Chance to Hit

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Chance to Hit

When one of your characters attacks an opponent, the game conducts a series of calculations. These calculations represent the events that would transpire in a real-life attack. It's too bad that we can only see the outcome and not all the actions that the calculations imply. Maybe it'll be in MM16.

Therefore, permit me to dramatize an attack to help explain what, to the best of my knowledge, the game is doing. Notice that the attack continues until all Chances have been used.

My Paladin is ready to attack a Magyar Matron. She sneers at him and says, "Nyald ki a seggem." He raises his Sword and begins.		Character attacking with +39 Attack Bonus Attack Value = (10+AB)/100 = 0.49 Target is Magyar Matron, Armor Class 28 Defense Value = (100-(AC+10))/100 = 0.62

He tries a direct thrust to her chest, but she slaps the blade away.		1st try: Chance to Hit = .49 x 100% = 49% Roll percentile die; Result > 49 => Miss (100%-49%) x .62 = 31% Chance remaining.

He feints, again to the chest, but then turns the point towards her belly. She parries him neatly.		2nd try: Chance to Hit = .49 x 31% = 15% Roll percentile die; Result > 15 => Miss (31%-15%) x .62 = 9% Chance remaining.

He swings his Sword around and slashes at the Matron's head, but she ducks and evades the whistling steel.		3rd try: Chance to Hit = .49 x 9% = 4% Roll percentile die; Result > 4 => Miss (9%-4%) x .62 = 3% Chance remaining.

Tiring now, he makes a vain attempt to strike her leg but she effortlessly brushes his weapon aside.		4th try: Chance to Hit = .47 x 3% = 1% Roll percentile die; Result > 1 => Miss (3%-1%) x .62 = 1% Chance remaining.

"Te feszfeg!" she says. He looks dejected.		5th try: Chance to Hit = .49 x 1% = 0% No Chance to Hit; Turn over.

The Total Effective Chance to Hit was 49% + 15% + 4% + 1% = 69%, and I still missed! Looks like I'd better keep my day job.

Our Attack and Shoot Bonuses are the only factors that we can control that affect our Chance to Hit. These values are determined in similar ways, so we will cover them at the same time. The following discussions will help you understand the Recommendations at the bottom.

1) The Math

Only our character's Attack Bonus and the opponent's Armor Class are used in these calculations. The method used to figure our Chance to Hit with Bows is very similar, the only difference being that Shoot Bonus is used instead of Attack Bonus. The Attack and Shoot Bonuses can be found on your character's Stat Screen. The opponent's Armor Class is available in the Monsters table in the Appendix.

You don't need to calculate your characters' Chance to hit. We'll be able to derive some insights from the math that will make it unnecessary. Please consider the following chart.

You'll have noticed that the Chance to Hit increases more rapidly at first and then gradually levels off. Also, there is always some Chance to Hit. What isn't apparent from this chart is that there appear to be no further increases beyond an Attack or Shoot Bonus of 60. We'll look at some different Chance to Hit charts and draw some conclusions in the Recommendations below.

The calculations for succeeding with a Magical Attack are different. They will be covered in the next section under this heading. The calculations for an opponent's Chance to Hit our characters are slightly different and will be covered in the Defence section.

If you want to figure out a character's Chance to Hit, or maybe just look at your character's Chance to Hit curve, then you might want to use the Excel spreadsheet in the Downloads section.

If you're interested in the details of the math, then you'll want to note the following. The character's turn ends when either the opponent is hit or the Chance to Hit goes to 0. All calculations of Chance are truncated. The Defense Value may not be negative. The constant values of 10 used to determine the Attack and Defense Values -- well, I don't know where they come from, but they make the curves fit the data and I'll let you know if I find out what they mean.

2)    Accuracy Bonus

Changes in the Accuracy Statistic raise or lower the Attack and Shoot Bonuses in a Breakpoint manner. (If you haven't memorized the Breakpoint Table yet, you can refer to it here.) For example, with an Accuracy Statistic of 13, the Stat Bonus would be 0. Thus, if there were no other contributions, the Attack and Shoot Bonuses would be 0. Of course, that doesn't mean that we would have no Chance to Hit.

