Could not get this out of my head. I've been thinking about some sort of easy algorith that could return decent results. And I coded a little something.
It is attached to this post. It's only a webpage with a JavaScript (I used JS so you can use it without internet connection) but as usual download only at your own risk.

What it does:
Calculates traits which are in a range of -2 to +2 from the average of the parents. This difference is random, if you click the button several times you get different values.
I added some restrictions, namely that each value must be between 0 and 10 and that the total must be between 25 and 35 as per Maxis example, and the roundabout affects to those trait values - hence you may get some unexpected numbers, specially if you use only one parent.

I wonder if the idea of "running of points" is why I see this:
If I deliberately make a sim with extreme points (like 0 nice) their children will have the OTHER extreme (10 nice points). That happens even if the other parent has nice points in the "normal" range. But when I tried to create a slob family (messy, lazy, playful) the parents who had those non-traits produced kids that were active neat-freaks.

@Amura

I love this little app! Thank you. It seems to work very well too:

:lovestruc

I think the app is a fabulous idea! The only problem that I see is working with a base of the parents' scores averaged. True, there are genetics at play, and there is a +/- of 2 points to give the kid some individuality, but I think that over time you will end up with a neighborhood of average Simmies.

An example of this is seen in simsample's chart where the parents' sloppy-neat scores are 1 and 9, respectively. The app creates a child that is 5, with a chance to be plus or minus 2. So the only scores a 1 and 9 parent can give their child is 3, 4, 5, 6 or 7. If you use this for many generations with game-born Sims procreating with other point-averaged game-born Sims, such as in a legacy game, I think you run the risk of ending up with an entire generation of Sims who are 4-6 on every trait.

This is why I've decided to work within the entire range of both parents, with a plus or minus variable of 1. That way, my Sims offspring can be the average of both parents, or even the extreme of one extreme parent.

I'm glad you like it, simsample

SIMelissa, I agree absolutely, it's a very simple take which leads to average scores.
Which is part of what some people were talking about, I mean, it works for those cases in which you want (or the dice rolled that you ought to) get average traits. It's simplier than doing the maths yourself plus you get a bit of randomization.

Ideally I would like an algorith that took in account standard deviation, so different parents would get quite different children even in other traits - and generating variety in more than one aspect.
But a simple JavaScript app which does some simple maths was a much faster/easier approach XD

I have to agree with those who wonder if this isn't just a matter of statistical clusters. Like some others here, I have a wide variety of Grouchy/Nice ratings among my born-in-game babies. I did once hit a statistical cluster when adding several downloaded neighborhoods to my game and most of them ended up spawning several incredibly sloppy maids and butlers. It's annoying, but doesn't seem to be a permanent or stuck feature.

I have a LOT of grouchy children. I have about 1/2 to 2/3 of my kids born with 1 nice point. and the parents are all in the nice end of the spectrum. I usually have to use insimenator to change their points, AND I make it genetic.

Have not been in the right mood to answer to things in this thread, so I apologize for the long post and long-overdue replies.

To all the posts saying "I don't see this in my game" or expressing doubts in general, you'll notice I have always phrased it as a possibility. I did so intentionally because I don't know for sure. I do not in any way claim that this is an absolute problem that I know exists because I looked at code. I've seen it mentioned, and it matches what I see in my game so I choose to believe that there is a flaw in the system, but I won't claim it absolutely is one because I have no proof beyond observation and in this case that is not sufficient proof. It could be a statistical cluster some of us get, it could be biased interpretation. What do I know. All I know is I don't like how it's done by the game, regardless of the reason

Andrew, it's fascinating. I ended up writing up a system after posting, and your post suggests a whole lot of the things I ended up doing in it. I roll a D20 to decide if they ignore genetic influence, where 20 means ignore, and 18-19 means i can choose to ignore if I want to. If they ignore, I roll a random number between 0 and 10. I didn't try to write a VB-program to automate it, but now you've mentioned it might make an excel spreadsheet that does some of the calculations for me.

SimMelissa, I did worry about the same thing, that I would end up with a lot of middle grounds personality. I am not good enough at understanding how chance works to determine if that is a risk, but the system is not set in stone. I will try these rules, and if I end up with a lot of middle ground I will make adjustments.

Some people suggested basing it on who the child takes after more. To me, that does not make sense. It makes sense to have their personality shift that way as they grow up, but not be born with it. I use encourage to have parents influence their children in one direction or another, but I would not set their genetic personality that way.

Glad to know I'm not the only one baffled by Lua scrips, Lamare One of these days I'll tackle the tutorial and try to understand them, but for now they remain a mystery.

Thank you to everyone who shared their ideas and thoughts on how they'd do it, very helpful At first I found child just copying either parents personality in a trait was boring, but now I've thought about it I do see it could be interesting. I think I'll consider implementing that if my approach ends up with a lot of middle ground kids.

Amura, very cool script. But to me, the rule of 25-35 defeats the point since half the purpose of doing it manually (for me) is to not be governed by that Maxis rule, I don't see why a kid should have to have at least 25 points, or be unable to get 50. To me, that implies that having more points is better, and I don't see why being neat, outgoing, active, playful and nice are automatically the best personality traits. Yes, a sloppy, shy, lazy, serious grouchy person might not be the most commonly seen thing, but it's not unheard of. So why can't a Sim be born that way?

I've noticed this in my game as well. I don't really care about (or believe in) genetic personality, so I've just started randomizing sims' personalities with the Sim Blender when they age up to toddlers.

Well... why not go beyond spreadsheet? hint-hint

Agreed.
In fact when I firt read this thread what I found more appealing of the idea was having quite "low score" personality. Maybe some "high score" personalities too, but those seem a bit more boring XD

After I posted the first version of the script I started working on an improved version, which would suit myself better.
(I have just submitted to the MTS queue for review, in case someone else finds it useful. And so I don't clog this thread with that little thing, because there is so much more here to discuss!)