Random Catches - El's Extreme Anglin' - WoW Fishing Guide


Patch 2.4 introduced 5 daily fishing quests. One is available each day. 4 of these quests required a single fish to be caught from open water:

I invited anglers to record the number of successful catches it took to catch the quest fish. For example, Bait Bandits requires a Blackfin Darter, which can be caught in parts of Terokkar Forest. If the first 6 catches at the correct location were other fish, and the 7th catch was the quest fish, the angler would record "7".

Summary of Numbers

724 results were recorded (by the time I started analysing them), from 30 different anglers. I am grateful to those people. The table below summarises all the data, using terms familiar to Gnomish "statisticians". There's an explanation coming up for the dwarves!

Summary Statistics
Value/QuestThe One That Got AwayBait BanditsCrocolisks in the CityFelblood FilletAll
Mean (Average)
Median (Middle)77746

The sample is the total number of records. We don't have enough records to be very sure that the results are correct, but we can be reasonably sure.

The minimum number of catches recorded against each quest was 1 in all cases, however the maximum is much higher: In one case it took 110 casts before the fish was caught. Balazar is a patient angler! In theory the maximum is infinity, however anglers will give up before they reach infinity. Indeed, most will give up before they reach 100.

Of course neither 1 nor 110 are typical. The mean and median tell us what's typical. What's the difference? The mean is the average, the median is the middle value. So on average, Bait Bandits will take just over 10 catches to complete (the mean), but we should expect it to take 7 catches (the median). Precisely why those numbers are different will become clear when we look at how the data is distributed.

3 of the quests - The One That Got Away, Bait Bandits and Crocolisks in the City - share very similar means and medians: Means of about 10, and medians of 7. Felblood Filet is easier to catch, with a lower mean (7.5) and median (4). So, I have grouped the first 3 quests together, and examined how the data is "distributed".


The graph below shows the percentage of all data, distributed by the number of casts to catch the quest fish, for the quests The One That Got Away, Bait Bandits and Crocolisks in the City. The hatched grey blocks show the raw data. The solid curved line shows the underlying trend. For example, just over 9% of all records caught the quest fish on the very first catch. Catches are only shown up until 20, which includes 2/3 of all records. The trend line will continue to the right, all the way to 110 (or infinity, if you prefer). However, we do not have enough records for most of those points to make it worth graphing them.

Distribution of Data (The One That Got Away, Bait Bandits and Crocolisks in the City)
Graph: Distribution of Data (Away, Bait and Crocs).

The most common single value is 1: The very first catch. The distribution then gradually tails off away from 1. It is that tail that starts to explain the difference between the mean and median. The middle value may be 7, but the data is not distributed between and 1 and 2x7 (14) - the upper value is far higher. So the average is more than the median.

The trend line shown is a polynominal. Or what the dwarves call "a curve". This is a slightly better fit than a simple logarithmic trend line; also, "a curve". Both lines fit pretty well, considering the modest sample size. How well? The line shown has an r-squared of 94%, the logarithmic 89%. R-squared is a measure of fit, where 100% means the line perfectly matches the raw data. For the curious, the equations derived for the percentage of all data (y-axis) are 0.0002c2 - 0.0084c + 0.10 and -0.032Ln(c) + 0.11 respectively, where c is the number of catches.

Random Loot

Catch rates are not constant. But you knew that. What's interesting is not that "random loot is random", but that the trend line apparently tails off to infinity.

Of course the chance of actually reaching infinity is infinitely low. But there is a very small chance you could get annoyingly close. This is the explanation for all those annoying moments when a fish seems to be taking "forever" to bite.

It would be interesting to know whether the same patterns are found in other forms of loot. The apparent randomness of rare dungeon loot is legendary. Quite literally, in the case of Warglaive of Azzinoth. However, I have not seen any robust attempts to analyse that randomness. All the widely used reference sources (such as Thott's book) show the averages for "drop" rates. Perhaps they should use medians, which give a better indication of the typical number of kills required to gain an item?

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