His friend is an very serious and high level former physicist turned quant and he'll tell you for free that this is not a debate about the law of large numbers (which was last interesting before I hit puberty) or any of the other elementary statistical explanations listed above - none of these things are relevant or revealing. It's essentially a debate about the nature of a "trade".
The original debate was whether Jim Simmons or Warren Buffet was a better investor, and the crux of the debate came down to my good friend asserting that Simmons was a better (read: less lucky / more "skillful") investor because he had done a (much) greater absolute number of trades than Buffet over the course of his career, despite Buffet's career being substantially longer (almost double the length). This is because Renaissance tend to run computer driven trading strategies that are often very high frequency and use complex and quick dynamic portfolio rebalancing techniques based on live, noisy, incoming signals - lots of very small and funny trades with a very short life span and no objective purpose other than because the computer deems them necessary as part of its greater objectives. The majority of these trades, on their own, do not even intend to be profitable - rather, they're geared towards preventing potential unprofitability.
Buffet, on the other hand and as we all well know, does infrequent and enormous trades based on months of fundamental research. These positions are usually held in perpetuity (he has been a major stockholder in Coca Cola for more than 20 years) and are often intended to maximize dividend and other cash flow income, although he is also fond of distressed opportunities as well (LTCM). Consequently, it should be exceedingly obvious that Buffet does far fewer trades, but all of them are intended to be profitable.
The assertion that this makes him less skillful than Simmons (or Soros, which is an entirely different kettle of fish completely and one only brought up in said debate because my good friend revers Taleb to an unhealthy degree and believes anything he has said can be used to crush an argument) is completely ridiculous. I really shouldn't have to explain why, but my essential point is that 1 trade does not directly equal another. Me buying shares in Anglo American on my dinky little online broker is in no way reminiscent of RBS bundling up 10,000 mortgages and selling the multi-billion securitization to an SPV - yet both are single trades. So applying the law of large numbers to the absolute number of trades done by these titans of the game over their careers (and thus assuming all trades are equal) to establish luck is really, astonishingly, stupid. Its the same as saying all pieces of string are the same length. A more intelligent appraisal would be to look at absolute returns, drawdowns, running costs and receivables. Both have delivered outrageous returns for a very long time, though Buffet has done so for far longer with fewer, smaller drawdowns and at considerably less expense. Additionally, if Simmons turns off the machine tomorrow, profit will instantly become negative and stay so in perpetuity - he has no receivables. Buffet hasn't had to get out of bed for 30 years and he would still earn hundreds of millions for himself and his shareholders in dividend income alone, not counting his other cash streams. Performance wise, they are historically comparable, but it is worth pointing out that performance wise Buffet beats Soros into the dust in every metric you care to pick, except the breadth of securities he traded and the number of absolute trades he did. Some of his misses and drawdowns are gargantuan, and it does surprise me that he never blew Quantum up at one stage or another.
The notion that he was in any way lucky over the course of his 50 year career as the most successful investor who has ever lived is so preposterous that it speaks to an astonishing lack of common sense, and the application of the law of large numbers to this comparison has no basis in mathematics, logic or finance. This debate is ultimately about fundamental vs quantitative analysis, and if there was a clear winner in that debate one or other side would cease to exist quite quickly.