In anyone's favorite tabletop sports simulation board game, the associated player ratings and game engine can make up the crux of how much one enjoys that particular game.
While the game engines themselves are important, typically game designers put significant thought into a game's structural design. Moreover, most games are play tested long enough to notice lacking areas and inconsistencies in the game engine, leading to most game engines being relatively stable over time and not causing too many headaches for players.
This may not be the case as often, however, when it comes to the aspect of statistical distributions of player ratings. As a player of over 20 different tabletop sports simulation games, I personally have noticed a striking reality: that some games seemingly to pay more attention to their player ratings distribution and variation between players than others, and this significantly impacts one's enjoyment of the game!
It is first worth noting the following distribution types as common statistical distributions, for those who are unaware. Think of the x-axis as having the player rating, going from less to more as you move to the right, and the y-axis having the frequency of those ratings:
Source: DailydoseofDS.com
As you can see from the image above, there are a multitude of statistical distributions that exist mathematically, all of which could be reflected in the varying nature of player ratings based on their real-life capabilities.
A key component of statistical distributions themselves is variance, or the spread between numbers. I will not opine here on which distribution is the best for sports gaming, as that is particular to the sport and game at play in many cases.
It is worth noting, however, that a distribution that's bunched up too narrow, such as the rather-common Normal distribution for example, will generally not necessarily reflect differences in player abilities where they likely perhaps should to a greater extent. In this sense, if John Olerud is just as good of a fielder as Rico Brogna, while only being slightly better than David Ortiz at 1B, then that game has lost some of its appeal and accuracy as a result.
My background in data science and statistics has led me to conducting some introductory analyses around various games (not going to name any specific games out of respect for them). To be succinct, I have found that certain games will have player ratings that are different from a player of slightly different capabilities come into play around 1 in 3 dice rolls, whereas other games it can be closer to 1 in 15 or even 1 in 20. This is a striking difference between games!
I have also noticed that for some games, there is a certain near-maximum capability that a player can take on, and the games don't do a good job reflecting the nuances of the player's abilities nor who is better between superstars and mega-superstar players with the highest ratings, because they've already "max'ed out" so to speak.
Another component worth considering, and it would be a great question to ask game designers, is the extent to which statistical simulations and modeling were done to test for the implications of the way that players were rated. It's one thing to play-test a game 100 times with the help of play testers, but what about using computer random number generators and complex models to simulate a particular game 10,000 times over? The games that undertake this level of scrutiny and mathematical examination should yield a better experience for players in-turn.
While seemingly unimportant at the surface, a look "under the hood" statistically can yield significant insight into how players are rated in a game; if they're accurate, how much players ratings vary and also exemplify their attributes and capabilities.
With this, it is worth remembering that some games are aiming for fun and/or simplicity over statistical accuracy. Moreover, game designers always have justifications for designing a game or rating players a certain way. So, as a consumer it is worthwhile to show respect to this!
What games do you think have got statistical distribution of player ratings down the best? What games can be improved in this regard? Comment below!
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