I think there's a few things we should establish before we begin contemplating the optimal circumstances under which a defending army would choose to face an invading army in an open set piece battle. I'll try and explain things in a South Asian context.

First and foremost, you as a ruler or the general are most likely at the capital of your kingdom in command of the Imperial troops, paid for and maintained at the expense of the Imperial treasury (let's suppose you have the resources for such a force). You have a kingdom, your territory is charted with strategically placed forts that are garrisoned with a number of troops that might not be equal to the fort's capacity but still is enough for the fort to be defended against a siege and these forts are supplied with enough resources to sustain themselves at least for a month (hypothetically), against a siege. You also have a number of thriving cities, some walled and fortified while others not, and these cities have a certain amount of troops as garrison in them as well to maintain law and order and to act as defenders against an invading army. These forts occupy key passages into your territories while these cities are centres of economic activity located conveniently for traders, merchants and officials along these passages that eventually lead up to the capital.

Now, suppose a neighbouring kingdom declares war upon you, this declaration won't be a formal one as was the case in 19th century warfare and later. Your realisation that your territories have been invaded by enemy forces will be sparked by reports from border provinces or forts or cities or perhaps spies from within the enemy territory, that a enemy force is either entering your territory, or has entered you territory and is currently raiding, pillaging and looting your people and villages. This could also be the report of a captain or commander of a fort who sends you news of an enemy force which is currently on the path towards or in the process of laying siege to the fort under his command.

The time it would take for this information to reach you would depend on the nature, extent and efficiency of the postal system in your country, or any other networks of communication you may posses such as spy networks etc. For example, in the Mughal Empire the keeping of exact and detailed records was a major concern of the Mughal administration. The Mir Bakhshi supervised the corps of court writers known as waqia nawis, who recorded all documentation presented to the court, and all imperial orders known as farmans. Agents known as wakil of nobles and regional rulers recorded the entire proceedings of the court under the heading “News from the Exalted Court” or Akhbarat-i Darbar-i Mualla with the date and time of the court session pahar. The akhbarat contained all kinds of information such as attendance at the court, grant of offices and titles, diplomatic missions, etc.

News reports and important official documents travelled across the length and breadth of the regions under Mughal rule by imperial post. Round-the-clock relays of foot-runners qasid or pathmar carried papers rolled up in bamboo containers, there were bells attached to these containers to alert the qasid at the next station or chauki, which allowed the qasid to prepare his horse or camel and himself to immediately receive the container and rush at full speed to the next chauki and so on until they reached their destination. This system was prevalent before the reign of Akbar, who himself added camel and horse corps to this system further reducing the time taken to relay information from distant Provinces of the Empire to the capital to within a few days. The empire was connected by a surprisingly rapid information loop for public news.

Now let us assume that you are Akbar and you have recieved news of Uzbek raiders entering the frontiers of your province of Kabul from the North West, via the report sent by the local garrison of a fort and patrols. Reports have suggested that the force is "quite large" and the local officials have estimated it to be between 5-10,000. You, send your trusted general and relative Man Singh, to crush this enemy and force them to retreat. You send with him around 5,000 Imperial musketeers, and 8,000 Imperial armoured cavalry. Man Singh also takes with him his own corps of 5,000 Rajputs as well as a park of light artillery such as zamburaks or swivel guns mounted on camel backs, and the famous Mughal artillery of the stirrup or horse drawn cannons which were light but easier to march with. Let us assume that the reports arrived around the 5th of January, you set off on the 7th, and you presume that the reports you recieved on the 5th were at least 3-4 days old, maybe more. Therefore, as you begin on the road to Kabul, you keep receiving latest reports at shorter intervals regarding enemy movements, the couple forts they managed to capture, the villages they might have looted etc. And with each report the vague enemy position hidden in the fog of war becomes more clear and precise. Until you finally reach the fringes of the Kabul province. Reports arrive about the Uzbeks receiving reinforcements and currently besieging Kabul itself. Your army, is two days march from Kabul and as you inch closer your reconnaissance assures you that the enemy numbers are roughly 15,000, all cavalry, no artillery or infantry to speak of. This gave Man Singh an amount of confidence since, he had a slight advantage in numbers and in terms of firepower, since had he brought only cavalry, he could have been in a tricky position here. Now, keep in mind, there's a host of circumstances here that we're not taking into consideration out of convenience. For example, the reconnaissance could be wrong, the Uzbeks might be waiting more reinforcements, the Siege of Kabul could be a distraction from the main attack, Uzbeks having good reconnaissance of their own etc etc. But let's assume things are going as they are.

Here, Man Singh decides that he cannot afford to sit idly by and allow Kabul to be starved out and forced to surrender. Though the enemy may actually outnumber him and have more than 15,000 troops, he must act and take initiative. He is faced with the option of either maneuvering his forces into a battle or taking his forces to a crucial fort between the province Kabul and Punjab and waiting for the Uzbeks to attempt a siege where he would hope to frustrate their efforts and force them into a retreat. However, the latter option would mean, allowing the Uzbeks a strong foothold into a province, namely its capital Kabul. Allowing them to gain a foothold from where to launch future campaigns and allowing them to gain the treasure of Kabul itself. Here, passivity would mean defeat for the defender. Also, a victory for the Uzbeks and the capture of Kabul would also play on the morale of the troops, and morale so often decided the side which would win or lose engagements. Hence, Man Singh takes his roughly 18-19,000, marches them around the Uzbek position and takes a defensive and tactically advantageous position. Uzbeks realising their path back home has been cut off, decide they must give battle. The next morning, the two forces engage in battle and given his superior arms and tactics, Man Singh prevails.

Given this example we have managed to come to a few conclusions, and I'll try and list them here. A) During wars in the medieval period, armies operated under uneasy and uncomfortable uncertainty about the position of the enemy and depended heavily on reconnaissance, communication systems and spy networks. B) The aggressor had the advantage of surprise and initiative while the defender had to respond to the aggressor. C) Two forces, equally matched in terms of technology and manpower would prefer to avoid pitched battles, a force or a commander which had superiority in arms and numbers would be confident in giving battle and would actively seek them out to deal a decisive blow to enemy machinations . D) A centralised army or force which does not require the ruler to raise feudal levies and wait for their arrival is crucial for meeting immediate needs of military concerns. E) Once a defender has ascertained enemy position and strength, the element of surprise and initiative may be siezed upon and mobility plays a crucial role in achieving tactical superiority or surprise.

In conclusion, battles are sought by a defender who has one or more of these things - the element of surprise, intelligence on the enemy, mobility and initiative, superiority in arms or numbers or both. Ofcourse, there are circumstances when defenders had neither but still prevailed, here superiority in discipline, organisation and morale comes into play. Battles are forced upon a defender when - the capital or the Kingdom or a province is threatened, the enemy is currently besieging a crucial city or fort, the enemy has better reconnaissance and out maneuvers the defender and forces battle upon them. Ofcourse, this is not an end all be all list, but rather a broad category of circumstances which played out with unique variations in real life. For example, during the Mughal-Maratha wars, for 27 years, larger Mughal forces were usually ambushed and routed by smaller Maratha forces since the Marathas possessed the element of surprise, intelligence on the enemy, initiative and usually had higher morale than Mughal troops.