Many have noted that their opponent's hats make no sense. You might face someone who has a gold sling, but their birds are wearing party hats or no hat at all. Why is this? Why would competitive players purposely handicap themselves when they must have a full set of higher level hats? To try and figure this out, I recorded data on my area opponents over the past two weeks. From each of the streaks 1-7, I have at data on at least 11 opponents.
Specifically, I noted their star level, sling level, bird level, and their hat modifiers. Hat modifiers refers to x0 (no hat), x1 (party hat), x2 (crown or street cap), or x5 (cowboy hat).
I calculated 1) mean bird level (the average level of all their birds without hats), 2) mean effective bird level (average level of birds+hats, and 3) mean hat modifier for all of my opponents at each of streak 1-7.
My ObservationsOpponent bird level
All my opponents (99 in all) have the same star level and sling as I do. There is no benefit to leveling up your sling.
My opponents' mean effective bird level increases lock step with mine. There is no benefit to leveling up your birds.
You are highly likely to have an opponent weaker than you at streaks 1, 2, and 4.
You are virtually guaranteed to face a stronger opponent during steaks 3 and 5-7.
Opponents faced during streaks 3 and 5 are equivalent in their mean effective bird level.
Streaks 6 and 7 are significantly harder than streaks 3 and 5.
Streak 6 opponents have the highest mean effective bird level.
Opponent hat usage
Opponent hat usage is random -- too random to be natural.
Only 13% percent of my 99 opponents had a mean hat modifier that was equivalent to their sling.
Opponent hat variance always benefits us. Opponents' mean effective bird level is always less than their actual mean bird level.
So, what does all this mean?
My Interpretations
I think that our opponents are playing with their best hats on, and the hats displayed to us are chosen randomly server-side to level the playing field in response to our complaints about difficulty. In the histogram below, each of these opponents had silver slings, yet their hats add up in a predictable way. If these are serious players, their mean hat modifier would never be below the red line, but it is a whopping 87% of the time. Hat are an additional modifier, added about a year after the initial release. Code wise, I think it would be fairly simple to modify the hat after the run.
I have 99 observations of mean hat modifier that form a near-perfect bell curve (considering the small sample size). In nature, we often expect data to be distributed as such. For example, if you measured the height of all boys in the 3rd year of school, you'd find a similar distribution. We have reason to expect that.
However, we aren't talking about something that should vary naturally. We are talking about players choosing to handicap themselves. It's fishy. It think that Rovio is selecting hats from a normally distributed probability density function that results in a mean hat modifier centered on about 1.5. Like I said, though, it works in our favor so whatever :)
The figure below shows the difference between my and my opponents' mean effective bird level (left) and mean bird level (right), with the red horizontal bars denoting the 1-standard deviation range. A positive value of 1.5 indicates that, on average, the total of my birds and hats put me at 1.5 above my opponent. For example, if he averaged 12, I averaged 13.5.
If we consider only the mean bird level of our opponents (right), we see that there is 1) very little variance in our opponents' relative difficulty with 2) all around lower values (i.e., higher difficulty). Adding in the hats increases the variance, meaning you will see more randomness in your opponents' level (Rovio likes Random, right).
Finally, the difficulty in Streaks 3 and 4 is reversed. 4 should be harder, but perhaps Rovio doesn't want to give away chests too easily, so Streak 3 is made purposely disproportionately difficult.
