Market Efficiency and Bayesian Probability Estimation via the Beta Distribution
[Ganchrow]…
What is Bayesian inference you might ask?
Well it’s really a different way of looking at probability that allows for a different methodology in forecasting. Recall that I earlier wrote that a frequentist would view the expected value of a bet as the average profit per game were the bet to be repeated an infinite number of times. Well that’s just not how a Bayesian sees the world.
A Bayesian considers the probability of an outcome as a (possibly subjective) measure of the degree of informed belief in that outcome. We talk about “informed” belief because the process of Bayesian inference involves updating one’s prior beliefs based on the availability of new evidence.
A Bayesian doesn’t in general think about hypothetical frequencies of an event given a hypothetical infinite number of repetitions because in general events can’t be repeated an infinite number. To estimate outcome probability what a Bayesian does is gauge prior knowledge of that event and then update that knowledge as future information becomes available.
Note that this methodology doesn’t hold value for all types of experiments as for some events can know everything there is to know about it a priori. These events (take the game of Craps for instance) are frequentist in nature meaning that there is no value to new information (although Craps could deemed be otherwise were we to suspect either an unfair game or the presence of a skilled dice roller).
This can be a particular convenient tool when looking at the progression of a betting line. One can build a forecast in any way one chooses and then continually reevaluate that forecast based on upon the availability of new evidence (e.g., a change in the market line).
By way of contrast, a non-Bayesian might place a bet at a line of +3, and then after observing the line move to +5 simply declare his original bet “bad” in that the market hadn’t backed up his opinion. A Bayesian, on the other hand would realize that his bet was made conditioned only on the information he had available at the time the bet was made (which would have only included the then current line), and while he would almost certainly view the bet as “unfortunate”, he could accept that the bet was still a good bet at the time it was placed. Certainly he’d use the new information to revise his current opinions on game probabilities, and going a step further might even use it to discount the value of his model, but a Bayesian can accept that a decision might be perfectly valid at the time it was made, even as new information sheds doubt on it in hindsight.
Having only a vague understanding of the concepts, I feel less than qualified to offer commentary. But I will say, assuming a state of rationality, with new content comes a re-evaluation of the odds, probably correlating to the content. Notwithstanding some books may feel inclined to manipulate the market to deceive their clients.
Either way, I think it counter-intuitive to some sports, and essential to others. Certainly for baseball, its difficult to imagine one sitting in front of the computer all day and reconfiguring probability in accordance with new information. Games are everyday, and sometimes teams, and gamblers, have 12 hours between the end of one game and the beginning of the next. There are obviously many different methods of baseball handicapping, but time doesn’t necessarily breed enhancement of probability measures. Not every line in baseball is driven by injuries or new information such as the weather, lineups, listed pitchers. The line is often set and undergoes consequential line movement in light of no information (other than money) as all other factors remain constant. This doesn’t mean that the linesmakers assessment of the lines is as precise as it was prior, if even it was precise at all.
This is true to an extent for every league in every sport. Yet for football Bayesian Estimation of Probability is a more appropriate institution because of the amount of days between games, and the amount of variables that can be affected or new ones that may appear during that week.
Having said that, again we are under the assumption humans are rationale. Its debatable if we are endowed with the ability to truly understand how to re-assess and modify the odds based on new information. What kind of information should affect probability, and in what direction? The Bayesian philosophy is overly optimistic, and makes a rather arrogant assumption of the ability of our brains to isolate information from drivel.
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