Edit: 10/7/2018
It appears the developers have changed shield power strenghts since this guide, still it can be used as a reference as rerouting and power blocks for shields haven't changed. Also it seems I am no longer leading in the Maru simulation. Congrats to those who have persisted!
End of Edit

Index
1. Introduction
2. Pattern Gamma (Balanced)
3. Attack Pattern Alpha (Aggressive Shields up)
4. Attack Pattern Omega (Aggressive Shields down)
5. Defense Pattern Sierra (Shield Movement)
6. Defense Pattern Delta (Phaser Movement)

I truly love this game and I want to see more people have success, and while I was working on a Kobayashi Maru guide I stumbled on a few things for the engineering role, as that station can make or break a crew

This guide however is designed for those who are after mastering the role for contributing with the least amount of effort. I also suggest taking a look at my suggestion post in the feedback thread and if you agree please comment on it there to alert Ubisoft to some much needed tweaking.
http://forums.ubi.com/showthread.php/1679903-Suggestions-amp-Feedback?p=12704705&viewfull=1#post12704705

If you were to learn any pattern at all, pay attention to Gamma. The most power for your settings.

*I understand that most players do not want to be this complicated as it's just a game, but this guide is not designed for everyone*

I selected these patterns to keep in line with Starfleet code.
The reason to name these patterns is to enable the captain/engineer to communicate more with less. Telling the engineer Pattern Omega is much easier than asking for power to be taken from shields into engines.
Once the captain and engineer know each other well enough to call out these commands, you can order up tactics for the engineer to prepare. Sierra -> Alpha -> Omega -> Gamma
When a pattern has changed, it is important for the engineer to repeat the order back to the captain and call out the new max speed so helm can be aware of the new power setting to take full advantage of the situation.
Example, capt: pattern delta
Eng: Aye, Pattern delta, New max speed 7600

Another important note, a torpedo can be dodged with engine power at 3000 or more.

-My background for this guide-
I currently as of posting have 197 hours into this game as reported by steam.
I currently (to my knowledge) as of posting hold the Kobayashi Maru world record of saving 222 by leading a team in the tactical station and coming out ALIVE with 21% hull.
All achievements (except for playing as a Vulcan) were completed in the first 2 days without even knowing about any achievements until logging into uplay. Awesome! (Yet so sad)

It is very important for which dot you move in rerouting. In pattern Gamma, it is important to move the fourth dot from engines to phasers as any reroute above distribution has NO effect on performance. However, each routing dot has an effect on power flow for overloading even if its not affecting the performance. for example, in pattern gamma, if you were to leave the phaser row 5 dot on phasers, it will overload phasers, EVEN THOUGH it will have 0 effect on distribution level 4 phasers.


Here are two screenshots of fun moments I have experienced and helped generate.
The score for 222 was post patch so there are no exploits in achieving this score! the date was 06-17-2017


Server first All Redshirt crew

Of all the patterns I have figured out, this one is my personal favorite.

Excluding the maru simulation challenge, Pattern Gamma is the most “bang for your buck”
This setting is useful for all situations as you have strong shields and movement speed that does not raise your signature, yet has 19.5k phaser range to deal with mines/objects/enemies
The power distribution for this pattern is 4-2-4 but the actual gain is 5-4-4 and with one change it becomes 5-2-5
19.5k phaser range
3750 or 2000 speed
3.6 or 5.0 shields
With this configuration, the engineer can focus on repairs and distribution. No monitoring of routing is required as the power settings are balanced enough to never overload any node. The only power setting the engineer needs to configure is changing the 1 distribution from engines to shields as needed for incoming damage or torpedoes that are unavoidable. This configuration also allows for warping with 5 engines when taken from phasers. A torpedo can be dodged with engine power at 3000 or more.

This pattern is most commonly seen when a hostile situation has happened and the captain does not expect to dodge/move. Generally this stance is used when the Aegis has a superior combat situation and wants to stamp out enemy ships as fast as possible.
The unique thing to take notice with Pattern Alpha is that engines are at 2000 instead of the average engineer pulling everything out to 500. 500 engines does not leave the helm much chance to face a target from behind.

Note: Only phasers will overload

This pattern is most commonly used when Attack Pattern Alpha has worn out on shields. In a combat situation, it is paramount for helm to have the greatest potential to dodge torpedoes while shields are down. Pattern Omega is the solution. As Engineer, You do not need to wait for the Captain to give this command. This pattern should be engaged when shields are 10% or less to give everyone a chance to be defensive when no shields are left. The Captain might also call for this pattern when chasing down a fleeing fugitive.

Note: Only phasers will overload

This pattern is used when retreating from enemy ships with no intention to engage. A captain should call on this when outmaneuvering targets that have detected you. The Tactical officer should disable engines on chasing ships to succeed in building distance. Episode 4 is a prime example for using this when holding out as long as possible.
Note: Engines will overload and Shields will begin to overload later but if monitored you can stabilize the shield power with engines fourth row routing.

This pattern is important to use when traveling as fast as possible while clearing any mines/objects in your path. It is the mirror equivalent to pattern Sierra in terms of power to shields vs phasers. You may find captains calling for this pattern more than others during story missions to push through slow parts. a perfect example of this pattern is used during episode 5 in the final phase of the nebula. When you avoid the cruisers by giving a wide path at full speed, you run into explosive objects.

Note: Only Engines will overload