How does hoth leia or poggles ce interact with tactics broker? As is, I say it goes tactics broker defeats the piece, save 16 negates the defeat, but tactics broker still gives your opponent a 1 even if the piece is not defeated.

Both of Leia's and Poggle's CE states "would be defeated" yet the Tactics Broker straight up states "this characters is defeated" so there is uncertainty about it. Thus you cannot use the CEs to resurrect them.

Wrong, this is covered in the FAQ I believe. You cannot combine the two abilities. MTB must defeat the figure, there is no save allowed to bring it back to life.

The key to all this is the glossary definition for defeat/defeated:
defeat/defeated: A character is defeated when its Hit Points drop to 0 or lower. Remove defeated characters from the battle map. (u/l mine)

If you do not fulfill all the parts including the last part of the definition, removing the character, then the character is not defeated.

On the one hand, I don't mean to be nitpicky. On the other hand this is the rules forum, and that's kind of the point.

The fact that Tactics Broker says "is defeated" does not change its interaction with Avoid Deafeat or the CEs. Avoid Defeat and the CEs step in right before a character is defeated and potentially prevent it. The rulebook also says "is defeated" for when a character's hit points reach zero, so in that sense there is no difference with Tactics Broker.

However, Tactics Broker's glossary doesn't say "is defeated". It says "Remove the chosen character from play (it counts as defeated)," which is a big difference. The actual step of being defeated is skipped and they go straight to being removed from play. The 'defeated' characteristic is applied after the fact.

Even given that, I still think it would have been debatable. The real reason in my mind that Avoid Defeat and the CE don't trigger on Tactics Broker is because that's what the FAQ says. This is a situation that needed a clarification, and I'm glad we have one.

Actually, it says it must be removed from play...

Tactics Broker: Once per round before initiative is determined, if this character is in your squad, choose one other character in your squad. Remove the chosen character from play (it counts as defeated) and choose an opponent. That opponent’s initiative check result is automatically 1. If a tie requires rerolling initiative, this ability cannot be used again for tie-breaking. (u/l mine)

Hmm...what's really ironic is the wording on the CE:
Poggle the Lesser
Whenever a Geonosian ally would be defeated, with a save of 16, it instead immediately returns to play with full Hit Points. Geonosian allies gain Self Destruct 20. (u/l mine)

The underlined part could lead one think that it was actually removed from play (fulfulling the Tactics Broker stipulation), but then returns to play. Interesting...

For scoring purposes only, ie the opponent get the kill points.

WRONG. The character is removed from the board and the opponent get the kill points. There is no possibility of a save from Leia or Poggle because it was not defeated.

From the "Resolving Effects" steps on the Holocron:
...
XIII. Resolve any remaining "when defeated" effects such as Impulsive Shot, Impulsive Sweep, Self-Destruct, Cleave, Rolling Cleave, Mon Mothma's commander effect, and so on. Use the simultaneous effects rule as usual. As in previous steps, Impulsive Shot and Impulsive Sweep can begin new attack sequences that interrupt this sequence; resolve the new attack completely, then continue where you left off with the original attack.

XIV. Remove the defeated character from the battle grid.

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[wrong: see explanation below]
Obviously, the Leia and Poggle saves occur in step XIII.
Effectively, the definition of Tactics Broker skips directly to step XIV without going through step XIII.

Incorrect. Since the piece is considered defeated, those abilities skip to step 13, since you resolve all "when defeated" effects with those abilities. Effects that prevent defeat happen in step 12.