This is a continuation of my Theorycraft 101 post that introduced trinket uptimes and RPPM. I’m going to assume here that you read that post. The main audience for this post is people trying to any theorycraft work, whether making a full-blown spreadsheet or simply doing a standalone calculation about some trinket. You should be able to find the equation you need here without needing to redo a lot of work.

A bit of terminology from last time:

• PPM is the proc’s built-in PPM constant.
• H is your haste factor (1 + your average haste %)
• D (used below) will be the duration of a buff

Our first basic conclusion was that if you ignore the possibility of proc overlaps, the uptime of a proc is:

$PPM \cdot D \cdot H / 60$

We called this value $\lambda$ (lambda) for any given trinket. It’s a good approximation of uptime as long as uptime is low (overlaps are unlikely), and it will also come into many later results. Conceptually, $\lambda$ is the ratio of the buff’s duration to its mean proc time.

The next conclusion was that if you account for the possibility of overlaps, the uptime is:

$1 - e^{-\lambda}$

# Various comments on Bioshock Infinite

Not exactly a comprehensive organized review, but just a series of reactions I had. Focusing more on gameplay than narrative elements, since the latter has been discussed everywhere and the former is where I have some specific criticisms I want to highlight.

First though, a few loose comments on story (since I want to remain spoiler-free for now). The best part is the plot structure and associated twists. The game does have its “would you kindly” moment for sure, and the most important part of a story that visibly about a running mystery like this is that the reveal is properly anticipated (but not too overtly) by what came before it. In this they succeeded. It is rather enjoyable, bordering on necessary, to replay at least the opening portion of the game immediately after seeing the ending. You’ll feel some disbelief at the sheer density of clues, foreshadowing, and double meanings to which you were completely oblivious the first time.

The other story/atmosphere points I want to touch on are really gameplay comments in disguise. Combat based on big, open set pieces was new to the Shock series, and a setting that still “alive” was also new. Regardless of what you think of these individually, their mixture causes some deep problems with suspension of disbelief. Doing FPS-y stuff like looting everything in sight and leaving piles of bodies everywhere and fighting pitched battles with squadrons of enemies does not jive with a living, breathing city that you’re trying to take seriously as an immersive environment. I know you do those things in every FPS, but most FPSs don’t take a city and its identity as their main character. In Bioshock you explored Rapture once it was dead, and learned very vividly what it was like when it was alive. Deviating from that setup did not bring much of anything new to the table, and only caused Infinite to slide more into familiar FPS tropes than its predecessor.