First good search result for: "too many hit points" |

### Method of Calculation

So, in GURPS, you do not die at 0 HP, on the contrary, you can go several multiples of

*Max Hit Points*into the negatives before sweet release is yours. But, each struggling shuffle towards the end of the mortal coil also gives you a small chance of dying before reaching this assured decimation at -5 x*Max Hit Points*. Salvation is given if one succeeds at an*HT*roll at each of 4 checkpoints on the highway to the afterlife.
This means that sheer grit and staying-aliveness is a function of

*HP*and*HT*.*HP*increases the number of absolute possible steps before the final destination, and*HT*increases your chances of not dying before you reach that point.
Mathematically, we call this a binomial probability, because we have two outcomes at each fatality check: we succeed or fail (there are some optional rules for slightly more sophisticated and varied outcomes, but they are still mostly degrees of failure and success than a total paradigm shift. So, some

*Hit Points*are locked behind the chance that you might die, and sometimes, the chance that you might die. You are (mostly) guaranteed that you can go from*HP*to -*HP*without dying, so everyone has 2xHP. After those*HP*though, you have to stay alive to get the next*HP**Hit Points*, after that, you need to stay alive again, and after that, you need to stay alive again, so your chances of getting the next bit of hit points is cumulatively dependent on your odds of getting all the*HP*before it.
So, "Effective HP" is:

2 x HP + (HT Success Odds) x HP + (HT Success Odds)^2 x HP + (HT Success Odds)^3 x HP + (HT Success Odds)^4 x HP.

2 x HP + (HT Success Odds) x HP + (HT Success Odds)^2 x HP + (HT Success Odds)^3 x HP + (HT Success Odds)^4 x HP.

I graphed these values, and got the charts below:

### Health held constant with HP as the Independent Variable

The vertical axis is "Effective HP" and the horizontal axis is the number of real

*HP*. Each line corresponds to an*HT*value of 10 to 16, and*HP*goes from 10 to 20.
The improvements are literally linear (look at the trendline equations, and the R squared value of 1, which means a 100% perfect match.) the lines are a little wobbly because I rounded them to integers before graphing, but this means, point for point spent on

*HP*, the "return on investment" so to speak is always the same. At higher levels of*HT*, each*HP*is more valuable, and at 16*HT*a single*HP*is worth almost twice as much as it is worth at 10*HT*, as we can see by the increasingly steep slope of the equations.### HP held constant with Health as the Independent Variable

This graph is a little more interesting and follows a more polynomial plot, almost a 4th order equation (not important, but an observation.) We see that with this graph value rises a lot faster per each

*HT*added than in the previous graph, but not all*HT*are created equal, as beyond 16, the graph completely flatlines (because 17 and 18 are always a failure.) Not that going beyond 16*HT*is worthless, but it loses value in terms of simply staying alive. Looking at the trendline equations and looking at the line, the fits are**obviously**not as close as those for the previous graph, but to kinda get an idea of how much each point of*HT*helps, take a look at the constant in the equation being multiplied by*x*. We are getting, in the best situation, an improvement of survivability almost 6 times what we get from increasing*HP*. The constant next to x^2 however, is negative, indicating diminishing returns; each increase in*HT*is worth less than the previous, as opposed to*HP*where increasing*HP*by one when you are at 10, or when you are at 20 still "extends the lifebar" the same amount.### Final Notes

At the low end, increasing

*HT*does a lot more to help than increasing*HP*. If I knew how to draw a 3d graph, that'd be nice, but I don't, I don't have a license for*Matlab*either, but taking a look at these charts, if you ask yourself, "Should I get another*HT*or another*HP*?" You can answer that by looking at the graph you like the most, let's say the first one because it's linear and easier to eyeball at a glance. If the dot above your dot (on a different line) is better then the next dot on your line, it is better to improve*HT*(if you have the choice) If the next dot on your line is better, then it is better to increase*HP*. Of course, this isn't always accurate because really, one point of*HP*costs a lot less than one level of*HT*. If you like the other graph, just swap*HP*and*HT*in that statement. That being said, one level of*Hard to Kill*is closer in price (I think the same price) so you can use that, and some advantages like*Fit*improve*HT*for the sake of staying alive, and come with a slew of other helpful benefits.
Also, a lot of this is hypothetical, and depends on certain assumptions like, "being -20

Edit: Thought about it, and here's a reasonable approximation of what the graph might look like according to Wolfram Alpha if it were in 3d, note

*HP*with a lot of*HT*is no worse than being at 10*HP*with a lot of*HP*," and that is not exactly true either.*Move*and*Active Defenses*will be penalized, and you might need to roll often to stay conscious... but at least you aren't dead!Edit: Thought about it, and here's a reasonable approximation of what the graph might look like according to Wolfram Alpha if it were in 3d, note

*HT*is from 0.5 to 1, which is 50% odds of surviving (or,*HT*10) to 100% chance of surviving (*HT*16 is like 98.5%, technically, not possible in GURPS except for maybe with some "no nuisance roll perk" at 18*HT*.)
Interesting. And improved HT will protect you against disease and such, improve your fatigue, and give you additional Basic Speed, while HP will give you additional slam damage. Your analysis does seem to tilt things in favor of HT, that's for sure.

ReplyDeleteOne thing I didn't include, which might also be interesting information is a matrix that shows at each step which is better, more HP or HT.

DeleteGiven a choice, if survival is your primary concern, one should get to 14 HT, then after that, it gets a bit more shaky, I think something like "take 4 HP, then one more HT, a few more HP, and finally, 16 HT."

And yeah, this analysis is way oversimplified, because, like you said, there are tons of benefits of HP and HT that I'm ignoring.