As I’m sure you’ll remember, there’s been a lot of debate on TA over the years about adjusting the DLC ratio formula as many people felt that it didn’t approximate DLC achievement difficulty particularly well.
Here’s a little history...
Back when the site started, DLC was incredibly rare - certainly more the exception than the rule. When DLC started to appear on the Xbox LIVE Marketplace, we used the standard TA ratio calculation for the DLC achievements:TA Ratio = Square Root(Gamers With Game/Gamers With Achievement)
As time went on, however, the mood toward DLC shifted. It was no longer something that only arrived for the occasional blockbuster title, but something that came to a larger assortment of games. It quickly became clear to the site users that the initial way that DLC ratios were calculated resulted in crazily high ratios for pretty much every DLC achievement. As DLC take up is so small (currently averaging 17.9% across the TA database as a whole), even the simplest of DLC achievements would have ratios of 3+.
It was proposed that a slight change be made to the standard TA ratio:TA Ratio = Square Root(Gamers With Content/Gamers With Achievement)
Thus we would only count the pool of gamers that had an achievement in that DLC pack as its base number, and this resulted in a “better” approximation of difficulty than the previous formula. I liked this change, and we implemented it.
Since that time, the site has grown considerably, and the number of voices calling for a change has increased. We recently had a poll on the site to see if the general site population agreed with these voices.
You can see the poll here:DLC Recalculation: What's Your Take?
and the results here:DLC Recalculation: The Results
Almost three quarters of the site wanted the ratios to be changed, so we put together a panel of statisticians and interested parties from the site to come up with and compare various alternatives.
They poured over their spreadsheets and one of the suggested formulae stood out as a clear winner - the Geometric Mean (GM), which is explained below.
The Geometric Mean formula uses a base pool of gamers that is a combination of the DLC population and the known main-game population (specifically, the geometric mean of the two populations, hence the name).
The Geometric Mean has the following calculation:((Gamers With Game * Gamers With DLC)/(Gamers With Achievement^2))^0.25
As the number of DLC owners approaches the total number of the main game, the formula also approaches that of the non-DLC main game achievements, which is neat.
It also handles single DLC achievement packs in the same formula, which would mean that we would no longer take the average Ratio of the game for those achievements - which could also be seen as a bonus.
Here’s a spreadsheet that shows all DLC achievements, alongside the existing ratio and the new ratio given by the Geometric Mean (note this was compiled 2 weeks ago so some values may have changed slightly):Geometric Mean vs. Current Ratios Spreadsheet
While most achievements will change, here are some specific DLC achievements the panel have highlighted as having a “better” ratio using the GM:
We currently have the level 50 achievement with a ratio of 1.81, which the level 100 achievement is 1.51. The GM formula increases the level 100 to a 2.34.
In order to unlock the Il Principle DLC achievement, the other achievement must have been won. Currently, the main game achievement is a 1.64 ratio, whereas the DLC achievement is lower at 1.56. Using the GM formula moves it up to a 2.34.
Earned by completing every campaign challenge in the DLC. The current ratio is 1.08. Using GM moves it up to a 2.84.
Unfortunately, there are also achievements that appear “over-inflated” with the GM and it’s only right that we highlight a couple of those:
This is an unmissable first mission that has a start marker right in front of one's character. This is Inflated from a 1.00 to a 1.85.
This is also unmissable for going to the DLC zone, and is inflated from a 1.00 to a 2.10.
Many other formulae were suggested and tested, but none of them achieved as much positive feedback as the GM formula.
To make this poll as straight-forward as possible, we are offering you a simple choice for DLC ratios - keep what we have now or switch to the GM formula. The poll will close in one week, on Monday, March 4th, so be sure to get your vote in before then!
An alternative to changing the formula was also suggested, which was to split the TA Ratio badges into 2 - one for Main Game and one for DLC. If the status quo option wins the poll then we will have another one to determine if we split the badges.