I recently discovered this forum when wondering how the attack and block chances worked in the game. Fortunately, you guys made that information easy to find (it's in the wiki). When I saw how the battle system works, though, I realized that it is completely non-obvious how a change in one's stats will affect the outcome of a battle. This gave me the idea of creating a calculator will provide this information.
You simply need to plug some easy-to-find information into the calculator, and it will spit out some useful statistics, such as your hit probability, your average damage per swing (each time you press attack), your average damage per turn (each time you refill AP points in battle) and the average number of periods required to kill your opponent.
For simplicity, the calculator makes the following assumptions:
1.You will always attack in battle (it does not explicitly account for the use of healing items or moving)
2.There are no status effects imposed on you or the opponent
If somebody has any ideas on how to model any of those assumptions into the calculator to make it more robust, please let me know. Regardless, I think that the information it provides is still useful, only you will have to strategically account for healing item usage, moving, and status effects.

This is how the calculator works:
1. In the left table, plug in your statistics and the monster you're fighting's statistics. Only the green spaces need to be filled in, as the red are calculated automatically. Your statistics can be found in-game by pressing the image of your character in the left-hand corner of the game, under the "Overview" tab. A monster's statistics can be found by clicking "Info" in the battle initiation prompt, or during battle by clicking the icon of the monster underneath the attack button (or in Pyrizzle's Bestiary). For all statistics, if you cannot find the value, just leave it at 0. The information in this table will be your current battle information.
NOTE: Do not use percentage signs anywhere in the calculator - it automatically converts from numbers to percentages. Thus, a 162% attack chance should be entered as 162, a 9% effective critical chance should be entered as 9, and a 63% block chance should be entered as 63.
2. Next, to see how a change in your stats will affect a battle, fill out the middle table, which asks for the stats you wish to see changed and by what magnitude of an increase or decrease they are changed by. These numbers can come from equipment and leveling or skill upgrades. For an increase, simply enter a positive number to represent the increase. For a decrease, use a negative number.
3. The table to the right should now show the updated battle statistics, given the change inserted in the middle table.
4. If you wish to use the calculator for comparison purposes, you may copy the middle and right-most table, then paste it directly below. Simply repeat step 2, using different increase/decrease parameters for the copy. This can be done as many times as desired. This method is especially useful when deciding what equipment to purchase, or what skills or stats to upgrade. See the picture below for a visual example.

NOTE: To most easily and accurately see the effect of a change in equipment, you should remove any equipment that you are questioning replacing, then fill out the left-most table. You can then use steps 2, 3, and 4 to reflect an increase/decrease in statistics as a result of using the different pieces of equipment. Alternatively, you may keep your equipment on, but make sure you use the middle table to represent the difference in the piece of new equipment's statistics and your currently equipped equipment's statistics. That is, either way you do it, make sure you account for the loss or gain in statistics that occurs from unequipping a piece of equipment you are currently using.
I have attached the calculator to this post as an excel spreadsheet. I would have made it a Google Doc, but Google doesn't provide the option to make the document both view-able and editable, but not save-able. This would mean multiple people using it at the same time would pretty much break it. Plus, someone may accidentally tamper with it. I figure using excel is the most low-maintenance option and makes it more customizable for you. Please request a different file format if you cannot open excel files.
Also, I may come out with a new version that recommends what choices you should make when you level up your character (+5 HP, +5% Attack Chance, +1 Damage, or +3% Block Chance)
To make using the calculator easier, especially if you don't have some information readily available here are some useful resources created by other users:
Bestiary by Pyrizzle
Gear List by JohanX
Additionally, you may wish to use the opponent search feature. This requires downloading the .xlsm file. When using opponent search, simply click on the box that contains the list of monsters and pull down the dropdown list. Choose the monster you are looking for, then press search.
I hope you find this calculator both useful and fun (try plugging in other players' stats into the opponent column and see how you stack up). Now, instead of merely speculating on what equipment or upgrade is preferable over another, the calculator can actually give you a reasonably good idea. If you have any ideas on how to the calculator better, please let me know.
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Change Log
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V2.
Other minor consistency changes
V3.
Changed some wording
Changed the color of "Total AP" for the Opponent from Red to Green (thanks phydeaux)
Updated the Hit Probability to reflect the current version's battle system by removing the 50% minimum (thanks ncer)
Added a searchable database of every monster's stats - filling in the opponents' stats is now automated (requires the .xlsm file). See the screenshot below.

V4.
Fixed the right-side table's hit probability calculation
Added a "None" option to the Opponent Selector