the hot hand paradox
argued both ways
Let’s assume your favourite team is called ABC. Does being in form, mean ABC is going to win their next game? This point can be argued in fact from both sides.
Usually being in form, translates to feeling good, mentally as well as physically. ABC in good health is likely to do well in the game they play. With every game ABC plays, they gain confidence. They get rewarded with dopamine. With this, they are ready to play in almost any circumstance. Although, too much of dopamine, can make them overconfident, almost always resulting in cocky, unsportsmanlike behavior, bringing us to the other side of the argument.
So coming to the other side of the argument, well maintaining consecutive wins while in good form is in fact hard. The team must not be complacent, tired or lose motivation. Any one of these can affect the performance and bring an end to their record.
Then, there’s the gambler’s fallacy, which argues that 5 wins and 1 loss is the same as 6 wins, which is true if the events are independent. But are they independent?
Suppose the probability of winning a game is 0.4. ABC has won 5 games in a row and the stakes are being decided for the sixth game.
Did I say there were only 2 arguments to this, when in fact there are 3 sides to this coin. The sides / arguments being:
Winning 6 games in a row is highly unlikely as probability of it is (0.4)6 which is a significantly lower number(0.004096).
Every game is treated independently, which brings the probability of ABC winning to 0.4. A better chance of winning.
We take into account the current “form” of the ABC, now that they have won 5 games in a row, we divide 0.4 by a number k(let’s take 0.8)<1 and arrive at an answer = 0.5. We update k everytime we get a new result. In other words, k decreases on a win and increases on a loss.
The question is, if you were deciding the stakes, which approach would you take?