Sigh.
It doesn't need the logical base you are looking for. The beauty of chaos theory and and how statistics work, all you need is the current system of dice rolls that affect outcomes over a large number of instances. I'm not kidding, that is all you need.
Tom Tippett was asked about adding clutch hitting and hot and cold streaks to Diamond Mind Baseball, probably the greatest and most accurate baseball sim ever developed. Seriously, based on the projections of each player, Tippett was able to use DMB to beat the vast majority of sports writers in predicting the upcoming season by playing it out 50 times and averaging the the results.
He refused to add clutch performance, and to have hot and cold performances. The problem was, without these artificially added results, the game would produce all the streaks and clutch hitting you see in real life. But if you added a boost, it would warp the hell out of the results. You would get more realistic variations in performance by just letting chaos dictate results than by trying to affect the results.
Leave it alone, and you get an accurate amount of no-hitters, hitting streaks, slumps, and magnificent comebacks. Yet, when any of these events happen to an individual, it feels scripted and wrong. It doesn't feel "random." But that's what "random" feels like. It's not an even distribution of events, its clumps of things happening and not happening.
Humans are TERRIBLE at picking up on randomness. We are hardwired to find and see patterns. We use those patterns to make decisions. Much of the modern world has been shaking off the misconceptions humans have of the world resulting from need to see patterns. Science overcomes this with data, using the scientific method to avoid getting trapped by anecdotal evidence.
Now, do I believe that modern action sports games on consoles are anywhere close to as accurate as text sims driven purely by data are? No. It's why I mostly roll my eyes at the insistence that these games be considered sims. They are so far off, it just seems like a silly argument. Fun>Realism.
But, that doesn't mean they are programmed to beat you. It just means that it will always feels that way. Humans are not capable of observing randomness in small samples. It always feels forced.