```xml <result> <column_name>home_score</column_name> <family>additive</family> <subtype>intensive_additive</subtype> <confidence>0.85</confidence> <requires_user_confirmation>false</requires_user_confirmation> <sum_meaningful>false</sum_meaningful> <signed>false</signed> <reducers> <primary_reducer>mean</primary_reducer> <valid_reducers>mean, min, max, median, mode, distribution</valid_reducers> <excluded_reducers>sum (summing scores across entities is meaningless), product (not a ratio)</excluded_reducers> <average_semantics>arithmetic_mean</average_semantics> </reducers> <inner_outer_measure> <inner_measure_reducer>min</inner_measure_reducer> <outer_measure_reducer>max</outer_measure_reducer> </inner_outer_measure> <multiplicative_partner_derivable>false</multiplicative_partner_derivable> <reasoning> Gate prior: DIMENSION table with no sequence axis makes multiplicative highly implausible. The column name "home_score" indicates a game outcome level (an intensive quantity), not an extensive accumulation. The data is bounded [0, 10], non-negative with 21.6% zeros, mean 1.78, median 1.0 - characteristic of a discrete score level, not a ratio near 1.0 or an unbounded extensive quantity. Summing scores across different games/entities is meaningless; averaging is the natural aggregation. Classified as intensive_additive with high confidence. </reasoning> <table_type_conflict>false</table_type_conflict> </result> ```