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Known observations:

-There is carry-over of your current part health into the calculations for your part health the next race.
-Deaths and even minor scrapes that do not require repairs can cause post-race damage.
-With equal numbers of droids and parts, your parts will always be at full health regardless of deaths / damages.
-When the number of parts exceeds the number of droids, there is no guarantee that parts will all be repaired to full health, although it is possible with sufficient pit droids and clean enough racing.
-It is possible for all 7 parts to become damaged.
-Direct relationship between how much damage you take during a race and post-race.
-Some parts can end a race with max hp even though other parts take damage.
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Hypotheses: 

-Each pit droid contributes (an equal amount of) 100 hp to the repair pool (equivalent to 1 part), rather than being committed to any individual part
-No overflow in assigning damage or repair pool to parts
-Repair/damage calculation:
Step 1: Calculate total accumulated post-race damage
Step 2: Based on step 1, decide how many parts in total will be damaged
Step 3: Assign damage to parts (split randomly)
Step 4: Assign pit droid repair pool to parts (split randomly)
-Variables included in calculating final post-race health of a part:
(1) Damage taken during the race
(2) Health of parts before the race
(3) Pit droid repair pool
Formula: (2) - (1) + (3) = Final health of part post-race
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Explanations for observations using hypotheses:

-Since pit droids contribute a limited amount to the repair pool, it's not possible to simply repair all your parts to full health after 1 race without sufficient pit droids, proving that there is carry-over.
-Since there is no overflow in assigning damage or repair pool to each part, and because a pit droid contributes only 100 hp, you can keep parts at full health when there is a 1:1 ratio of parts and pit droids.
For instance, a part with 40 hp can only take 40 damage at worst, dropping to 0 before drawing from the repair pool. With a 1:1 ratio, each damaged part is able to draw up to 100 hp from the pit droid repair pool, and be repaired to full health. Since parts do not draw more from the repair pool than required, all damaged parts can be repaired to full health.
-Since it is possible for all of your parts to become damaged, it is clear that pit droids do not commit themselves to any individual part. (They do not have a 1:1 bond with any part during a race)
-Pit droids do not contribute more than 100 hp as they are incapable of maintaining parts at full health when there are more parts than droids. (Technically, this only mathematically proves that droids contribute less than 125 hp; 4 droids against 5 parts in the best case, however, there is experimental evidence suggesting a contribution close to 100, and it is most certainly at least 100 to be able to maintain all parts at full health with a 1:1 ratio of parts and droids)
-Since the game decides how many parts will be damaged before assigning the damage to parts, it is possible to keep some parts at max hp.
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Refuted hypotheses:

-By default, all your parts will go to full health at the end of the race regardless of droid count.
Evidence: With 7 damaged parts and 1 droid, parts did not go to full health despite clean racing (0 damages and deaths)
-There is a priority queue where parts which can retain full health will collect from the repair pool first
Evidence: It's possible to damage all 7 parts. Some of which with only minor post-race damages.
-Droids select a part and are entirely committed to repairing it or preventing it from taking damage.
Evidence: It is possible to damage more than 4 parts post-race. In addition, droids can repair damages to multiple parts even with low numbers of deaths.
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Thoughts / refutations?

[WIP] Pit droids and damages

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