Joe Orr Road Rod wrote:
Darkside wrote:
This is insanity.
It's insanity to expect a "Great Cy Young Candidate Top Ten Pitcher in the Majors" to allow less runs than Doubront, Gibson, and Ricky Nolasco?????????
When they're not facing the same offenses, yes.
And I know you're going to say "well most major league offenses are within one run of each other, so they're all essentially similar". This is where your disingenuous arguing--and lack of understanding of some aspects of mathematics--shines through.
If all offenses are essentially the same, why are there so many teams that are so bad? There is in fact no bottom-feeding team that is outside of 1 run of the league average, and no team that is at the bottom of its division is outside of 1 R/G of the corresponding divisional leader. Cincinnati is 25 games back of the Cubs, but their offenses are within 1 run of each other. How can that be? If you're going to try to argue that pitching is the reason, that the teams that have fallen behind so much because of bad starters, why hasn't that collection of suck manifested in more R/G differentials greater than 1? If there are roaming bands of starting pitchers that are so bad that they can fall behind 20+ games despite a truly "similar" offense...shouldn't other offenses be markedly better as a result of the bad pitching? It's much more likely that though two offenses appear nominally similar in their R/G averages, even a slight variation (.2 or greater) can result in wildly divergent run totals,
because the game is only scored in whole runs.
Take a team that has a 4.2 R/G and one with 4.5. To you they would be "similar", because you think both teams are equally likely to score between 4 and 5 runs in any given game. When in reality, the team that averages 4.5 R/G is much more likely to score 5+ runs a game, and much less likely to score fewer than 3, than the team with a 4.1 R/G average. This is because of how a distribution centered on a given average interacts with a resolution only in whole runs. A team centered on 4.5 has a much larger portion of their R/G distribution resulting in 5+ R/G than the 4.2 team, and a smaller portion of their distribution resulting in fewer than 4 runs than the 4.2 team.
And that's assuming a normal distribution, using a simple arithmetic mean. I still think a better way to rank offenses is by the harmonic mean of their R/G, as it is likewise a measure of consistency, and a better measure of how likely they are to score about their average. Whereas an arithmetic mean, even over 162 games, can be unduly influenced by one or two games with 12+ runs.
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