# User:Cook Me Plox/RuneScape Research Project/Hit Accuracy

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One of the most sought-after questions in RuneScape is this: "What is my chance of hitting my opponent?" After some thinking and a small amount of research, I have a hypothesis.

It's a well-known fact that there are four things that factor into your chance of hitting an opponent; your Attack level, your offensive bonus, your opponent's Defence level, and your opponent's defensive bonuses. I believe that you can combine these four variables into two, by creating what we'll call "effective Attack" and "effective Defence" (hereon referred to as EA and ED.)

Before we calculate these, I need to explain how attack style affects accuracy. The Accurate style gives an invisible boost of 3 to Attack level. Agressive does the same for Strength, and Defensive does it for (you guessed it) Defence. Controlled adds +1 to all three. From now on these new levels (which show the correct skill levels for accuracy) will be referred to as "styled levels", such as styled Attack.

Both EA and ED can be found by applying the maximum hat formula to Attack or Defence instead of Strength. To find EA, we would subsitution Attack for Strength and offensive bonus (the bonus of your attack style) for Strength bonus. In addition, Attack or Defence boosting prayers and potions will affect EA and ED, just as Strength boosting prayers affect max hit. If a player boosts Attack by 15%, then the EA will be boosted by 15%.

## Example

To calculate the EA and ED, let's take an example. Let's say we have a player with full rune and a Rune scimitar, with 70 Defence and Attack, and that he's using the Accurate slash style. His styled Attack level is 73, but his styled Defence level is still 70. Let's find out his EA first. His styled Attack is 73, and his slash bonus is +45. Entering that into a max hit calculator, we get 142. That is his EA. For Defence, let's assume his opponent is also using slash. That means the player has a styled Defence of 70, and a slash defensive bonus of +210. Entering this in, we get an ED of 338.

## Dice

To actually determine if a hit is going to be made or not, two dice are roled. One of them is an offensive die, and it has as many "sides" as your EA. The other is defensive, and has as many sides as your opponent's ED. Each outcome for the dice is uniformly distrubited from 0 to your EA/ED. The two dice are rolled, and if the offensive die rolls higher than the defensive die, there is a "hit". If the defensive die is higher, there is a miss. Not that there can never be a tie as the random numbers generated seem to be irrational.

## Implications

There are two major, provable implications of this theory. First of all, if two players are evenly matched (one has an EA of 250 and the other has an ED of 250), there is a 50% chance of hitting. This goes for all evenly matched players. Secondly, there should be a point where EA reaches 0. If it is at zero, there is no chance of hitting. For a while now people have noticed that you always splash magic spells with a -65 bonus.

## Magic and Ranged

We have been operating under the assumption that the combat involved here is melee. However, it is quite likely that similar, if not the same, formulas are used for Ranged and Magic accuracy. This is a little more complicated because Jagex has said that 30% of Magic defence was from Defence, and the rest was from Magic. The same may be true for Ranged. More to come on this later.

## Notes

There is a possiblity of "hitting" zero. Because all numbers from 0 to your maximum hit (including 0) are distributed when calculalating what your hit will be. More information to come on hit distribution.

## Practical uses

This could be a goldmine for combat. With this, we can find out with minimal testing the EA of monsters, which could help us decide definitively which weapons are best for certain monsters. In addition, it could help end the question of "Strength vs. Attack".

## How you can help

We need lots of data on this. Help by collecting data regarding this. Please contact me first.

## Calculator

Calculate your chance of hitting and their chance of hitting you.

``` template  = User:Cook_Me_Plox/RuneScape_Research_Project/Hit_Accuracy/Template
form      = CalcForm
result    = CalcResult
param = YEA|Your EA|45|number|
param = YED|Your ED|210|number|
param = TEA|Their EA|45|number|
param = TED|Their ED|210|number|
```
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