Fishing Stats and Analysis

Introduction:
Ever since I started fishing on a regular basis, there were plenty of
questions I wanted to ask, but it just seems as if no one has the
answers to how fishing works. As I continued to progress through fishing
I began to make some sense of fishing and that is the reason I wrote my
theoretical perspective on how fishing could possibly work on the Fishing Tips and Stats thread.

Now that I have maxed fishing, there are still plenty of questions I
would like answered, but I’m sure no one knows the full details on how
fishing works, with the exception of TT devs and execs. Since I still
have plenty of questions to address, I decided to do a comparative
analysis of the number of fish each species and fish position requires.

Paired Comparisons:

• How many fish it takes for rare fish
  
• How many fish it takes to catch a new species at each fishing position
  
• How many fish total for fishing positions 67-70
  

Fishing Position: Represents #70 being the last fish needed, #69 being the second to the last and so on and so forth.

Standard Deviation: A measure of dispersion in a frequency distribution. It measures the spread of data values.

This comparative analysis should shed some light as to how fishing might
work. There are many theories on how fishing works (I will take them
into consideration) and I am willing to use a statistical approach to
try and elucidate the mysteries of fishing and broaden our knowledge of
this “wonderful” task.

Format:
Please input your data in the following format:

65 - Grand Piano 3974 fish (MM tenor in River)
66 - All Star – 4688 fish (Home Pond in River)
67 - Full Moon – 6265 fish (DDL PG in River)
68 – Grizzly – 9795 fish (TB Walrus in Giggleyham)
69 – Ray – 9110 fish (TB PG in River)
70 – Concord – 40,963 fish (TB PG in Gigglyham)

Results:


Table 1 – Fishing Results.

This is a summary of the fishing data I have been collecting. I have
collected data from over 35 people and have compiled it into this table
(Table 1). Table 1 is organized by the fishing position and the average
number of fish, and standard deviations that it took to catch a new
species at that specific position. Each average represents the average
number of fish it took to catch the next new species at any particular
fishing position. The same was done for some of the rare species. In
addition, I have included the average fishing position these species
usually showed up in. The higher the average position, the more likely
that specific species was the last fish to be caught by the majority of
the individuals in the data sets I collected. Furthermore, I have
included the total number of fish required for the last 4 fish, which
averaged out at 62,485.15 fish, with a standard deviation of almost
37,000.


Fig. 1 – Average number of fish required to catch for each fishing position

One of the simplest and most useful comparisons to do is to compare the
number of fish required vs. fishing position. In comparing the two, the
number of fish required for each position seems to incrementally
increase from the lower positions to the higher positions. The trend
steadily increases from a few hundred to several thousands, which is
suggestive that the number of fish required to catch heavily favors the
fishing position. The mean number of fish required to catch the 70th
fish is 24,416.48 which is larger in amount when compared to the 65th
position (5,492.09 fish, Table 1). This is one of the expected
outcomes, because as you fish and catch more and more species, the next
new species seems to require more fish than the previous one. In
contrast to that theory, if you look closely at table 1, the standard
deviations for each fishing position have a large variance. The large
variance from the mean indicates that the number of fish required for
each fishing position is insignificant, suggesting that each fishing
position can require the same number of fish regardless of what position
that specific species is caught in. One thing is for sure is for some
odd reason or another, the trend does favor higher fish requirements for
higher fishing positions as seen in the trend line in (Fig. 1), but yet
the results are not of significant values due to the large variance.


Fig. 2 – Average number of fish required to catch for each of the denoted species

Since the number of fish required for each fishing position is
insignificant, I decided to try and determine if each species of fish
had anything to do with the mean number of fish required before catching
that specific species. In comparing one species to the next, the three
fish that required the most fish (average values) are: Concord
(16,016.45 average fish), Grizzly (15,364.82 average fish), and the Full
Moon (17,057.89 average fish). There is no significant difference in
the number of mean fish required when trying to catch the Concord vs.
the Full Moon. The same problem exists with this comparison as with the
comparing the average number of fish to fishing position; the standard
deviations are far too great. These results suggest that regardless of
what species you are trying to catch, there are no fish requirements for
catching a specific species. Each can be caught in as little as 1 cast
or 100 casts.


Fig. 3 - Average fishing position for each of the denoted species

Since the average number of fish required to catch a new species seemed
to not be dependent on the fish species itself, I decided to look at
what the average position is for each of these species when it was
finally caught. Maybe by looking at when people catch a specific
species can help elucidate if there is a specific trend when it comes to
catching a new species. Out of all the denoted species, the Concord
had the highest average fishing position (68.50) as compared to the All
Star (64.82). This help to elucidate possibly why the Concord
(16,016.45 average fish) seems to be a more difficult fish to catch than
the All Star (6,066.18 average fish), because most people seem to have
the Concord as their last fish due to its difficulty. This comparison
is seemingly much more valid than comparing average fish values to
specific species. In contrast, when you compare the number of average
fish required to catch the Devil Ray (9,111.50 average fish) at an
average fishing position of 67.45, you would expect to catch the Grizzly
with the same difficulty as the Devil Ray since its average position of
the Grizzly is 67.59 if this theory were true. This is not the case,
because when you look at the average fish required for each the Grizzly
(15,364.82 average fish) and Devil Ray (9,111.50 average fish), the
Grizzly is more difficult to catch than the Devil Ray. Again, there is
no consistent trend to these values, which is suggestive that the number
of fish required is independent on fishing position and on rare
species, suggesting that there are no fishing requirements to catch a
new species.


