In the Equipment in Combat thread, people kept throwing around analyses about what a certain level of ability is likely to produce. I think that some of the analysis is somewhat flawed, because it only looks at the most likely outcome (and not even that in some cases). That is, to really compare options you can't just look at the outcome that's most likely to occur, you have to look at what we statisticians call the expected value, and what gamblers call the payoff. That is, over time what's the average result that the ability will tend to produce. Because, sure, when an ability produces a +6 augment, it's great. But if it produces -6 just as often, then it's really sorta simular to an augment that produces 0 all the time, no?
Well, there's unfortunately (from my statistician's POC, but actually fortunately for play) no way to calculate this without looking at the exact values of the ability used, and the target. But there are some interesting trends that we see. I haven't looked at it in perfect detail yet, but I think that in most cases the expected value for any gamble is actually right around zero as it turns out. That is, you're as likely to lose as many points as you are to gain any. In fact, in many points its lower than zero. As you lower the target, this increases, actually but never reaches the amount of the auto augment.
The half result for a marginal victory is one of the most common. Assuming that the player is targeting a resistance equal to his ability (which theoretically provides double the augement of an auto augment), the most likely form of success is to get an augment equal to the auto augment. The next most likely event is to get a negative augment of some sort. The third most likely event is that the full augment is achieved. This makes the expected value near, or below zero in this case.
The full augment becomes the most common result only if the augment is dropped to somewhere between the auto-augment and double (absolutely no reason to take it at that level or less), but then failure of some sort moves into second. You never get anywhere near the auto augment iteslf in terms of expected value - it may become positive, but still way lower than the auto augment. For characters looking to variably augment with abilities at the 17 level, this is a non-existant range anyhow. Only when you get to about 5W do you have any options at all that have a better payoff, and these points are only about one point better than the auto augment. Why gamble for one point? Especially when the payoff is still lower than the sure value of the auto augment. If I'm going to gamble, I want to make it pretty significant.
At the point that you're rolling for very high abilities, a strange effect occurs in that the player can start to shoot for the augment in between and start to rely on bumps to ensure that they get a multiple of the bonus. But even then I think that the payoff never equals the auto augment unless we're talking about nearly irrellevant margins. In other words, when you're a 10w4, you don't worry about +2 additional augment over the auto augment, I'm guessing. In any case, if this is true, then it's a bad thing because I don't want powerful things to have an incentive to minmax small margins.
So, what does this mean for the player looking at variable augments as an option? Well, it means that they're longshots to produce any benefit at all in most cases. Now, longshots are often attempted in HQ because they're fun, and you can use a HP to bump to success when neccessary. The problem here is that it's senseless to use a HP to assure a level of an augment. Because that same Hero Point will be much more effective in adding 20 to your score in the original conflict (bumping is the equivalent of doing this). Remember that you're comparing the marginal benefit, so the HP is only getting you the difference between the two levels of success in the case of the variable augment (doesn't get to be 20 unless you're a great god or so). So, unless you really need both to win - a rare circumstance, I'd argue - you won't bump the augment often if ever.
So, we're left with a bad gamble. Now, is that so bad? I'd agree that variable augments shouldn't ever have a better expected value than the auto augments. That may sound contradictory to what I've been saying above, but if you have variable augment provide superior payouts, players will never use the auto augments. They should, at best, have an equal payout to make the two options equally attractive. I'd actually want the auto augment to be slightly less beneficial in order that it be used only in appropriately dramatic and/or desperate situations. Makes for less rolling, and makes augments special.
Well then are they at the right level of payoff? Not for me. As they stand, they're too low for players to use them at all, other than on an uneducated lark. They ought to be attractive enough so that the players will seek them out occasionally. If you like them to be really rare, then leave things as they are.
I think that, cognitively, what stops me from trying them is the effect of the marginal victory. Psychologically, looking at that, and seeing that often the most common form of victory is to just get the auto augment or less back, why try? The result tends to be undramatic - the roll is for nothing. Might as well have gone with the auto augment.
So, the tiny tweak that I'm advocating right now, I think, is to make marginal victories have a full (x1) effect (is this how it worked in HW?). In fact, what I'm going for is making both sides, success and failure, nearly parallel. Easier to remember, too, if they're parallel. So an even smaller change would just to make them parallel with the -.5 on each side of marginal.
This doesn't change the curve much for the high ability beings as compared to the low, but for the low ability beings it means that if you go for it, you'll get some sort of dramatic result no matter what. What does it do to the Expected Value? It places them right around zero for the case where you're going for the doubling, and higher with lower bets. Actually it equals zero on ability values evenly divided by 10 - the auto augments benefit from the rounding up, and are worse when rounding down. This still never makes the auto augment a good bet, but it makes it, at least, more dramatic, and slightly less bad. So I think it'll get the attention of the players more.
So, have I made any errors in my analysis? Does it seem like a sensible tweak to accomplish my goals? Should I go further, and try to get the payoff closer to the auto augment? Any other methods that would suffice?
Thanks for your attention,
Mike
Powered by hypermail