Martial Wizard

While their friends drink and make merry in the tavern below, the Martial Wizard mutters to themselves upstairs, interrupted only by brief gasps of air when their form falters. They are performing their daily routine of push ups, hand stands, one-legged squats, and planks in sync with the continuation of last nights studies. They are likely brushing up on their arcane fundamentals or possibly even the history of antiquity. Valuing modesty, they wear simple robes of muted colors, or perhaps that of their family. While their exercise does warm and exhaust the body, the Martial Wizard passively notes their level of exertion and unconsciously adjusts so as not to detract of the concentration of study. It is almost as if they have developed a second mind which manages the body so that the true mind can focus on higher pursuits. Once they've come to a natural stopping point in their studies, they stand, now focusing their mind on the body which they have relegated to innate processes. They ask each fiber of muscle, each tendon, each part of each organ, "what do you require?", noting points of famine and those of relaxation. Satisfied with their state of being, they go downstairs to join their party. When queried on the reason of their absence, the Martial Wizard simply replies, "getting ready."

The Martial Wizard is primarily a spell caster, but has chose to actively improve the areas of weakness often overlooked by other mages. Rather than specializing in any one school of magic, the Martial Wizard takes a holistic and pragmatic approach to arcane studies. Rather than asking themselves "what nook of evocation have I neglected?", they ask "in what aspect of combat or conversation am I deficient?"

While the morals of Martial Wizards are varied, they tend to be steadfast in their convictions and stoic in daily life. That is to say, they are generally even tempered and mild mannered. They may serve as council to individuals of power or authority, or they may live in relative solitude, going out only to accomplish a task they deem important enough to interrupt their studies.

Combat Savant

Beginning when you select this school at 2nd level, the gold and time you must spend to copy a spell which directly deals or deflects damage into your spellbook is halved. For example, both Fireball, an evocation spell, and Shield, an abjuration spell, would qualify for this feature. However, a spell like Gust of Wind, another evocation spell which could potentially cause damage depending on the circumstances, is not eligible. Players should communicate and confirm with their DM that a given spell is eligible, and DMs should judge spells strictly so as to maintain balance.

The Study of Defense Against Harm

Through years of physical and mental training, you have honed the science of limiting harm to your physical form via a combination of intellect and resilience. While you are not wearing any armor, your Armor Class equals 10 + your Intelligence modifier + your Constitution modifier.

Potent Cantrip

Starting at 6th level, your damaging cantrips affect even creatures that avoid the brunt of the effect. When a creature succeeds on a saving throw against your cantrip, the creature takes half the cantrip’s damage (if any) but suffers no additional effect from the cantrip.

Preferred Tactics

Pick three level 2 spells. You can permanently cast these three spells using a level one spell slot to the same effect. Level 2 spells cast at level 3 or higher still cost the associated level spell slot. 

Overchannel

Starting at 14th level, you can increase the power of your simpler spells. When you cast a wizard spell of 1st through 5th level that deals damage, you can deal maximum damage with that spell.

The first time you do so, you suffer no adverse effect. If you use this feature again before you finish a long rest, you take 2d12 necrotic damage for each level of the spell, immediately after you cast it. Each time you use this feature again before finishing a long rest, the necrotic damage per spell level increases by 1d12. This damage ignores resistance and immunity.