Table 2: A. The probability factor for the indicated species from
fishing position 67-70. B. Overall fishing statistics including boots
and jelly bean jars

Since it appears that there is no consistent trend when comparing the
number of fish required versus fishing position or species, I wanted to
see if a probability could be compiled for each species. Although it
does give some insight, the above data has some limitations because it
is still represents the number of fish required in between new species,
and not the overall probability. An overall probability would give a
better statistical value. Since each of the data sets is lacking some
information fishing positions 65 to 70, I decided to only run a
probability factor from fishing positions 67-70 (the last four fish)
since the majority of the data sets contain all this information. From
catching one new species to the next one, the 3 most difficult species
to catch were in fact the Concord, Grizzly and the Full Moon. Although
the standard deviations suggest that there is no significant difference
between these three fish and the other rare species when trying to catch
the next new species (Table 1); the overall probability gives better
statistical input showing the difficulty of catching these fish (Table
2). Although these numbers are limited to only fishing positions 67-70,
a probability factor can still be assessed. In comparing the 3 most
rare species, Concord, Full Moon and Grizzly, the Concord and the Full
Moon have the equal probabilities of being caught, approximately
1:41,000 of a chance for each (Table 2A). Out of all the data sets I
have collected, the majority of all the individuals had the most
difficult time with the Concord and Full Moon. The Grizzly was the next
less likely fish to catch, with a probability of 1:29,000 (Table 2A).

Although these data sets are important, neither of them factor in boots
or jellybean jars. These results only contain the number of fish, which
upon factoring in boots and jellybean jars the probabilities will
worsen. Since none of the data sets contain the information of the
number of boots and the number of jelly beans, I had to do a projected
or hypothetical probability by running a trial run to determine how
often boots and jelly beans are caught on the fishing line. The
experiment I decided to run was count the total number of boots and
jellybean jars caught while fishing for 1,000 fish, then use these
actual results to make a projected probability. The total number of
fish, boots and jelly bean jars will are presented as a percentage and
actual number caught (Table 2B). During my experimental run, a total of
87 boots (7.94%) were caught and only 9 jelly bean jars (0.82%) out of a
total of 1,096 total objects (Fish, Boots and Jellybean Jars) (Table
2B). Since boots and jelly bean jars are caught 7.94 and 0.82% of the
time respectively, these values can be used to make a projected
probability for the 3 most rare fish species (Table 2A). Using the
figures of Table 2B, and factoring in how often jelly bean jars and
boots show up, it is only expected that the probabilities will worsen,
in which they actually do by approximately 3,000 points (Table 2A,
Projected probabilities).

Again, these probabilities are only based on fishing positions 67-70,
and I am also assuming that each individual caught only one of these
species upon reporting their fishing figures. Plus the projected values
are only theoretical and can’t be taken as true results since the
actual number of boots and jellybean jars were not reported.
Furthermore, since these probabilities are based on fishing positions
67-70, one would assume that these probabilities would worsen if total
fish (fishing positions 1-70) were factored in.

Summary:
In conclusion I found there is no significant difference when trying to
estimate the fish requirements when looking at fishing position or
specific species due to the large variation of the standard deviations.
Since these values are seemingly insignificant and have no correlation,
one can only assume that species are based on a random probability,
similar to a lottery. This is validated by the probabilities I
generated, with the Concord being the most difficult fish to catch. Not
everyone will have a difficulty catching the Concord, but most people
will based on the results. Some individuals having difficulties while
others seemingly catch these rare fish easily are all suggestive of
random probability. These probabilities are distributed in a way that
some species might have a probability of 1:10 (common species) while
others might have a 1:10,000 or even 1:50,000 or more of a chance. The
data suggests that, since the standard deviations are so great, and
these fish run on probabilities, each of the species can be caught in as
little as 1 try to never, regardless of fishing position or rare
species. This is why you might see some people that have been fishing
for years and still have not caught their last fish, while others catch
their rare species in a few rod casts. You might ask then why do the
last fish require so many fish in comparison to fish at the beginning if
it’s not dependent on fishing position. Well if you look at fig 3, you
will see that most of the time the rare species are the remaining fish
and since these fish have such a low probability of being caught, they
will in most cases be the last few fish remaining; thus requiring a
large portion of fish to finally catch one. In conclusion, fishing is based on RANDOM PROBABILITY!

The only suggestion that I can give, since fishing is purely random, is
to use the strategy of catching all the fish your current rod may catch
before proceeding to buy the next new rod. I know that gold rod looks
tempting, but it gives no more of a benefit than any other rod, with the
exception of catching the bull dog fish. If you compare using the
steel rod to using the gold rod, you are at a loss because you sacrifice
extra jelly beans per cast for using the gold rod. The only reason the
gold rod should be bought is to complete your list of fish and catch
that last bull dog species.
<blockquote>Strategy:<blockquote>• The strategy of catching all the fish for your current rod over buying the next one has 2 added benefits: <blockquote>1. You use less jelly beans
2. Your total pool of fish is smaller, making any ultra-rare fish within that pool more achievable.</blockquote>•
You have a higher probablity of catching an ultra-rare, such as the
Concord, with a twig rod because the twig rod can only catch a small
pool of 38 fish. It is easier to catch 1 fish out of 38 possible
species with a twig rod than it is to try and catch 1 species out of 70
with a gold rod.

• Its similar to reaching into a bag of marbles. Its easier to fish out
1 blue marble amongst 19 red ones, than if there were 49 red marbles in
the bag. You have a higher probability of finding the blue marble in
the smaller pool of 19 red marbles. Same goes with fishing.</blockquote></blockquote>You
might ask why I would go through all this trouble to come to a simple
conclusion. I’m the type of person that would rather know with actual
results than just have a guess at what is going on and never really know
the truth. If there is anything I have missed please feel free to
comment or add your own conclusions. Thanks.[/size]