So, I’m not asking about fighting itself, but how about the disturbances left behind after a fight and what you can learn about the fight and the fighters based on that?
It depends. Anything from who they are to absolutely nothing.
Evidence collection comes in two pieces. Examining the site, and reconstructing what happened based on the information obtained when investigating.
So, when you say disturbances, that doesn’t really narrow down. Damage to the environment can be instructive to what happened, but it’s not 100%.
For example: finding a bullet hole will tell you several things. First, that used a gun, which isn’t necessarily as obvious as you’d think, and the path the bullet took. It can determine where the shooter was probably standing, or their height (if the range is known). Further this will tell you the caliber (roughly at first glance, and precisely once the slug has been retrieved.) Stippling (tiny burns caused by flaming powder) can help determine the rough range up to a couple meters. The presence or absence of a casing, combined with the caliber can tell you if it was a semi-auto or a revolver. The casing itself may have prints, and will have mechanical wear points, which can sometimes be used identify the make and or model the of the gun, even before the slug can be matched to a specific barrel. Where you find those casings can give more insight to where the shooter was standing when they fired, cross-reference that with the bullet’s trajectory and you can make an informed guess at the shooter’s height.
The problem is, it’s difficult to speak in generalities. Everything you do to your environment leaves evidence of your presence behind. Pay enough attention, and you might notice some details as you go. A lot of this is too generic to be useful when it comes time to figure out who you are after the fact. This is where the cheese comes in, with things like exotic brands of cigarettes, torn clothing, and other traces that are singular to a small subset of people or an individual. That said, things to break in fights, clothes do rip, so it is entirely plausible that something will get dropped in the fight, waiting for someone to find it later.
When it comes to a fight, a lot of the information that can be gleaned is going to be pretty generic. It’s not possible to know, reliably, if a garbage can was damaged during a scuffle, or if it happened last year, when someone took out their frustrations on it. In some places it’s going to be difficult to know if anything happened because, at some point, something did, and it may not be related to your investigation.
Coming to an apartment you know, that’s usually kept meticulously, and finding the place has been tossed is going to tell you something happened. It won’t tell you what. But, if you poke around, you might find some hints. At that point, the nature of the damage becomes critical. Someone searching for a hidden trinket will be tearing the place apart in different ways from someone that got thrown into the coffee table or bounced off a wall. Also, bloodstains are pretty good indication that something went wrong. Blood trails mean you can kinda guess where someone went, though this will fail when they enter high traffic areas.
The site is critical for your investigator. Interior locations that see little traffic, like private residences, are best, because the evidence will remain undisturbed until investigators get there. (Though, if your character isn’t a member of the police, they’ll be left scraping at the leftovers.) Exterior locations can quickly turn into a nightmare, especially when you factor in weather. Heavy rain or snowfall can quickly conceal or destroy evidence. Even just high winds can be a problem. Also, animals, and other humans could easily disturb the site unintentionally.
Now, one of the richest possible sources of evidence is a dead body. If someone didn’t walk away from that fight, you’ll have far more information about what happened. Blood trails can lead you to this. A corpse can tell you everything from how long ago they died to what weapons were used on them, if any. It won’t tell you things like fighting styles, but if they were bitten, it’ll give you a pretty solid way to identify your killer. The severity, or absence, of defensive wounds will give the investigators a pretty good idea how much of a fight the victim put up before they died. Back to the gun example earlier, entry and exit wounds can be very informative. They will tell you the trajectory that the bullet was fired at. In some cases this can even tell you what the victim’s position was when they were hit.
Some quick corpse trivia: Bruises take several minutes to form (which you may have noticed if you’ve ever been bounced around.) They’re actually subdermal hemorrhages; so you’re bleeding, but the epidermis (the outer layer of skin) wasn’t ruptured, so you’re bleeding under your skin. If you suffer an injury that would lead to bruising, but are killed within a couple minutes, your heart won’t be pushing blood (obviously), and no bruise will form. In some cases, this will give you insight for how long the fight lasted.
When the body dies, blood tends to pool at the lower extremes: die on your back, it’ll pool along your back, your buttocks, and the back of your legs, and arms. Die in a sitting position, it will pool in your lower legs. Thing is, this can inform you if a body was moved after death, particularly if it was allowed to sit around for a couple hours, or if transport took any considerable amount of time, because the blood will be pooled in some strange places.
Like I said, a dead body is a jackpot, if you’re trying to figure out what happened, because they’re a pile of incredibly detailed evidence.
Individual evidence is rarely definitive. They become pieces of a puzzle that you use to reconstruct the events as best you can. Some evidence is only useful in hindsight, or downright deceptive if you don’t know the context. Put enough of this together, and your character might be able to figure out where the fight started, where it went, and maybe even have a pretty good gauge on who was coming out on top. It might also give some rough indication of how many were there. Not an exact number, but an estimate that ranges from “a couple” up to, “lots.”
It’s possible one of your characters might know the context. If they’re familiar with one of the combatant’s methods, they might see things that point back to someone they know. At it’s cheapest, this might point them towards the character, though it may simply suggest what group they should start focusing on. It might also point towards other, unsolved, crimes, which in turn might be cross-referenced to get a more complete picture of the killer’s methodology.