**Your questions answered . . . **

^{
Copyright © 2011, Dwight Gill}

The **XERA** of a
hitter represents the e**X**pected **E**arned **R**un **A**verage of
an average pitcher against a TEAM of similar hitters.

The **XERA** measures
the hitter's productivity with a normal distribution of his stats.

The **XERA** of a
pitcher, similarly, measures his e**X**pected **E**arned **R**un **A**verage
with a normal distribution of his stats. Long term probabilities always tend
towards a normal distribution - a pitcher with good stuff and command may have
an occasional bad day (and vice-versa), but he'll nearly always "return to
form." That's why, when there's a significant difference between a pitcher's **
XERA** and his standard **ERA**, the **XERA** will __usually be a
better judge of future performance__.

Yes, the **XERA** formulas are quite easy to use
in spread sheet form. They're equally useful (in relative terms) at other levels
of play - minor leagues, college, high school . . .

Ultimately, we optimized the formulas by
plugging years of known data, measured against actual earned runs, into a Linear Programming Model
which we ran through a computer. That's why **XERA** works so well, when
compared to actual data. Every few years we make minor adjustments to
accommodate additional data that becomes available (after each season).

**
**

**We've upgraded
the XERA formulas, following the 2010 season (the newest formulas are used
everywhere on the site). Unfortunately, we no longer publish them, because
someone violated the copyright, on the previous formulas. **

**Team vs team probability:** Let's say that
team D has a record of 50 - 40 while team C, against similar competition, has a
record of 48 - 42. Then (50 x 42) / (40 x 48) = 2100 / 1920 = 1.09375. [(D's
wins x C's losses) divided by (D's losses x C's wins)] That number
divided by that-number-plus-one (2.09375) = 1.09375 / 2.09375 = .522388 . . .
meaning that team D would, typically, have a 52.2388% likelihood of beating team
C. Dwight's evaluations give equal weight to the teams actual records **and**
their would-be records based on runs squared. That weighted winning probability
is then plugged into a * Binomial Distribution* for the Playoffs and
World Series. All our systems are
based on precise mathematical applications, not subjective opinions.

**Projected Wins**
simply applies a team's current R^{2} percentage to the balance of its
games, and adds that to its current record.

**The Magic Number:** In
MLB, it's simply 163 minus
(A wins + B losses), that is, the total of __wins__ by team A and __losses__ by team B
(generally, the team in second place), subtracted from 163. That same rule can
be applied to __any__ two teams in a division. If, for example, the first
place team had 80 wins sometime in September, and your team was in fourth place
with 78 losses, then A wins would be 80 and B losses would be 78. So, 163 - 158
(80 + 78) = 5. That means that any combination of wins by the first place team,
and/or losses by your team, that adds up to 5, would eliminate any possibility
of your team overtaking the first place team this season. If two teams in the
same division are tied at the end of the season, a tie-breaker
rule (the team with the better record in head-to-head competition during the
regular season) takes effect. Keep those cards and letters (and emails) coming!
You can reach Dwight at xerastats@gmail.com.