bismuth9
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Production update 2023-09-20
🕑 Added 2023-09-21 01:24:16 +0000 UTCHello everyone!
It's been a while, but I have a lot of news. Last time, I was talking about how my next course of action would be to figure out if Frigate 00A would make a good video topic, and I have come to the conclusion that yes, it would!
Frigate 00A probability theoretical analysis
Now, the major point of interest in Frigate speedruns is the extremely low probability of the hostages escaping fast enough for Objective A to complete in time. You can play the level and complete everything in about a minute, but the probability that all the hostages you released actually managed to escape in time is on the order of 1% at best. This is why you often see runners waiting by the boat for Objective A to complete, and why you can see some runners going for a target time and just leaving the level at that time no matter what, banking on the off chance that the final hostage will escape during the fadeout.
Anyway, all of this is a juicy story to tell. The video isn't simply gonna talk about the speedrun itself, which, by my standard, is relatively unremarkable. It's also going to explore the process of calculating the probability of success. For that, I made a model very similar to an already existing analysis of the potential of 1:02 (current WR is 1:03) by Onslatt. It takes in split times for reaching each hostage, possible death animations for the hostage taker, and all 6 escape points the hostage can choose. From there, I calculate combine all animations and escape points into a probability table, and from there, I can find out the probability that all hostages escape before a time threshold.
Repeat this table for all 5 hostages (2 are shown here), and the total probability is all 5 of them multiplied together. With some preliminary figures for hostage split times and a threshold of 63 seconds, the total probability comes out to be 1.2%.
Simulation based on empirical data
Now, here's where the scope of the project took a turn.
The biggest problem with a model like this is that it woefully underestimates the factors that can slow down hostages. Which means, it greatly overestimates the probability of hostages escaping in time. How much, though, is an impossible question to answer, because there's no way to model two dozen guards running in circles and blocking hostages, throwing grenades and generating all sorts of lag.
So, instead, we're going to measure it empirically! Whiteted is currently working on a romhack that will log data on hostage escapes, and Perfect Ace and Seanjohn (+ possibly others) will run as many trials as they can without going insane. They will log data on how long hostages take to run to a given escape point on a normal 1:03-ish pace run, and we will obtain a reasonably accurate representation of the probability function of each escape time .So, instead of being a flat number like it is right now, escape times will be a probability function.
From there, calculating the probability of hostages escaping before a time threshold is getting quite complicated, so we're gonna solve that problem with a Monte Carlo simulation with the help of Onslatt.
Once we have a million simulated trials, we will have a pretty decent approximation of the real odds of a 1:03 completion, as well as any theoretical time, from 0:58 to much longer, even 1:30 or more. This could also be useful information for real-time runs like 100% and full game 00 Agent.
You can also fairly easily tweak the settings and only look at Agent or Secret Agent hostages, although the empirical data for the time they take to escape will be based entirely on the state of the level during 00 Agent runs. It should work the same for Secret Agent, but might not be very representative on Agent.
Production schedule and timeframe
I also completed the production schedule for this video. It's a bit different this time because I haven't finished the whole script; I'll be waiting on the data we get from runners to finish this analysis. In the meantime, I'll record and edit the first section of the video, and I'll revisit it once it's the last thing to add.
Here's what the schedule looks like:
As you can see, it's pretty packed, and I have a deadline on October 22nd. I took on a sponsor deal that expires on the 22nd: if I can't release the video in time, they will drop it. So I have an incentive to work efficiently, and I have the motivation, since I find this project quite exciting! It will not only be a cool way to teach some probabilities and statistics, but it will also advance the level of knowledge there is on Frigate, and perhaps give a bit of insight on other NPC-dependent objectives.
And this is the current progress. Total length is extrapolated based on roughly how many talking points are left to write about, but there's a chance it reaches 7k words. The initial plan was about 20-25 minutes, but right now we're looking at near 35, maybe even close to 40.
So, with all that said, I'm going to enter turbo mode. I'm prepared to really dive into this project and do everything I can to get this out in time and make the best analysis possible.
That's it for now! I'll prepare and announce a production livestream shortly. Stay tuned on Discord, and I'll post about it here as well!
