diff --git a/milli/src/search/new/ranking_rule_graph/fid/mod.rs b/milli/src/search/new/ranking_rule_graph/fid/mod.rs
index e3ccf23fa..4832aa532 100644
--- a/milli/src/search/new/ranking_rule_graph/fid/mod.rs
+++ b/milli/src/search/new/ranking_rule_graph/fid/mod.rs
@@ -68,13 +68,38 @@ impl RankingRuleGraphTrait for FidGraph {
         }
 
         let mut edges = vec![];
-        for fid in all_fields {
+        for fid in all_fields.iter().copied() {
             edges.push((
                 fid as u32 * term.term_ids.len() as u32,
                 conditions_interner.insert(FidCondition { term: term.clone(), fid }),
             ));
         }
 
+        // always lookup the max_fid if we don't already and add an artificial condition for max scoring
+        let max_fid: Option<u16> = {
+            if let Some(max_fid) = ctx
+                .index
+                .searchable_fields_ids(ctx.txn)?
+                .map(|field_ids| field_ids.into_iter().max())
+            {
+                max_fid
+            } else {
+                ctx.index.fields_ids_map(ctx.txn)?.ids().max()
+            }
+        };
+
+        if let Some(max_fid) = max_fid {
+            if !all_fields.contains(&max_fid) {
+                edges.push((
+                    max_fid as u32 * term.term_ids.len() as u32, // TODO improve the fid score i.e. fid^10.
+                    conditions_interner.insert(FidCondition {
+                        term: term.clone(), // TODO remove this ugly clone
+                        fid: max_fid,
+                    }),
+                ));
+            }
+        }
+
         Ok(edges)
     }
 }
diff --git a/milli/src/search/new/ranking_rule_graph/position/mod.rs b/milli/src/search/new/ranking_rule_graph/position/mod.rs
index d364112d3..c6fd3e302 100644
--- a/milli/src/search/new/ranking_rule_graph/position/mod.rs
+++ b/milli/src/search/new/ranking_rule_graph/position/mod.rs
@@ -93,8 +93,10 @@ impl RankingRuleGraphTrait for PositionGraph {
             positions_for_costs.entry(cost).or_default().push(position);
         }
 
-        let mut edges = vec![];
+        let max_cost = term.term_ids.len() as u32 * 10;
+        let max_cost_exists = positions_for_costs.contains_key(&max_cost);
 
+        let mut edges = vec![];
         for (cost, positions) in positions_for_costs {
             edges.push((
                 cost,
@@ -102,6 +104,15 @@ impl RankingRuleGraphTrait for PositionGraph {
             ));
         }
 
+        if !max_cost_exists {
+            // artificial empty condition for computing max cost
+            edges.push((
+                max_cost,
+                conditions_interner
+                    .insert(PositionCondition { term: term.clone(), positions: Vec::default() }),
+            ));
+        }
+
         Ok(edges)
     }
 }