It is late and I am tired, but could you explain how you arrived at 52%?
1 or 2 on 1D6 is a 2/6 chance = 1/3 = 33%.
If I roll 2D6 and assign the low dice to Effect, then 20 of the 36 permutations should have a 1 or 2 = 55.5%.
I think you've just made the same mistake as the designer.
The problem is that a failed roll (or a successful roll) is a
subset of the normal 2d6 spread. Therefore, if a roll fails, there is *not* a 1/6 chance of any number appearing on each die. The reason is that many of the higher individual die rolls will result in a success, so they aren't available for a failed roll. The reverse is true with a successful roll.
Assume a no modifiers roll. If the roll fails, it must be a 7-. Here are the 21 possible combinations for 7- on 2d6:
1 1
1 2
1 3
1 4
1 5
1 6
2 1
2 2
2 3
2 4
2 5
3 1
3 2
3 3
3 4
4 1
4 2
4 3
5 1
5 2
6 1
As you can see, you are six times as likely to roll a "1" as a "6".
On either die, 11 of the 21 combinations (52%) are a 1 or 2.
If the lowest die is automatically assigned to the effect die, then a whopping 18 of 21 rolls will be an abject failure.
If the highest die automatically assigned to the effect die, then 3 of the rolls will be an abject failure. But in that case, 18 of the rolls (85%) will yield a very bad timing result (5 or 6).
Since you can't account for specific allocations of timing or effect, I choose to look at the probabilities for each die. Alternatively, you could average the chances of automatically allocating the best die to timing or effect. This will work out to about 50%.
Another way of saying this is that there's a >50% chance of getting a very bad effect or timing result on any miss with no modifiers.
And the stats get weirder as negative modifiers are applied to the effect die. The timing die produces even wierder outcomes if no modifiers are applied:
Failed Rolls
No Modifier:
1-2: 52%
3-4: 33%
5-6: 14%
-1 Modifier
1-2: 46%
3-4: 34%
5-6: 19%
-2 Modifier
1-2: 40%
3-4: 36%
5-6: 23%
Successful Roll
No Modifier:
1-2: 06%
3-4: 33%
5-6: 60%
-1 Modifier
1-2: 0%
3-4: 30%
5-6: 70%
-2 Modifier
1-2: 0%
3-4: 16%
5-6: 84%
So...the worse you are at a task, the faster you tend to do it, whether you succeed or fail.
... And wouldn't this just indicate that 'most' of the time (>50%), the character will choose not to 'rush and shoot wild' [the basic definition of choosing a better Timing than Effect?]
I don't think I understand the question.
The net effect of the T/E system's statistical qualities is:
1. Successes will tend to be exceptional. In other words, exceptional successes will be very common.
2. Failures will tend to be abject failures. In other words, abject failures will be very common.
3. The worse you are at something, the less time it will take you to do it (pass or fail).
4. The effect on the combat system will be to make damage extremely predictable, especially if the player tends to choose the best die for effect (damage). This is true regardless of whether you use the original straight damage rating or the current multiple.
5. The effect of this system on autofire is even worse--poorer troops have very little chance of hitting with autofire, while good troops find it pretty easy to hit automatically with all shots. (Pretty much the exact opposite of what we see in the Real World.)
This does not look like a task roll system I want any part of. And it
cannot be fixed. If you move the break points, you just break the system differently. For instance, one idea was to define a "6" as exceptional and a 1-3 as marginal. This change still resulted in exceptional successes occuring far more often than marginal successes. It also meant that an exceptional success would be impossible if the net modifier was a -1. So...no modifier, 33% chance of exceptional success. -1 modifer, 0% chance of exceptional success. Reversing the order of success and failure failed as well (see my previous posts on that), plus it wouldn't work with the combat system.
And since no one brought any of this up until I posted my analysis, I think that the designer failed to do a statistical analysis of the system. I think that he believed that a normal, no modifier roll would produce the same number of exceptional successes as marginal successes. A big mistake.
The problem is that statistical trends like this are hard to identify in just a few games. Hundreds of rolls would need to be tracked before the trend emerges. And I just don't think that Mongoose's playtesters have done this. So at best, you might notice that exceptional results are awfully common. But in the short term, players like that...at least until the NPCs start getting the same benefit.
I'd also add that the MGT system makes it pretty easy to get modifiers of +2 or +3 on most tasks. With a +2 net modifier for effect rolls, there's an 81% chance of each die being a 5+. This means that the player will get at least one effect result of 5+ a whopping 96% of the time.
At the end of the day, the T/E system is an awful lot of trouble for the dubious benefit of producing exceptional successes most of the time.
I have no need for a nostalgic fixation on d6.
