Do character associations have any in-game impact?

Having completed the game's story mode, I spend more of my time in online matches.

Ranked online matches are always team matches, where other than the character you control you choose up to two additional characters to support you in various ways during the fight.

According to the association between your character and the selected support character(s), the character selection screen displays the name of the formed group (as detailed in this faq). Characters that do not form any sensible group register as "Originals" as can be seen in the following picture:

If the player on the left were to pick Minato and Naruto, then instead of "Originals" the text would read "Father and son" (as these characters are indeed father and son).

My question is: Do these associations have any actual effect, or is this merely a novelty?

After doing a bit of research, it seems that these combinations actually do have an in-game effect. What I noticed is that "good" character combinations light up more dots next to the three icons seen above the team name.

I tried playing a few matches against myself in order to figure out just what each of these icons mean (since, surprisingly, that's not written in the game manual) and was very happy to see that someone has done that work for me:

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The first icon is a measure of how much extra damage your TEAM ultimate jutsu does. I believe 6 dots is a full bar of damage.

The second bar is a measure of how much faster your support characters can be used again. I am not sure exactly how much faster it is. However, if you try out the Kakashi and Minato combo (which has 6 dots in this category) since only selecting one support already lets you use that support character 2x as much, your gonna get to call Minato every other second!

The third and last column, is a measure of how fast your team gauge charges. Every time you call your support character in, this gauge charges a little (this is constant). When ever your support characters successfully hit or preform their secondary roll (such as shuriken support for balance, combos and hit backs for attack types) the bar charges more (I'm not sure how the defense type gets more gauge though). How much more gauge they get from this is based on this stat. If you have the Lee/Guy combo (which is 6 dots in this category). Every time Guy hits with his attack, your gauge charges a half of one bar! Meaning if you hit with him four consecutive times, then you get you team ultimate!

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So it seems that picking meaningful character combinations is a good idea, as it will give you a definite edge when using your support.