I didn't have time to work on my talent-luck simulator much lately, but here's something that might be interesting. Those not following this regularly should consult the link for an overview (and code). Briefly, I'm exploring a claim that it's luck, not talent, that's largely responsible for success. If abilities follow a Gaussian distribution, then luck is one plausible mechanism to transform this into the power-law distribution of wealth that's actually seen. The basic model is that agents (who have some starting wealth and fixed talent) pseudo-randomly encounter events which can either be lucky and (if they're sufficiently talented) double their wealth or, if they're unlucky, halve their wealth (regardless of talent).
One of the other claims of the previous paper is that luck is strongly dominant : "almost never the most talented people reach the highest peaks of success, being overtaken by mediocre but sensibly luckier individuals". This is basically true in the model, but there's a significant caveat that they didn't discuss.
By default, the model has 1000 agents who have a Gaussian distribution of talent. Plotting the distribution of talent against money at the end of the simulation reveals a textbook case of no correlation. The wealthiest individuals may be of slightly above-average abilities, but not very much, and the most talented individuals can be among the poorest. So it seems that talent barely matters at all, except that the least talented people aren't likely to do very well.
But this is not necessarily the case. Previously I've shown that this is because the model gives talent the minimal possible role, and if it's allowed to affect the luck status of an event as well as giving a chance to mitigate unlucky events, a clear correlation emerges while preserving the same power-law of wealth distribution. Here I've found something different : even in the standard model, talent does correlate with wealth, it's just hidden in the noise.
It seemed to me that since talent does have a role, once we compare individuals who experience the same number of events, there ought to be a correlation of talent and wealth. Comparing the whole of society "washes out" the role that talent plays : someone who only encounters a single event is never going to become the richest, regardless of their talent. Lumping all the individuals together isn't really a fair comparison as far as the role of talent goes. So it's useful to compare individuals who experience the same number of events.
In the first plot I used the standard model conditions. The lines are linear regression fits to the agents who experience the specified number of events. That doesn't reveal very much, the slope of the lines is basically random. If talent was making a difference, I'd expect the lines to generally increase in gradient with the number of events. So it looks like luck actually does dominate here.
In a sense that's true. Whether an agent experiences an event or not is largely a matter of luck. As shown previously, this is mainly due to an agent's location (essentially a postcode lottery if you like) because the position of the events is random in space but not in time.
But it's not the whole story. This plot is misleading for two reasons. First, the number of agents is small, so the number who experience high numbers of events is small. This means the trends are largely affected (or even dominated) by scatter due to small number statistics. Luck does indeed have an important role, but it only looks so strongly dominant here because there just isn't enough data to see the trend. If we increase the number of agents to 5000 (second plot), we see something very different. There's a clear overall increase in slope of talent-wealth with increasing number of events. Agents who are equally lucky are more likely to succeed if they have higher talent.
Second, the Gaussian distribution of abilities is questionable in reality but not helpful in the model : it keeps the number of extremely talented individuals low, so again there's just no data at the extreme end. Hence it's scatter-dominated and the effects of talent cannot be seen. If a uniform distribution of talent is used (third plot), the increase in slope of the lines becomes clearer.
These are subtle effects, hard to see in the raw plots but quite evident in the linear regression slopes. It should be emphasised that in this model agents do have to be lucky to succeed. But once we control for that, once we compare agents who have equal opportunities, we still see that talent really does matter. It's just not clear in the original plots because it's hidden by the noise.
So Teela Brown is the most successful being in the universe?
ReplyDeleteWell, I don't think you can be lucky and unsuccessful, by definition...
ReplyDeleteThat's genuinely interesting. I'm trying to let that soak in for a bit, but it does seem to correlate with what I've come to believe.
ReplyDeleteI contend success is measured in two components, but arises from three other components:
Success Components:
1. Doing what you're any good at in life.
2. Getting paid for it.
But achieving success:
1. Wanting to do something well - and finding it. Many people don't find it. Furthermore, many people don't want it badly enough.
2. Finding the people who will get them over the initial obstacles and into the Success Realm, where they can grow in their successful nature. Teachers, mentors, people who love us and believe in us, the people who are always ( and genuinely! ) mentioned at awards ceremonies.
3. Luck.
In the old Horatio Alger stories, which have passed into the language as a curse and a byword for self-made men - in the actual stories, these talented and ambitious boys ( they're all boys ) meet helpers along the way, men who recognise talent and know how to utilise it. Yes, there's an element of luck. But luck favours the prepared.
Dan Weese I'm strongly inclined to agree. What's interesting to me here is that the effect of talent is still contained within the model used, it's just a bit subtler than might be expected.
ReplyDeleteAt this stage it's also quite fun to consider the nature of both talent and luck and how adjusting the model makes it approximate to different interpretations. In this case, with events only very weakly influenced by talent and events that can only multiply wealth, it's a bit like having wealth only from winning the lottery or getting taxed (a strange economic model to be sure). In contrast, if talent is allowed to determine the nature of events (i.e. favouring the prepared mind), then I think of the events as being somewhat similar to Discworldian "inspiration particles", ideas flit around the world but which are only useful to those able to use them.
I'm probably going to try and publish this. Originally I thought to do a rebuttal paper, but I don't like those. So I'll probably try the angle of "this simple model has lots of interesting interpretations, come play with it".
What I didn't explore yet was the effect of varying talent : experience is, surely, the best teacher. Another idea I've had is to allow agents to move - not randomly but towards the areas of greatest event concentration, where they have the greatest chance of success. Tonnes of other ways this could be extended; it'd be nice if someone decided to run with it.