about the homefield advantage:

in a coliseum, there is no ambush, but the apache can still unleash arrows and do hit and run. therefore, there's still a good chance the gladiator will die from an arrow even with a scutum, because arrows are unpredictable. given that the arrows don't hit, eventually the gladiator will have to move in, where he will meet knives. if he gets past that, only then does he have a chance of winning. so even in a coliseum, the apache has good chances of hitting the gladiator before the fight even starts. when the fight does start, apaches have a good chance too because tomahawks are pretty good in close range. i do give a slight edge to the gladiator in a coliseum because of the straightforward combat, but not by much.

in a forest or mountainous area, it's no contest. the gladiator will be picked apart by the apache from ambush and hit and run. there's nothing that the gladiator can do in the situation. all that gear will just be a burden to his fatigue level.

so if we combine both situations, the apache is the better warrior because he can be effective in more than one kind of area or battlefield. the gladiator has a slight edge in a coliseum, but that's it. in a real battlefield where there is unpredictability, strategy, tactics, and ambush, the apache would always win.

as long as the apache is infront of the gladiator the gladiator can just duck down and he is entirely covered by the sheild. That is an almost 100% chance of blocking then when the ammo runs out they are forced into close combat and then the gladiator has the advantage. The gladiator also would have a lot of experiance fighting a wide veriaty of opponents as Rome spaned half the world and used fighters and wild animals (including tigers, lions and elephants) from all over the world. Gladiators hey were also closest thing they had to profesional athletes and trined relentlessly.

there's no such thing as 100% chance of blocking. there's always a chance of something getting through. even a knight's full plate armor + shield had some weaknesses that arrows could get through to. if you want proof of this, it's very simple. look up medieval warfare, and look up how english longbowmen were so feared by all armies of the western world. if 100% blocking was possible, why didn't the knights just walk up to them and kill the archers? the answer is it isn't possible. arrows are unpredictable. it's impossible to cover everything. the gladiator's shield is no comparison against a knight obviously. it can't cover the legs if he's covering his chest. he can't cover his chest and head if he covers his legs. if he ducks down, as you suggested, then the apache can just sit and wait for him to stand up, or run around him to shoot him from his side.

your suggestion for him to just duck down... why would the apache waste arrows on a shield right in front of him? that's utter foolishness. of course he'd run around it and flank him. lets face it. you're trying to find a very unreasonable solution to the bow and arrow problem. there is no solution aside from getting your own range weapon to counter. this is what armies have been doing for years. if you don't have archers in your army, you lose. it's plain and simple. genghis khan actually ran over almost the entire world behind just arrows on horseback.

all that aside, the gladiator can, yes, possibly block much of it or the apache could miss. but this is only possible in a coliseum. outside of it, in a real world battle situation, the gladiator stands no chance. can he predict where the arrow will come from if he can't even spot the apache? can he use his shield to block every possible angle?

aside from that, i agree that gladiators were professional athletes. but think about it. have they been at war with enemies that have far superior weaponry? the apaches were up against colonial infantry armed with guns and cannons. i think that's far stronger competition than a fellow sword wielding guy. sure, they were athletes. but apaches were soldiers who fought for a cause. therefore they were far more motivated.

Obviusly the gladiator would duck down as the apache was firing then after the projectile hit look above the sheild if the apache tries to flank it's easier to turn on the spot than run around. Also there is a massive difference between a long bow that could fire an steel tiped arrow over 228 m (249 yds) and a short bow firing a plain wood or possibly stone tiped arrow. I think you are over estimating the range and penetration power of such a weapon. 

Apaches were fearless worriors up against a military force that was trained to line up into rows and fire inacurate muskets that took longer to reload than a bow, and used cannons that took ~ a minute to reload and aim and wore no armor, and were conscripts. And the apache still lost even with the advantage of hit and run tactics and an unprodictable nature. The colonial forces tactics and weaponry was actually very poorly suited to combat the apache.

Gladiators on the other hand often have nothing to lose, are battle hardened against every different oponent imaginable, and lived a life where every day was a battle of life and death. 

You are right tho in a forrest situation where there is plenty of cover the apache has a massive advantage but so does the gladiator in a wide open battlefeild. 

i'm aware that longbowmen had better arrows and better bows, but knights also had far better armor than a gladiator. it's the same comparison. high tech bow vs. high tech armor and primitive bow vs. primitive armor that only covers certain parts of the body.

you're trying to say that the colonial armies were less equipped than the natives? that's crazy. guns won that war. for sure. history has shown us that over and over. the reason that every single native populace was demolished by europeans is because of guns and artillery. therefore, whether you think they're bad weapons or whatnot, they were still effective. you can't argue with history.

gladiators were slaves. as such, they were literally given no choice but to fight for survival. but whatever your motivation is, you can't stop an arrow just from willpower. range will always win against someone without any range whatsoever. this is the truth in every single battle that has ever been fought in mankind's history. look it up. from the dawn of mankind, the army with the better range weapons has always won. this is why guns changed the world. it delivered an effortless means of dealing death at a distance. it has always been this way and it will never change.

There were actually very fer knights running arround in full plate mail as it was expensive and heavy, the vast majority of medevil armies were comprised of chain mail wharing (at best) men at arms and peasent militia. Full plate would actually turn aside arrows that were not stright on direct hits. 

Guns are superior to bows for several reasons, they allow larger amounts of ammo to be carried, they are easier to use (bows take real skill to use well) and most importantly they have greater penetrating power than most bows and arrows. A british long bow actually had a longer kill range than a colonial musket. The point I was making was that taking on a heavly drilled army with hit and run garilla tactics was actually the best way to combat the colonial army.

The Roman scutum was designed specifically to protect soldiers from vollies of arrows protecting a soldier from arrows is what they do, the apche on the other hand has a hunting bow and has no experiance fighting against armor or sheilds.