User blog:Jemann/"I think I deserve a predictable unlock level"

Increasing Notability
Most users of this wiki are probably aware of the Notability/Making Waves system by now; increase Making Waves through various actions, wait for a visit from Slowcake's Amanuensis and (hopefully) increase your Notability with the "I think I deserve a more emphatic type-face, at the very least." option. That option tests your current Making Waves quality against a fairly unique difficulty level: [20 - (B+D+R) + 6 * N], where BDR is the total of all your Bizarre, Dreaded and Respectable bonuses, and N is your current Notability. This means that as Notability increases, the difficulty level gets higher and higher. Since Making Waves is a pyramidal quality (it takes X change points to rise from level X to level X+1), it takes increasingly longer to raise Making Waves high enough for the chances of success to be reasonable.

Some users adopted the system of trying the option as soon as it became available, with quite low levels of Making Waves and consequently low chances of success. Since failure halves your Making Waves level, the cost of failure at a low level is much less significant. Obviously this was paying off, because the developers noticed and introduced a minimum Making Waves level as an unlock to the option.

Minimum Making Waves
I don't know how this Making Waves unlock is calculated.

It appears to be related to the same core [20 - (BDR) + 6N] formula, but working out a possible ratio has been problematic. Here's a table of data, with explanation to follow.

This data was collected at different levels of Notability, but appears to be consistent e.g. the same Making Waves level is required with Notability N, BDR X or Notability N+1, BDR X+6. This is why I assume that the same core [20 + 6N - BDR] formula (or possibly just [X + 6N - BDR]) holds.
 * 20+6N-BDR: 6 * Notability - (Bizarre + Dreaded + Respectable)
 * MW unlock: Minimum level of Making Waves required to unlock the option.
 * Minimum multiplier: Smallest possible ratio (inclusive) to get MW unlock from 6N-BDR.
 * Maximum multiplier: Largest possible ratio (exclusive) to get etc.
 * Minimum probability: Probability of success of challenge if attempted at MW unlock level.

If the Making Waves unlock level were determined with a simple multiplier of this formula, looking at the minimum and maximum possible multiplier for each level should allow us to narrow in on the exact number. Before I hit Notability 7 it was looking good - minimum multiplier 0.7111 (32/45), maximum multiplier 0.7115 (37/52). But at a 20+6N-BDR of 55 (Notability 7, BDR 7), the maximum multiplier is 0.7091 - less than the minimum multiplier at 6N-BDR 45.

Perhaps there's a new feature in StoryNexus - one that allows the developer to specify a minimum probability level, below which the option is locked? In the fifth column I show the chance of success at this minimum unlock level. Mostly this holds - the minimum probability is always 41% or higher. However, in those cases marked with a *, a MW level one lower would still be above 41%.

At this point I throw my hands up in disgust. I'm reasonably confident that my collected data is correct. I thought I knew how Broad difficulty was calculated. Would a number other than 20 fix it? Is the Pentium floating point bug still alive and kicking? If I've made an error, I can't see it. If someone else can work out what's going on, I'd love to know.