Games 3 Volatility and Randomness – common confusions

We have seen from the two previous posts (Games 1, Games 2) that games can be categorised as high/low volatility and high/low skill. We have also seen that higher volatility games are generally more fun to play and certainly make better social games and spectator sports.

Volatility can easily lead to confusion about what sort of distribution of outcome we are looking at. Let’s look at a few examples of this:

High volatility makes relative skill between players hard to see

With any game of high volatility, it can be hard to tell what the skill mismatch between players is.

Take the two charts below. Both games of high skill with players of the same skill differential. In the lower volatility version, the skill differential is obvious, but in the high volatility much less so. In reality, a better chess player will win a high proportion of games, even if the skill advantage is slight. Whereas with poker, we would see a lot more short-term variation in the winning player.

This can have consequences. At a poker table, some people will often play with a very aggressive style, ensuring high volatility in the outcomes of their games. After the game, they will complain about poor luck in not hitting their intended flush on the river, or being regularly outdrawn by another player. They may consider themselves skilful or perhaps, that poker is a gambling game where luck is the driver, without realising they are playing against the odds. They will consistently lose. This is one way that better poker players consistently take money off weaker players, where their own volatility of results blinds them to their lack of skill, so they continue to play.

Volatility acts to disguise any underlying skill differential. This is extremely helpful for the enjoyment of social games but can lead to important mistakes in other areas of life.

High volatility can be mistaken for randomness

If you only had the results of the first 10 games of a highly volatile game, it would be easy to decide that the outcomes are random with no discernible difference in skill. It is quite easy to see why these concepts get confused. Unless you have a lot of data and are paying close attention, it can be hard to spot the difference between a random outcome and an outcome where the volatility is high relative to the skill element. Repeatedly playing a game is often not possible either.

This mistake gets frequently made in economics and economic forecasting. Economies are volatile and this makes precise forecasting generally impossible. This often leads to logic flaw we can saying nothing useful about the future and that experts should be ignored.

A recent example of this is Brexit. Any forecast of growth and living standards over the next decade has a huge error band with or without Brexit. In other words, we are looking at something with inherently high volatility. Adding a large economic shock like Brexit is likely to add even more uncertainty/volatility to any forecast.

It is then commonly argued, in fact often assumed, that since predicting what will happen after Brexit is so difficult given the volatility, it means that economists have nothing useful to say. If “anything” can happen, we should think of the impact as simply random. This is a huge mistake.

In a previous post, “Is Climate Science True” (https://appliedmacro.com/2017/05/17/is-climate-science-true/) I introduced the concept of conditional vs. unconditional forecasts.

To take an analogy, I am thinking of running the London marathon next year.
Please estimate how long it will take me to run it i) in running kit ii) wearing a gorilla costume.
I would strongly expect that your confidence in both of your answers is very low.
However, I bet you are very confident that ii) will take longer than i).

The addition of a gorilla suit adds volatility to the outcome. It does not mean that adding a gorilla suit has negligible impact and the effect is random.

Brexit adds volatility to the outlook for the UK economy. This does not mean the effect is random. It is clearly and strongly negative.

Similarly, average temperatures are volatile. This does not mean that climate change is untrue or that greenhouse gases are not causing it.

Volatility causes confusion on absolute skill of the game

We have seen that volatility can cause confusion on relative skill level.
It can also cause confusion on the overall skill level of the activity

1, High volatility does not mean low skill

It is a common error to assume that because a game has high volatility it means it has a low skill level. As an observer, you might see a relative novice beat an experienced player and conclude that this game is not very difficult to master (poker).
Or another example of an experienced player not consistently able to succeed (baseball home runs, a world number one player knocked out of Wimbledon early)
The nature of the game means that the volatility remains high (it is often designed that way) but the skill level may still be extremely high and difficult to master.

2, Low volatility with evenly matched players does not mean low skill
Think of a game where you only watch match-ups between players of very equal abilities. If you do not share the high levels of skill, then it is easy to think that the outcome is random and the participants’ skill level are not that high.

An example of this is in car racing. I see in Nascar that people drive flat out round and around in circles – not that hard. Even Formula 1 does not look too tricky. I know how to drive and what they are doing looks like my experience of driving. I didn’t really understand the level of skill involved until I went on a track day and witnessed how far even the best amateurs were from professional times, and how much further a decent amateur was from me.

Conclusion

Appreciating how volatility will mask the underlying features of a game is important, to the outsider it is easy to assume that an uncertain outcome implies randomness or low skill.

This is flawed logic.