Calculate enemy's hitpoints (extrapolate), based on change rate?

Question

In our game, we have a boss (NPC), who's life is being checked on a time interval, say 1 minute. I need to find a way to extrapolate known points (life,time), and approximately predict life after one minute (after 1 minute life will be checked again, and will be put in data set) Also, extrapolation needs to consider mostly recent change (for instance, if we have 10 points, and last two have changed rapidly, it should be able to predict even more rapid change at next point). I found multiple example this one and this one, but seems like I'm not able to translate all this in as3 code. Basically what I was looking for was 2D Extrapolation.

P.S. The point is that any calculated value should not get above any previous values, that is because the boss' hit points cannot increase, and also cannot stay the same; they can only decrease. I guess that means extrapolation wouldn't do. So I'm looking for another algorithm that will do.

Answer 1

Consider a calculus-inspired approach. If we have a list d[i] of the damage at a past time iand the current time is n, then we can estimate d[n+1] using the previous values in the list. d[n] - d[n-1] provides an estimate of the change from d[n] to d[n+1] based on recent values, (d[n] - d[n-1]) - (d[n-1] - d[n-2]) provides an estimate of the change of that change, and so forth. The idea is to use differencing to estimate change. If you have a time-series data list d[i] = [a,b,c,...], and another list d2[i] = d[i] - d[i-1], then d2[] is the change in d[] for all times i > 1. Since d2[] is also a time series, you can use it to create a d3[], chaining the terms to provide an estimate:

d[n+1] ~ d[n]    +    ( (d[n] - d[n-1]) )  +  ( (d[n] - d[n-1]) - (d[n-1] - d[n-2]) )  +  ...
         ^last value    ^ est. change           ^est. change of change
         d[n]           d2[n]                   d3[n]

Granted that this makes a lot of assumptions about incoming data. The two most important problems I can think of:

• This assumes that most recent change(s) are completely representative of future values- in cases where change terms are non-linear, this causes the estimation to lag behind the actual data
• The "lag" becomes stronger as more terms are added - a better estimate (more terms) must be balanced with better agility (less terms)
• Outliers in incoming data figure directly into the equation, and thus directly affect the resulting estimate