just scarce to Jackson and as a result City made a bad deal. Richie Jones was a good player but he was no Gary Jones at that point in his career.
On Andrew Davies the player was persona non-grata at Stoke City but allowed the summer to pass waiting for someone to make an offer to sign him. No one did and he ended up at City on a fitness boosting free loan. In the cold light of day Davies’s decision is baffling. He joined a club which had lost to Accrington Stanley and Dagenham and Redbridge in the first month of the season and that was so far down the league he may as well have retired.
That the deal worked out speaks much for his abilities and character but the deal itself is one of the most strange in football. Seldom to Premier League players drop to League Two. Davies was acting irrationally.
Having attempted – one assumes – to find a better club over the summer and with the transfer window closed Davies had no rational options left. He signed for City on 23rd September 2011 which is a good four months after fixtures had been announced and is one of the better signings in the club’s history.
Davies was out of rational choices. As game theory is applied he had lost and as a result City were able to approach him with an irrational proposition – sign for a League Two club – and Davies had to comply.
What is to worry about
The aim of a player in dealing around a transfer is to create the game conditions in which irrationality favours them. This is the power of game theory in transfer deals. The clubs can believe they are in competition for a player even when there is no other offers. You and I engage in this kind of behaviour every time we offer more than asking price on a house that has no other bidders on it.
For clubs to get good value they need to lessen the irrationality involved in a transfer.
If one imagines a footballer – a goalkeeper – who today is considering deals from Bradford City, Wolves, Wigan and Crewe then one can imagine a player who would be holding out for Wolves, and probably not interested in Crewe. If City were to make an attempt to make a deal for that player now they would effectively be bidding against Wolves, and Wigan, and Crewe. To make a bid in that context is to enter into irrational action. There are a great number of variables most of which are unknown.
In two weeks time though Wolves may have signed another goalkeeper and Wigan might have taken one on loan after making it clear they have spent all their budget on a forward. The number of variables is reduced and City end up bidding against Crewe in a game which favours them, and so can make a better deal.
Of course one can point out that in this situation had City made their offer two weeks ago – and matched Wolves and Wigan – they would have signed the player but they would have done it on the terms that were comparable to Wolves and Wigan, and have less money to make other deals, and so a worse team.
And this is common in almost all transfer deals. The best deals are done for a club when that club is in a stronger position.
In short, and to recap
There are a few cases where the club wants the (free agent) player and the player wants the club in which the best deal can be done early but in almost every other transfer a club to make a deal early in close season will be forced to do a worse deal than they would have had they waited.
There are exceptions of course. There is only one David Beckham and if you have to bid against other clubs to get him you are forced into a bad deal but League One is not like that and players of League One quality are not so scarce as to mean that there is not enough to go around.
Signing players early does not mean – in most cases – that a team will be stronger because it had first pick it means it will be weaker because it had fewer picks.