Tuesday, 2 December 2014

Stick or Twist?

by Jack Dry

Sabermetrics is the term for the empirical analysis of baseball. The term is derived from the acronym SABR, which stands for the Society of American Baseball Research. Statistical analysis was largely untouched in baseball, until 2001, when Billy Beane and Paul DePodesta daringly leapt into its mysterious darkness. The Oakland A’s had 1/10 the funds of other teams yet they still wanted to compete in the league. Billy Beane and Paul outrageously claimed that statistics such as ‘on-base percentage’ and ‘slugging percentage’ were the best indicators for talented players. This strictly went against the popular belief. Billy and Paul benefited since the players with these qualities were undervalued in a market where players were valued solely on their speed and their contact percentage (the amount of time they make contact with the baseball). Billy and Paul based all of their decisions on stats alone- something which no other club before had done. In this way they managed to spend a fraction of what the bigger teams spent. Their methods were laughed at by other teams until August 13th 2002 when Oakland began their winning streak of 20 games- a record number. 

In this way, a team with highly restricted finance managed to compete with teams with budgets ten times the size of their own. The incredibly small ‘team salary’ which the Oakland A’s had in 2002, illustrated by the graph, indicates how undervalued were the players who they purchased. Billy and Paul’s use of statistics drastically remodelled how sports teams across the globe operated, and gave hope to teams with diminishing funds. As their success was highlighted by media so publicly, the unfathomable power of probability and statistics was recognised.

Statistical analysis is the area of mathematics which vigorously studies data and uses it to suggest trends. Probability, much entwined with statistical analysis, explores the likelihood of certain events happening. Although, at first, these tools were most predominantly utilised by the baseball team ‘Oakland A’s’, the power of probabilistic and statistical analysis is now used far more widely in sport as well as in other areas. Bankers, Economists and Poker players all harness the power of stats to make decisions in the most logical way possible. Thinking probabilistically has several advantages. I will use the infamous Monty Hall Game Show problem as an example. In the game there are three doors- A, B and C. One door has a car behind it, whilst the other two have goats behind them. The game is arranged into the following four parts:

1.       Monty asks the player to pick door A, B or C.
2.       In order to heighten the suspense, Monty then reveals a door with a goat in.
3.       The player is then asked if they would like to swap doors.
4.       After this decision is made, the player opens their door and wins whatever is inside.

Although you may initially think that your chance of winning the car is fixed at 1/3, it isn’t. During the third part of the game, a probabilistic thinker would always swap doors as this gives them a greater chance of winning the car. 2/3 of the time the player will initially pick a door with a goat. Then, Monty reveals the goat in the other door. Therefore, 2/3 of the time the player will swap to the car.  If you don’t swap doors, your chance of winning the car is simply 1/3 as there are three doors. Therefore, although counterintuitive, you should always swap doors. The probabilistic thinker would capitalise from their knowledge.

In a game of ‘heads up’ poker, where there are just two players, A and B, Player A, with King and Seven of Spades, may want to know the probability that they win the hand in the situation below before deciding whether to bet. This can be worked out using a probability diagram illustrating all the cases when player B will win the hand. In this instance, if Player B has random cards, Player A will win 84% of the time. On this basis Player A would be more confident in raising than he may normally be. Again, the probabilistic player would capitalise from his knowledge.

Using probabilistic and statistical analysis, extremely accurate predictions can be made. As many of you are probably aware, Microsoft managed to predict the outcome of every group stage match of the Brazil World Cup. This is exceedingly impressive since there are so many factors which determine the outcome of a match. In business, companies predict changes in peoples’ incomes which will affect the demand for their products due to income elasticity of demand. This allows the companies to prepare for the future in the best way possible. Statistical analysis has well and truly been ignited over the past century and predictions are only going to become more accurate than they are already. A scary, yet cool, thought.

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