"significant difference"
The answer to your question is that it depends on how widely spaced are the teams with respect to overall ability. If they are closely bunched, it will take more games to accurately determine their relative positions. If there are big differences, fewer games will be needed. This is a basic question in the field of statistics and relates to what is called statistical power (the probability of detecting true differences). With smaller true differences, a bigger sample size is needed to detect them. This is a very strong relationship.
The interesting question would be, in baseball what is the specific relation between team differences and number of games needed to detect them? It would be somewhat complicated to answer that one.
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