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<blockquote data-quote="Gorgon Zee" data-source="post: 8487850" data-attributes="member: 75787">It's worse than that even. Whenever you say average, you are assuming something to average over. For roleplaying campaigns, you might assume that the average is over the campaigns (that would be the typical usage), but another reasonable option would be to average by time spent.The average (mean) by campaign says &quot;given I am about to start a campaign, how long do I expect it to last?&quot;. The average by session count says &quot;given I am playing in a campaign, how long do I expect it to last?&quot;. Example:I played 4 campaigns of length (in sessions) of 1, 1, 2, 16. The per-campaign average is 4 sessions, but the average over sessions is (1*1 + 1*1 + 2*2 + 16*16) / (1+1+2+16) = 13.Now this may seem a pretty odd way to calculate an average, but it's closer to people's perceptions, I would argue. People think in terms of how they spend their time, so for the person above who spends 80% of their time in a campaign lasting 16 sessions, it makes sense that their perception is that campaigns are long -- weighting by the time spent makes sense as our fun is generally thought of as per-session: You don't say &quot;I played one great campaign for a day, and one awful one for a year&quot; and think of that as an averagely OK experience!Mathematically, it has another good property. Adding in campaign that never got started doesn't scare up meaning. In the example above, suppose there were 4 other campaigns that were ideas, but never got started. They had zero sessions. For the per-campaign average, that reduces the per-campaign average to 2. But it doesn't change the average by session at all.Anyway, this was your bit of statistical arcanum for today</blockquote>

[QUOTE="Gorgon Zee, post: 8487850, member: 75787"] It's worse than that even. Whenever you say average, you are assuming something to average over. For roleplaying campaigns, you might assume that the average is over the campaigns (that would be the typical usage), but another reasonable option would be to average by time spent. The average (mean) by campaign says "given I am [B]about to start[/B] a campaign, how long do I expect it to last?". The average by session count says "given I am [B]playing[/B] in a campaign, how long do I expect it to last?". Example: I played 4 campaigns of length (in sessions) of 1, 1, 2, 16. The per-campaign average is 4 sessions, but the average over sessions is (1*1 + 1*1 + 2*2 + 16*16) / (1+1+2+16) = 13. Now this may seem a pretty odd way to calculate an average, but it's closer to people's perceptions, I would argue. People think in terms of how they spend their time, so for the person above who spends 80% of their time in a campaign lasting 16 sessions, it makes sense that their perception is that campaigns are long -- weighting by the time spent makes sense as our fun is generally thought of as per-session: You don't say "I played one great campaign for a day, and one awful one for a year" and think of that as an averagely OK experience! Mathematically, it has another good property. Adding in campaign that never got started doesn't scare up meaning. In the example above, suppose there were 4 other campaigns that were ideas, but never got started. They had zero sessions. For the per-campaign average, that reduces the per-campaign average to 2. But it doesn't change the average by session at all. Anyway, this was your bit of statistical arcanum for today [/QUOTE]

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