Your questions answered . . .
Copyright © 2011, Dwight Gill
The XERA of a hitter represents the eXpected Earned Run Average of an average pitcher against a TEAM of similar hitters.
The XERA of a pitcher, similarly, measures his eXpected Earned Run Average 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 R2 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 firstname.lastname@example.org.
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