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Does tougher weather in one shotgun round provide higher ratings for the same score shot on the same layout during calmer conditions in the other round on the same day?

Sometimes. Once the tournament scores and report are submitted to the PDGA, a preliminary SSA is calculated for each round. Then, the software compares these preliminary SSAs. If these two SSAs are statistically far enough apart, each round will get separate official ratings because the software identified a statistical difference in playing conditions between rounds. However, in most events these preliminary SSAs are close enough that they will be combined to produce a single official SSA so everyone gets the same rating for the same score in both rounds.