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August 12, 2005
Rules of Advancement
(The Rangers’ four-game swan dive has rendered this piece moot as far as Texas is concerned, but in the words of Blake, "I'm going anyway. Let's talk about something important.")
Eliminating a deficit against one team presents a basic problem. When the leading team wins, the laggard can’t gain any ground. When a team sits in third place, its ability to gain ground is further challenged. The question is, how much?
Let’s assume two scenarios: in one, Los Angeles resides in first with a winning percentage of .575, and Texas is in 2 nd at .500. In the other, LA and Oakland are tied at .575 and Texas looks up from third place with a .500 record. Assume that a team’s winning percentage indicates its probability of winning any particular game (except when LA and Oakland square off, then assume each has a 50% chance of winning).
With only LA in front, Texas gains a game in the standings when they win and LA loses. Simple enough. With LA and Oakland ahead, Texas gains on the division lead only if they win and <I>both</I> LA and Oakland lose. Conversely, they lose a game in the standings if they lose and <I>either</I> LA or Oakland wins. Thus, with two teams in front, Texas is more likely to lose a game in the standings than win.
| Change in Standings | One team ahead | Two teams ahead |
| Gain a game | 21.0% | 9.0% |
| Stay even | 50.0% | 50.0% |
| Lose a game | 29.0% | 41.0% |
Texas has another problem. When LA and Oakland are tied and playing each other, as occurred recently, Texas cannot gain a game in the standings. If Texas wins, they merely stay even. If they lose, by definition they must also lose a game in the standings.
| Change in Standings | Two teams ahead | Two teams ahead, playing each other |
| Gain a game | 9.0% | 0.0% |
| Stay even | 50.0% | 50.0% |
| Lose a game | 41.0% | 50.0% |
When two leading teams are tied and play a three-game series, the third-place team can do no better than regain one game in the standings during those three games. To do so, Texas must sweep and hope that the LA-Oakland series ends without a sweep. Any other outcome results in stasis or further decline.
| Change in Standings during three-game series | Two teams ahead, playing each other |
| Gain a game | 9.4% |
| Stay even | 31.3% |
| Lose a game | 37.5% |
| Lose two games | 18.8% |
| Lose three games | 3.1% |
Of course, Texas won’t make up ground on anybody if they continue to hover around the .500 mark. Let’s assume that the one-eyed Norse god Odin grants the Rangers supernatural baseball prowess, raising their winning probability to .750. The probability of gaining ground on two teams in one day increases surprisingly little, from 9% to just over 13%, because of the unlikelihood of both LA and Oakland losing. When LA and Oakland square off, Texas has about a 32% chance of gaining one game in the standings over the course of the series.
| Change in Standings, .750 chance of winning | One team ahead | Two teams ahead |
| Gain a game | 31.9% | 13.5% |
| Stay even | 53.8% | 53.8% |
| Lose a game | 14.4% | 32.7% |
| Change in Standings during three-game series when two teams are ahead and playing each other | |
| Gain a game | 31.6% |
| Stay even | 42.2% |
| Lose a game | 21.1% |
| Lose two games | 4.7% |
| Lose three games | 0.4% |
Posted by Lucas at August 12, 2005 07:14 PM