Z-VALUES
The z-value measures the likelihood that an observed event
would occur due only to chance. The larger the z-value,
the less likely it is that chance alone would cause the
event. A z-value of 2 or larger is typically called "statistically
significant" -- the likelihood is less than 5% that chance
would cause such an event. A z-value of 3 or larger indicates
that the likelihood is less than three in a thousand that
chance would cause the observed event. The Optimizer allows
you to save any situations with z-values of 2 or larger.
Z-values
are more useful than percentages in measuring the strengths
of win-loss statistics because, for example, percentages
don't take into account the total number of games played.
For example a record of 2-0 versus the point spread gives
a win-loss record of 100% and so does a record of 10-0,
yet 10-0 is clearly a better record. On the other hand,
the z-value of a 2-0 record is 1.41, whereas the z-value
of a 10-0 record is 3.16, correctly indicating that 10-0
is the stronger result.
If
each team in a game is equally likely to cover the point
spread, you can think of the game as a coin toss. Under
this assumption, a 2-0 record is equivalent to tossing a
coin twice and getting heads on each toss, which has probability
1 in 4. A 10-0 record is equivalent to tossing a coin ten
times and getting heads on each toss, which has probability
1 in 1,024. This is reflected by z-values. The higher the
z-value, the less likely it is that the record would arise
due to chance.
Technically,
z-values can be either positive or negative, depending on
the direction of the deviation from the average value. For
example, a win-loss record of 10-0 has z-value = 3.16, and
a win-loss record of 0-10 has z-value = -3.16. Because of
this symmetry, the Optimizer displays only absolute z-values.
When
searching through large amounts of data, it's not a good
idea to rely only on large z-values to identify predictable
patterns. An important statistical law, known as the Lottery
Principle, asserts that given enough opportunity, weird
events will happen due to chance alone. When you toss a
coin enough times, you'll eventually get ten heads in a
row. Similarly, if you use software like the Optimizer to
search through data, you will uncover seemingly strong situations
that may be due only to chance. Separating the good stuff
from random noise may require further work. For example,
you could apply situations with large z-values to fresh
data or look at them from different perspectives. The ability
to detect predictable patterns in a sea of data can translate
into long-term profits
Documentation