Aaron Milstein and SethK appear to have cracked the Mousehunt 3.0 Catch Rate equation. Sam Siebert’s equation based on Mousehunt 2.0 data was pretty far off in some regions after the release of Longtail (Mousehunt 3.0). These data also draw on Paul Humphreys’s updated mouse power and effectiveness estimates.
A summary of these updates can be seen on this spreadsheet.
The catch rate of a mouse is dependent on Trap Power (T), Trap Effectiveness (Eff), Luck, and Mouse Power (M). In the new equation for the Longtail release of Mousehunt (version 3.0), the catch rate can be estimated by this equation :
Why should you believe me?
Check out the plots Seth has provided, they have me convinced.
100%: PHYSICAL--Chillbot/magma/shield vs various Indigenous, Derr and other mice that should be 100% eff
150%: ARCANE--ACRo/MSB/shield vs Balack's Banished.
175%: TACTICAL--2010/Magma/shield vs Nerg, Furoma, and a few other mice 175% susceptible:
200%: ARCANE--ACRo/MSB/shield vs Bristle woods forgotten (note this should be unchanged from MH2 as (3-eff) in this case = 1
I am pretty much sold on this equation. Seth K however, does mention a few caveats
1) Data compiled by COMBINING results from Nick A and Nathan Y’s databases (submitted between 8/1/2010 and today)–yes we are aware there are people who post logs to BOTH, and therefore there is some data duplication, which means the error bars will be a bit larger than represented in the graphs…
2) Two anomalous mice have been noted (neither shown in these graphs). The first is the Squeaker claws which ought to be a 100% catch but isn’t–we are not sure exactly why–it is the ONLY anomalous event mouse. The other is the Swarm of Pygmy–it is acting in terms of CR like a 3000-power shadow mouse currently (it was 3000 power according to Paul Humphreys in MH2, but he raised it to 4000 just recently for MH3–I personally believe this is an error by Paul, because the in-game power order displayed on the mice page of the application supports 3000 but not 4000.3) Ideally I would like to have much more data for smaller error bars like we had at the time we were working on the MH2 equation that Sam Siebert ultimately solved, but we just don’t at this point. We have to make do with what we have.
Very impressive work guys. I hope that I was able to help out in sparking a reexamination of the equation, but I certainly wasn’t thinking it would come out like this.
A random walk through Mousehunt 
The Swarm of Pygmy Mice has had either its power or its effectiveness vs Shadow traps changed. The boundary between Difficult and Challenging is 2000 now – it’s not just a typo by Paul. Good work Aaron and Seth – I’ll take a better look over the next few days!
I can explain the squeaker claws discrepancy Seth mentions. The power value of 3000 they’ve used is simply wrong. It’s listed as difficult with Acronym/MSB so it has at least 5000 power, explaining why it doesn’t give 100% catch rates.
I am slightly concerned with the date range on the data though – my understanding is that for a long time 2010/magma/shield was showing 100% catch rates against students, but changed at some point, almost certainly after the 1 August start point.
Despite the large error bars, there should be a way to test it the formula conclusively, given the amount of data there are.
Congrats on this! I’m glad we can better estimate the actual catch rate for each setup. I understand that this formula better reflects actual catch rates – but does it change any of the estimated “best trap setups” now that there is a better formula? Or does it simply equally shift all setups to a more correct estimate without any of them changing position?
Great question Jason. Aaron has updated the catch rate estimates for “boss” mice in the spreadsheet linked above. In some cases there have been shifts.
hej,
nice job, i followed on the forums a bit of how much work went into this, just a quick (and probably stupid) question:
i am curious about the various effectiveness multipliers in above formula.
if you plug 0 in for eff, you end up with 0/mouse power which is always 0. isn’t this contradicting the lore that you can catch mice on luck alone? with the above formula that would be completely impossible, or?
i am probably overlooking something really simple, but it doesn’t make sense for me at the moment…
Hi Frank,
If the effectiveness for a trap type against a certain mouse was 0, the catch rate for that mouse would be 0, regardless of the value of luck. In other words, if the Eff = 0, you cannot catch that mouse with that trap. For example, the dragon mouse can never be caught with any trap type other than draconic.
The acronym can catch the acolyte because it is listed as “less effective” against the acolyte, meaning that there is a non-zero value for Eff against the acolyte.
You can tell if the effectiveness of a certain trap against a certain mouse is 0 from the Difficulty rating on the mice page or on the camp page – “Impossible” indicates Eff = 0, while anything else, such as “Near Impossible” or “Overpowering”, indicates Eff>0.
Hope that cleared things up for you.
haoala
So… what about effectiveness multipliers that are 3 or higher? Does this mean that luck does NOT affect your catch chance for a multiplier of 3 (e.g. Gauntlet – Tier 6 mice with arcane)? That would also apply for effectiveness multipliers of higher than 3 in which luck DECREASES your catch chance (e.g. Gauntlet – Tier 7 & 8). That doesn’t seem right.
Maybe there math behind the luck portion should have an absolute value in it: |3 – Eff|(Eff * Luck)^2. Or maybe there’s a different formula for the king’s gauntlet?
A short survey for capturing the Realm Ripper (Power 3200) with the ACRoNYM and Aqua base (4514 Power, 33 Luck w/ LGS, Eff 400%) from the Horn Tracker data shows 50 records with 100% catch rate. The amount of data yields a catch rate uncertainty of +0%-5.7% (95% confidence level).
Calculating the catch rate without luck gives a catch rate estimate of 84.94% which is very far outside the confidence interval. We can exclude the absence of luck influence on the catch rate in this case. It would be logical to assume that the (3-Eff) term or Eff in the whole luck term is capped.
Capping only the (3-Eff) term to >= 1 (by replacing it with Max[1,(3-eff)]) gives a rate of 167%.
Capping the Eff in the whole luck term to <=2 yields 105%.
Both are in agreement with data. Maybe someone could investigate this further. I don't know whether there is enough data available to do this.
PS: I think that taking the absolute value is not the right thing to do because it would increase the luck effect again for higher Eff.
Where can we check mouse power/effectiveness cos sometimes it’s 0.25/0.5/1/1.5/2?
how can you determine the mouse power of a mouse? i haven’t found one site discussing this ever since..
You look at the trap effectiveness for a given mouse for many many combinations of traps, charms and bases. The percentage catch rate excluding luck for each level of effectiveness (Moderate, Challenging, etc) is known. Thus you can constrain the possible mouse powers. Sometimes the effectiveness of the mouse is not known, so additional tricks are required. These will not be divulged here though, as the devs might fix them 😉
Here is the most up to date list of mouse powers, maintained by Paul Humphries.