sussexpob wrote:The key though is..... if making that decision an infinite amount of times, you will lose more than you win. Which makes it quite unjustifiable.
But isn't that the point though. The decision isn't being made an infinite number of times. It's being made once. Each test match is a unique set of circumstances that will never repeat. And so you have to take circumstances into account.
Suppose England are 2-1 down in the series, or that they need 60 points to make the final of the WTC, or something like that. A draw won't cut it - a win is all that matters. Is it a good decision then? Probably yes - there is only one result that will achieve your objective, so you take the decision that maximises the chance of achieving that outcome, regardless of the other possible outcomes. To take an extreme hypothetical analogy, playing the lottery is usually considered mathematically foolish. But suppose you have $5 to your name and need $1 million for a life saving cancer treatment or you'll die next week. In that case, buying a lottery ticket might be a good decision, because even though the odds are extremely small that you'll make the $1 million you need, they're non-zero and higher than the odds of getting $1 million through just about anything else you could do with that money.
sussexpob wrote:bigfluffylemon wrote:I I think you can argue it was a decision that was rational inasmuch as if your sole objective was to win the game and don't care about a draw, it probably gave England the best shot of doing so
If we were going to assess logic based on the subjective desires of a decision maker, then surely you can argue anything is rational, because any decision no matter how bad or good is based on some form of decision being based on the available information? I think in this case, its more pertinent to ask whether or not in an objective sense that logic makes sense - so is England's taking a high chance of losing to a lower chance of winning an objectively good decision?
Your argument to me is like trying to say a gambler as logic, because even though he bets on trash that will by the balance of probabilities make him poorer, the bets he makes are good because his objective is to win BIG..... the reality is, in the vast majority of cases protracted over time, he does the opposite. His action is therefore counter to his main goal of gaining economic rewards.
Of course you have to assess the desires of the decision maker. Again, take the $5 example above. Is it a 'good' decision to invest it in the stock market? It depends entirely on your circumstances and objectives. If your objective is to have more money than you started with, then putting it in the stock market might involve an unacceptable level of risk that your investment might go down, and therefore putting the money in some sort of guaranteed saving/interest account might be a better decision. But if your objective is to maximise mathematically expected return on your $5, then the stock market is likely to be a good decision, as in the long run you will probably make more money.
In decision theory, a rational decision is one which takes into account all the facts, circumstances and probabilities, and chooses the outcome that achieves the best utility for the decision maker. In classical economics utility normally equals money, but for real humans it doesn't always. You have to have an idea of what the 'utility' or objective is before you can assess a decision as rational. But then you are entitled to disagree with the 'objective' or 'utility' as a reasonable thing to be seeking to do. The gambler example isn't necessarily a fair one for this situation, because if the gambler's objective is to finish with a profit/make money, then gambling is mathematically an irrational thing to do. But if the gambler's objective is simply to have a good time, and they get entertainment from betting, and never bet more than they are prepared to lose, it might be rational. Not an objective I would agree with, but that's different.
In this case, Stokes and McCullum have decided that winning is everything. They were prepared to risk a high chance of a loss to achieve that. Their 'utility' was win = everything, draw/loss = nothing. You disagree, and fair enough - for you draw and loss are not weighted equally, so there is more utility in avoiding the loss, even if it also means a lower chance of a win.
So really, it comes down to whether you accept or not that the objective is to win at all costs. Reasonable minds clearly differ there. I wouldn't have made that call, and most cricketing wisdom is to weight avoiding a loss higher and only declaring when odds of a win significantly outweigh odds of a loss, especially in the first match of a series. But on the other hand, wins in Pakistan happen literally once a generation. England's overall record there is W3 L4 D18. Taking a 1-0 lead gives England an excellent chance to win the series, something that only has been achieved once by England in 60 years. McCullum and Stokes were clearly prepared to go for a potentially big payoff. Risky for sure. Too risky for many people's taste. But I don't think that makes it unjustifiable.
You won't agree , because to do so would mean your own initial instinct that the declaration was mad was simply a misjudgement on your part ; so you will keep pushing the line that there is some intrinsic measure of win/loss % that can be accessed at any point of a cricket match. I regard that claim as total nonsense.
