Speedrun Goal Time Theory

Speedrun Goal Time Theory
When most people speedrun a game they think about wanting to get a "goal time."  This paste is not a caution against doing that: it's vitally important to set a goal time in order to play optimally towards getting that time.  The part that is very often being missed is that there is a relatively objective way to determine how to play optimally towards getting your goal time.

That metric is "Expected total time to acheive a goal time."  In other words, how much total time you'll spend on average using a specific route to try to achieve a specific time in a speedrun category.

The most straightforward application of this is when equal levels of risk and timesave are obtainable at 2 different points in the same run.  An example of this follows from the Surge fight and Bike Voucher in Pokemon Yellow.  By pushing the bike voucher dialogue to after the Surge fight, you spend less time in each run that dies to Surge and therefore less total time while trying to obtain a finished run.  Another example that came up recently was the ordering of fights in Pokemon Stadium, where you can choose to do the fights in reverse order while losing only 2 seconds in menuing or choose to do the gyms in normal order.  The risk fronting available by doing the later fights first vastly outweighs the mere 2 seconds of menuing.  in other words, it's much easier to save the 2 seconds (and more) in a finished run by resetting for a faster run through the RNG of the hardest fights than it is to simply save the 2 seconds with quicker menuing.

Another step up from this is realizing that the route which people strategize and debate on for getting a new WR in a category is likely very inefficient to get goal times slower than the WR.  This is the theory behind the Beginner + Advanced guide split for Pokemon Yellow; If a new player saves at common race save points and uses the beginner guide, they're very likely to spend much less actual time finishing their first few runs.  As they strive for better times without deaths they can drop saving for major fights, because at that point the total time cost of getting top end RNG while saving will begin to outweigh the total time cost of not saving and resetting deaths.

Much more useful and complex applications of this theory are possible.  If you can approximate a normal distribution of run times that a given skill level and route can obtain, then you can approximate the level of luck that you need to obtain to finish a run with that route.  From there you can make precise evaluations of the value of a strategy.  A current example of applying this level of theory is Mega Punch routing in Yellow.  The current WR run time is already several standard deviations away from a median run time.  With Mega Punch you can increase the standard deviation of run times, both lowering the best possible times and increasing the worst times.  The increased variance of runs in turn increases the area under the normal distribution which sits past the current WR.  By comparing this percentage change to the change in total time spent due to deaths on Nugget Bridge, you could calculate exactly whether mega punch is valuable or not.