accurate), using the notion of 2 teams having a face-to-face winning percentage against each other in proportion to a "quality" measure. His quality measure was half the team's "wins ratio" (or "odds of winning"). The wins ratio or odds of winning is the ratio of the team's wins against the league to its losses against the league. [James did not seem aware at the time that his quality measure was expressible in terms of the wins ratio. Since in the quality model any constant factor in a quality measure eventually cancels, the quality measure is today better taken as simply the wins ratio itself, rather than half of it.] He then stated that the Pythagorean formula, which he had earlier developed empirically, for predicting winning percentage from runs, was "the same thing" as the log5 formula, though without a convincing demonstration or proof. His purported demonstration that they were the same boiled down to showing that the two different formulas simplified to the same expression in a special case, which is itself treated vaguely, and there is no recognition that the special case is not the general one. Nor did he subsequently promulgate to the public any explicit, quality-based model for the Pythagorean formula. As of 2013, there is still little public awareness in the sabermetric community that a simple "teams win in proportion to quality" model, using the runs ratio as the quality measure, leads directly to James's original Pythagorean formula. In the 1981 Abstract, James also says that he had first tried to create a "log5" formula by simply using the winning percentages of the teams in place of the runs in the Pythagorean formula, but that it did not give valid results. The reason, unknown to James at the time, is that his attempted formulation implies that the relative quality of teams is given by the ratio of their winning percentages. Yet this cannot be true if teams win in proportion to their quality, since a .900 team wins against its opponents, whose overall winning percentage is roughly .500, in a 9 to 1 ratio, rather than the 9 to 5 ratio of their .900 to .500 winning percentages. The empirical failure of his attempt led to his eventual, more circuitous (and ingenious) and successful approach to log5, which still used quality considerations, though without a full appreciation of the ultimate simplicity of the model and of