3)    Weapon and Bow Contributions

Every Weapon and Bow has an intrinsic value that is added to the Attack or Shoot Bonus repectively. Typically the more potent the Weapon or Bow, the greater the Attack or Shoot Bonus (as well as the greater the potential damage). If more than one Weapon is equipped -- eg, double Daggers -- both Weapon contributions are added to the Attack Bonus.

4)    Skill Contributions

The level of Skill in an equipped Bow is added to the Shoot Bonus. Similarly, the level of Skill in an equipped Weapon is added to the Attack Bonus. If two different Weapons are equipped -- eg, Sword and Spear -- only the greater Skill level is added to the Attack Bonus.

5)    Enhancements

a)    Enchantments

Items of Precision, of the Stars and Rogue's directly increase the Accuracy stat. If the increase causes a breakpoint increase, the Attack and Shoot Bonuses increase.

b)    Spells

Bless (Spirit #2 - 2SP) increases the Attack and Shoot Bonuses by 5 plus 1 per level of Skill. Hour of Power (Light #9 - 55 SP) also casts Bless at varying multiples of the caster's Skill in Light Magic.

Precision (Mind #4 - 4SP) increases the Character's Accuracy stat by 10 plus 2 per level of Skill with Normal Ranking in Mind Magic. If the increase causes a breakpoint increase, the Attack and Shoot Bonuses increase. Day of the Gods (Light #7 - 45 SP) also casts Precision at a multiple of the caster's Skill in Light Magic.

c)    Potions

Energy (yellow) adds 10 to all stats temporarily and Extreme Energy (white) adds 20 to all stats temporarily. Attack and Shoot Bonuses increase breakpoint increase in the Accuracy stat.

Bless (white) grants a 5 point increase in both Attack and Shoot Bonuses for 6 hours.

d)    Certain Wells, Fountains and NPCs can also affect Attack and Shoot Bonuses. Both the Diseased and Drunk Conditions decrease the Accuracy stat. The Weak Condition has no affect on Attack and Shoot Bonuses but might affect the Chance to Hit nonetheless. I'll let you know.

6) Recommendations

a)    Consult the Breakpoint Table as well as your character's stats when allocating items with stat-boosting Enchantments. Do the same before casting a stat-boosting Spell, drinking a stat-boosting Potion, or committing a Beacon slot to a temporary stat-boosting well or fountain. As your characters develop, any given stat boost becomes less adventageous. That's why you find more potent boosts as you progress though the game.

b)    The most potent way to increase your Attack and Shoot Bonuses is with the Bless Spell or Potion. Whereas increasing Accuracy increases the Bonuses in Breakpoint fashion, Bless directly increases the Bonuses. This is especially useful later in the game when it becomes progressively harder to reach higher and higher Breakpoints.

The Bless Spell and Potion are not additive. Your character will only get the sole benefits of the one applied most recently. At only two spell points the Bless Spell is a great value. It is probably one of the least appreciated Spells available, especially at Master Ranking.

c)    Check out these two charts. The first is the Chance to Hit curve against a Goblin. The second represents a fairly tough Monster such as a Minotaur King.


Please notice that in this range, if your A/S Bonus is 10 more than your opponent's Armor Class, then your Chance to Hit will be right around 70%.

d)    As you increase your character's Attack/Shoot Bonus higher and higher, the corresponding increases in the Chance to Hit becomes smaller and smaller. You eventually reach a point where the resources needed to improve your success rate could be spent more wisely on something else.

I can't tell you how to know you've reached that upper limit because it depends on your other needs, but we may be able to answer that question in the future. Also, remember that it appears as though nothing is gained by increasing your A/S Bonus over 60.

However, I can tell you that the bottom limit for these diminishing returns appears to be about 55% -- slightly higher against lower AC and slightly lower against higher. This gives us a very practical Rule of Hitting: If your characters aren't Hitting at least half the time, you need to either increase your Attack/Shoot Bonus or consider retreat.