Fresh troops from where, though?
Any troops on the field will be as wilted by the heat, even if not put in the fight.
Arnold would be attacking with the same force assigned to Lee; 4,000 troops to launch his assault on the rear of Clinton's column as it leaves Monmouth Courthouse.
Here's one place I think Arnold has a bigger impact than Lee; he arrives at Monmouth Courthouse
earlier in the day, catching more of Clinton's column as they are about to leave Monmouth Courthouse.
If the battle opens earlier in the day, the opening engagement is fought before the oppressive heat of mid-day really hits the field. On top of that, getting to Monmouth Courthouse sooner could net him perhaps 1/3 to
close to half of Clinton's force either breaking camp or in the process of debarking.
Catching them flatfooted, while preparing to debark or just getting under way, an aggressive commander, such as Arnold, could definitely do some major damage, possibly (but by no means for certain) cutting Clinton's force into two. Not to say
literally in two, half his force, rather, cutting off a sizable chunk of Clinton's force and pinning it in place at Monmouth Courthouse, at a disadvantage, while awaiting the arrival of Washington and the main body of the CA in the theater, about 6,000 more men.
If Arnold could do that and then hold on long enough for the main body to arrive...
That's where I hit the wall in these scenarios. Lee's lethargic offensive and then general retreat resulted in Washington being forced to change his battle plan on the fly to adjust to Clinton's counter-attack. That's how Monmouth played out OTL; not with Washington's original plan, rather with a rather skillful counter to adapt to the circumstances he found himself in when Lee sounded his infamous retreat.
I believe Arnold can get to Monmouth Courthouse quicker than Lee, being more aggressive and less indecisive than Lee was. When he gets there would then dictate what his situation will be when he launches his attack; how many British soldiers is he facing and how many are caught in a vulnerable state, (just debarking, breaking camp, watering the draft animals, eating breakfast even) how hard he can hit them and what, if any, sort of gap he might have between those British troops and the rest of Clinton's army to exploit and possibly wedge a portion of his forces into to pocket the forces at Monmouth Courthouse. Fighting in the morning, before the temperature rises to it's mid-day levels would eliminate the heat exhaustion suffered by both forces in the opening phase of the battle. Arnold, because he has the initiative and element of surprise would benefit more from this, but the British troops he engages would likewise benefit from the cooler morning temperatures none the less.
Now, the next critical part: How fast can Clinton turn his column to counter- attack and attempt to break his forces out of what we'll call "The Monmouth Pocket"? When does his attacking force arrive and can they get there before Washington and the main body of the CA have time to deploy for a proper engagement?
Lastly, the elusive question: What was Washington's original plan?
Perhaps, if Arnold can accomplish all of the above, and Washington can get there before Clinton can, he can deploy into a trap, relieving Arnold's men holding the north side of "The Pocket" to withdraw to the rear to rest and refit, slowly bringing the rest of Arnold's forces off the line as fresh units arrive, to do the same. With Arnold and his men removed to the rear and Washington in command of the field at Monmouth Courthouse before Clinton can arrive but also before Clinton realizes that he's marching not into Arnold's exhausted men but rather into Washington's well deployed and fresh troops...
What does Washington do?
Can he draw Clinton in deep enough to pull off the encirclement?
If not, can he still deliver a smashing blow to Clinton, driving him from the field?
That's the frustrating part of trying to figure it out, I'm at a loss as to what Washington's plan was if Lee had been able to pin his opposite number in place, as it would seem was the plan, as Washington's fury at Lee's full retreat may illustrate.
Still, there's possibilities...
I would say no. Or rather, I would say that if the CA is threatening such, Clinton will make a good retreat - in good order and with most of his army intact, in other words. The CA isn't quite good enough to stop that (and probably doesn't have enough cavalry, specifically).
Good points, if Clinton can clearly see a trap unfolding, he's not going to walk right into it and will, in all likelihood, manage an orderly withdrawal under such circumstances.
Arnold and the CA are good enough for it to be an open question however, so Clinton's generalship on the other side and the heat being the main obstacles to me saying its probable - but I wouldn't call it implausible if written right.
So to answer the "what would constitute such a victory":
I can think of two things.
1) A decisive smash that sees the British skedaddling, and the consequences coming from there. This is actually possible.
Because I believe the scenario I laid out above most likely results in this outcome, we'll go from here.
What are the consequences of such a decisive smash?
For the CA, from the top down, the Patriot cause and the Continental Congress, this would be an incredible morale boost.
Washington and Arnold have dealt the British a severe defeat in the field not eight months after Saratoga.
Such a victory may begin to pull many fence sitters in the colonies into the Patriot camp, boost enlistments and bolster the CA's ranks.
Granted, these new troops need to be trained and fitted out, but with Clinton bloodied and driven back into the safety of New York, time is something they'll probably have surplus of as the British regroup.
A follow up campaign to secure positions around New York City would be the shrewd strategic follow up for Washington here and very much achievable.
The question now: What do the British do in the wake of such a battering?
They've just seen, in about eight months, the fortunes of war shift from capturing the rebel capital and chasing off their main army into the eastern hill country of Pennsylvania and a winter of misery, to the capitulation of one entire army in the field at Saratoga and now, a brutal defeat of a second (and larger) British army in the field and in the very sort of engagements that, prior to such, the British believed their colonial adversaries incapable of effectively fighting.
What do the British do? Morale would definitely be shaken. Such a loss would have to be viewed as totally unacceptable to Clinton's superiors in Parliament.
What does Parliament do?
What of British public opinion?
How safe do the Loyalists feel in the wake of a Continental Army victory on such a scale?
Does this change their perception of the war entirely, or just enough to seek a change of strategy and perhaps a new command officer?
What do colonial Loyalists make of this?
It raises some interesting questions.
2) Clinton surrenders. This...probably isn't. Clinton is a little too good, and the weather too bad. But you might get a very bloody defeat (with the British withdrawing at a time not of their choosing) even if their army isn't broken, which is almost as good.
The first probably has a limited impact on the war, in itself. How Arnold fares will be more relevant. The second gets into more dramatic possibilities.
Agreed. The only way I see this happening is if something goes terribly wrong on Clinton's end and even then, I still think the British can fight their way out of it.
Clinton getting thumped and driven from the field in a bloodbath is one thing, especially if Washington and Arnold can pull off what I outlined above...but I have to agree on the encirclement and capitulation.
They just don't have the numbers or the cavalry to do it.
Still, all in all, it's looking like Arnold would have been the much better choice over Lee and the Battle of Monmouth would only be the beginning of the dividends paid out if Washington gives that one command to Arnold over Lee.