Sunday, 13 October 2013

Inputs Needed

Jesse Livermore, the Boy Plunger, wrote:

At the risk of over quoting:
"Football prices are derived from goal expectancies, the current score and the time remaining, and with occasional blips where a goal is more probable, the trend is pre-determined."
"Whether they should be is debatable."
"How is this debatable?"
It's debatable because one might say:
The prices are real, the goal expectancies can be derived from prices using the inputs you mentioned, some you didn't and A MODEL. If someone has a different, better model (or believes one exists), or believes the model is bad then he would think prices should not be derived from goal expectancies etc.
Prices are indeed real, the current score is real, and any unknown in the equation can be solved if you know the other values, but what are these other inputs to the equation that I didn't mention?
18: The Cassini Formula?

The Black-Scholes formula uses five inputs for pricing options, while a similar model for football prices is unlikely to win a Nobel Prize for Ecomomics, the three inputs I have listed are all you need. The short term nature of the match means we can safely ignore risk-free interest rates.  

A model is just a fancy name for a tool that process the inputs you have. Pre-game you have 90 minutes of 'playing' time remaining, you have your estimated goal expectancies and from those inputs you can derive your prices. Or you can reverse engineer your model, and use price data to give you the goal expectancies per the market.

If you don't derive your prices from goal expectancy, what do you derive them from? It seems to me that any model that doesn't use goal expectancies is, because of its simplistic nature, unlikely to be profitable in the long term. For example, that a team placed placed between fifth and eighth has historically beaten a team placed 16th or below 60% of the time might be an interesting tidbit for readers of a match preview, but is it enough to justify lumping on if the price is available above the implied 1.67?


Emp said...

If I asserted that cricket results were based on "run expectancy" that could only be true in a highly technical sense that was practically unuseful. So I think that some degree of proof is required before we assert football depends purely on goal expectancies.

I could buy your point much better if this was like the NFL. There two teams repeat a literally identical situation again and again and again so by and large determining the expected outcome of Offense A vs Defense B allows you to price a match perfectly. In the NFL you can't make your offense stronger by weakening your defence or earn more offensive possessions by giving your opposition more of the same; as a consequence the result of the game depends highly on performance in a single pre-determined situation with massive sample size.

If soccer consisted of the better team getting 35 free kicks from 30 yards out and the weaker team getting 20, I could then understand your point about goal expectancies, because there is a set number of equally valuable scoring opportunities and a good sample to understand the true probabilities of various results from those.

Football isn't remotely like that though. Teams aren't equally likely to score throughout the game since they can bolster their defence by squandering attacking chances, throw everyone forward and everything in between. I refuse to believe that all of those highly different situations have goal expectancies that are even remotely close to each other.

Secondly, which strategy the teams will use is highly dependant on the score-line at the time, and thus a static goal-expectancy cannot be the most accurate way of doing this. I know it can still be profitable, but that's very different from it being optimal or theoretically correct. This is looking at batting stats and calculating "run expectancy" would do much worse than an experienced cricket fan just watching and betting based on his understanding.

Also, your final para attacks a rather ragged straw-man. No one who was using a model based on those considerations would use such crude categorizations or stats. I saw you making fun of a system based on this which was hilariously crude, but that doesn't mean one can't classify teams in an intelligent manneer. Alas, I don't want to divulge too many details of how my model works, so I won't go in depth, but I will say that performances of "Team Type X" vs "Team Type Y" are in my opinion a more accurate determinant of the result of a football match then any goal expectancy model.

J Livermore said...

"but what are these other inputs to the equation that I didn't mention?"
how about inputs which better capture the distribution of goals and any parameters for this?

Using your parallel:
Black-Scholes assumes lognormally distributed stock returns in continuous time. It is the error in this assumption which leads to the volatility smile. There are plenty of alternative models out there which allow for different underlying processes (including jump-diffusion and binomial and undoubtedly some secret ones).
In addition one could feasibly use options to profit from inefficiencies in stock prices without knowing anything about options pricing (ie buy calls on stocks I think will perform well).
What BS does provide is a transparent, clear way to express an options price in terms of it's volatility, and I actually believe this is it's main use these days (hence the ever-present volatility smile).

"If you don't derive your prices from goal expectancy, what do you derive them from?"
Goal expectancy models are pretty dam good, but if what we care about is the probability of team A beating team B it's not beyond debate that the only method is to go via a goal model.