**UPDATE #4 :**

**A new formula has been found! This page is out of date. GO HERE**

**UPDATE #3 :**

Double random variable model in blue, Derr Dunes

**UPDATE #2 :**

**New Model : The Head to Head model.**

Player has two chances to catch a mouse.

**First Chance :**

Player rolls a die from 1 to Trap Power * Trap Effectiveness

Mouse rolls a die from 1 to Mouse Power

If player roll > mouse roll, catch!

If not, go to the second chance

**Second Chance :**

Player rolls a die from 1 to (Luck*Trap Effectiveness)^2.4

Mouse rolls a die from 1 to Mouse Power

If player roll > mouse roll, catch!

If not, fail to catch.

The model never has a value above 100% and has a nice S-shaped curve at low mouse powers, similar to what is seen in actual data. So far I haven’t been able to distill it down to an analytical formula, I’m just simulating 100,000 rolls per condition.

Currently I am comparing this to other regions, and its looking pretty good across the board. For now, let’s just look at how it compares to the Standard Model.

Models vs. Actual Catch Rate for Derr Dunes

Actual catch rates are in magenta boxes.

Standard Model predictions are black dots.

Head to Head Model predictions are green dots.

Nerg for 2010/Magma/LGS using 1.5x effectiveness

**UPDATE#1 :**

As noted in a previous post, the current standard model for estimating catch rates from Trap Power, Luck, Effectiveness and Mouse Power works in many cases but there are some clear examples (Derr Dunes) in the Longtail release of Mousehunt where the equation fails to match real catch rates. I don’t have an answer to WHY yet, nobody does, though a dedicated group of mousehunters are trying to figure it out.

Standard Model of Catch Rate Estimates

One common complaint from people is that the catch rate estimate equation doesn’t look like it treats luck as a second chance, or roll, to catch the mouse. The developers have clearly stated that luck acts as a second roll. Well, about that…

Tonight, I was building alternative catch rate models in Matlab to see predicted catch rates, and one of the models gave the exact same predictions as the current model. That model was set up as two rolls! Just like how the devs say the catches work. Working through the fractions shows that the current catch rate model is mathematically equivalent to a system where there is :

**Roll 1 **- Catch if a random number from 0-1 is lower than

Eff * Trap Power / (Eff Trap Power + Mouse Power). If higher, then go to Roll 2.

**Roll 2** – Catch if a random number from 0-1 is lower than

(Eff * Luck)^2 / Mouse Power. If higher, miss.

So lets name these elements shorter names

T = Eff*Trap Power

L = (Eff*Luck)^2

M = Mouse Power

Standard equation is :

**CRE = (T+L) / (T+M)**

Let’s now look at the 2 Roll hypothesis.

Since the odds of failing to catch on roll 1 are (1-(T / T+M)), The 2 roll equation is

CRE = T / (T+M) + (1-(T / T+M)) * L / M

Multiply out the 2nd roll

CRE = T/(T+M) + L/M – L*T/(M(T+M))

Now we need to get the denominators all the same, so multiply by M/M for first term, (T+M)/(T+M) for the second term. We then get

= (T*M + L*(T+M) – L*T) /(M(T+M))

Multiply out the middle term

= (T*M + L*T +L*M – L*T )/(M(T+M))

Cancel out terms

= (T*M + L*M) / (M(T+M))

Remove the Ms

**CRE = (T + L) / (T + M) The SAME as the Standard Equation **

So the Standard Model PERFECTLY fits the description the devs gave regarding luck being treated as a second roll!

Now what to do about those pesky deviations from the expected catch rates?

A few possibilities…

1) The second roll is actually Eff Luck^2 / (Eff Trap Power + Mouse Power)

This will result in very similar catch rates to standard model for mice whose power is << Trap Power. As Mouse Power increases, the catch odds from the 2nd luck roll is decreased. This would seem to fit the data for Dragon. However, maybe not for Derr.

2) The Trap Power and Luck effectiveness multipliers are different.

That’s all I’ve got for now, will investigate these possiblities and any other suggestions and will update this page soon.