Statistically Speaking, It's Probably a Good Game, Part 2: Statistics for Game Designers

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Please, Can We Just Bookend the Quiz and Be Done?

Okay, okay, I hear you.

Q1a ANSWER – Level Times
The answer to this one is easy: you haven’t been given enough info to calculate the average yet. Just because the values ranged from 1:24 to 2:32 doesn’t mean they average out at 2 minutes. (Those two numbers average to 1.97 minutes, but we don’t know the other 18 results!) You need to know all 20 results to calc the average, and you really ought to calc the standard deviation as well...see below.

Q1b ANSWER – Level Times Part Deux
Okay, in this case you probably shouldn’t be satisfied because the standard deviation is pretty high...over 40% of the mean. This sounds like a bit too much variation in your level. There is potentially a sizable exploit that skilled players are using to their advantage. Alternatively, you might be punishing less-skilled players too much. As the game designer, you ultimately have to be the judge as to whether these results (high variation) are intended.

Q2 ANSWER – Soccer Moms
Stats only gets you part of the way there; you still need game design smarts. In this case, the score grouping is *way too close*...to have a standard deviation that low (500 / 52000 = 1%) means you are getting hardly any score variation, which means in turn that differences in player skill aren’t really mattering in the end game result. Therefore, players will most likely be turned off because they won’t see much of a progression in their scores as they get better at the game.

Here’s a situation where you’d really love to see a much higher standard deviation, because that hopefully shows that increased skill leads to increased scores. In other words, your current game scores the same no matter who plays it.

Q3 ANSWER – Play Times
This one is sorta tricky and underhanded but illustrates an important point about data collection: you need to watch out for obviously bad data. That one value, 0.2 hrs, looks suspiciously like an error. Could be a typo, could be an equipment malfunction, who knows. In any case, you should either convince yourself without a doubt that the 0.2 hrs is a valid data point before doing any calculations with it, or just throw it out and perform your calcs on the remaining data points.

Insert Other Cool Stuff Here

In efforts to keep this article under 723 pages, I have to skip over many other intriguing topics. Suffice it to say that a good understanding of statistics will help not only your game design, but your consumer decisions, voting decisions, and financial decisions. I’m 23.4% sure that at least 40% of what I just said is true.

As a designer, statistics is most useful when crunching data from a set of recorded play sessions (your sample), and trying to form conclusions about a larger field of unrecorded play sessions (your population). 

Learn By Doing

For example, in the game I just finished, we recorded data from play sessions and then set challenge levels in the game based upon the mean and standard deviation values from those recorded data. We set Medium difficulty to be equal to the mean values, Easy difficulty to be equal to the mean minus a certain amount of standard deviations, and then Hard difficulty equal to the mean plus a certain amount of standard deviations. Had we collected much more data, it would’ve actually been accurate! <wink>

Just like probability theory, statistics becomes more and more useful the bigger and bigger the scope of your project. A lot of the time, you can fumble your way through without applying any formal theory in either case. But the bigger your game, the bigger your audience, and the bigger your budgets, then the more there is to risk from embedded flaws in an unbalanced, seat-of-the-pants designed game. 

Stats, like probability, won’t do your game design work for you.  It’ll just help you do it better!

The Long Road Ahead

In the rousing conclusion to this series, I’ll be taking bits from parts 1 and 2 and then putting them together in ways that actually have some relevance to games.  Or I’ll croak trying!

Thanks for reading, and ciao for now.

Attributions:
*The Wikipedia images used in this article are licensed under the GNU Free Documentation License.

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