diff --git a/hlink/linking/core/threshold.py b/hlink/linking/core/threshold.py
index b0523d3..d5cd5ba 100644
--- a/hlink/linking/core/threshold.py
+++ b/hlink/linking/core/threshold.py
@@ -94,38 +94,44 @@ def _apply_threshold_ratio(
             'In order to calculate the threshold ratio based on probabilities, you need to have a "probability" column in your data.'
         )
 
-    windowSpec = Window.partitionBy(df[id_a]).orderBy(
-        df["probability"].desc(), df[id_b]
-    )
+    windowSpec = Window.partitionBy(id_a).orderBy(col("probability").desc(), id_b)
     prob_rank = rank().over(windowSpec)
-    prob_lead = lead(df["probability"], 1).over(windowSpec)
+    prob_lead = lead("probability", 1).over(windowSpec)
+
+    should_compute_probability_ratio = (
+        col("second_best_prob").isNotNull()
+        & (col("second_best_prob") >= alpha_threshold)
+        & (col("prob_rank") == 1)
+    )
+    # To be a match, the row must...
+    # 1. Have prob_rank 1, so that it's the most likely match,
+    # 2. Have a probability of at least alpha_threshold,
+    # and
+    # 3. Either have no ratio (since there's no second best probability of at
+    #    least alpha_threshold), or have a ratio of more than threshold_ratio.
+    is_match = (
+        (col("probability") >= alpha_threshold)
+        & (col("prob_rank") == 1)
+        & ((col("ratio") > threshold_ratio) | col("ratio").isNull())
+    )
     return (
         df.select(
-            df["*"],
+            "*",
             prob_rank.alias("prob_rank"),
             prob_lead.alias("second_best_prob"),
         )
-        .selectExpr(
+        .select(
             "*",
-            f"""
-        IF(
-          second_best_prob IS NOT NULL
-          AND second_best_prob >= {alpha_threshold}
-          AND prob_rank == 1,
-          probability / second_best_prob,
-          NULL)
-        AS ratio
-        """,
+            when(
+                should_compute_probability_ratio,
+                col("probability") / col("second_best_prob"),
+            )
+            .otherwise(None)
+            .alias("ratio"),
         )
-        .selectExpr(
+        .select(
             "*",
-            f"""
-        CAST(
-            probability >= {alpha_threshold}
-        AND prob_rank == 1
-        AND (ratio > {threshold_ratio} OR ratio IS NULL)
-        AS INT) AS prediction
-        """,
+            is_match.cast("integer").alias("prediction"),
         )
         .drop("prob_rank")
     )