diff --git a/src/ballistics.cpp b/src/ballistics.cpp
index 6c3a80944feb..74767bf8caff 100644
--- a/src/ballistics.cpp
+++ b/src/ballistics.cpp
@@ -10,6 +10,7 @@
 
 #include "avatar.h"
 #include "calendar.h"
+#include "cata_utility.h" // for normal_cdf
 #include "creature.h"
 #include "damage.h"
 #include "debug.h"
@@ -455,3 +456,25 @@ dealt_projectile_attack projectile_attack( const projectile &proj_arg, const tri
 
     return attack;
 }
+
+namespace ranged
+{
+
+double hit_chance( const dispersion_sources &dispersion, double range, double target_size,
+                   double missed_by )
+{
+    if( range <= 0 ) {
+        return 1.0;
+    }
+
+    double missed_by_tiles = missed_by * target_size;
+
+    //          T = (2*D**2 * (1 - cos V)) ** 0.5   (from iso_tangent)
+    //      cos V = 1 - T**2 / (2*D**2)
+    double cosV = 1 - missed_by_tiles * missed_by_tiles / ( 2 * range * range );
+    double needed_dispersion = ( cosV < -1.0 ? M_PI : acos( cosV ) ) * 180 * 60 / M_PI;
+
+    return normal_cdf( needed_dispersion, dispersion.avg(), dispersion.avg() / 2 );
+}
+
+}
diff --git a/src/ballistics.h b/src/ballistics.h
index b77ea40ef5c6..00936a77ac3d 100644
--- a/src/ballistics.h
+++ b/src/ballistics.h
@@ -34,4 +34,20 @@ dealt_projectile_attack projectile_attack( const projectile &proj_arg, const tri
         const tripoint &target_arg, const dispersion_sources &dispersion,
         Creature *origin = nullptr, const vehicle *in_veh = nullptr );
 
+namespace ranged
+{
+
+/**
+ * The chance that a fired shot reaches required accuracy - by default grazing shot.
+ *
+ * @param dispersion accuracy of the shot. Must be a purely normal distribution.
+ * @param range distance between the shooter and the target.
+ * @param target_size size of the target, in the range (0, 1].
+ * @param missed_by maximum degree of miss, in the range (0, 1]. Effectively a multiplier on @param target_size.
+ */
+double hit_chance( const dispersion_sources &dispersion, double range, double target_size,
+                   double missed_by = 1.0 );
+
+} // namespace ranged
+
 #endif // CATA_SRC_BALLISTICS_H
diff --git a/src/cata_utility.cpp b/src/cata_utility.cpp
index 1264b6289e94..337fa9e324d1 100644
--- a/src/cata_utility.cpp
+++ b/src/cata_utility.cpp
@@ -173,6 +173,11 @@ double logarithmic_range( int min, int max, int pos )
     return ( raw_logistic - LOGI_MIN ) / LOGI_RANGE;
 }
 
+double normal_cdf( double x, double mean, double stddev )
+{
+    return 0.5 * ( 1.0 + std::erf( ( x - mean ) / ( stddev * M_SQRT2 ) ) );
+}
+
 int bound_mod_to_vals( int val, int mod, int max, int min )
 {
     if( val + mod > max && max != 0 ) {
diff --git a/src/cata_utility.h b/src/cata_utility.h
index 402bf684f373..0a39a08269a7 100644
--- a/src/cata_utility.h
+++ b/src/cata_utility.h
@@ -130,6 +130,17 @@ double logarithmic( double t );
  */
 double logarithmic_range( int min, int max, int pos );
 
+/**
+ * Cumulative distribution function of a certain normal distribution.
+ *
+ * @param x point at which the CDF of the distribution is measured
+ * @param mean mean of the normal distribution
+ * @param stddev standard deviation of the normal distribution
+ *
+ * @return The probability that a random point from the distribution will be lesser than @param x
+ */
+double normal_cdf( double x, double mean, double stddev );
+
 /**
  * Clamp the value of a modifier in order to bound the resulting value
  *
diff --git a/tests/throwing_test.cpp b/tests/throwing_test.cpp
index 1abbc7e144d8..6e8b2236f57d 100644
--- a/tests/throwing_test.cpp
+++ b/tests/throwing_test.cpp
@@ -6,9 +6,11 @@
 #include <vector>
 
 #include "avatar.h"
+#include "ballistics.h"
 #include "calendar.h"
 #include "catch/catch.hpp"
 #include "damage.h"
+#include "dispersion.h"
 #include "game.h"
 #include "game_constants.h"
 #include "inventory.h"
@@ -105,6 +107,19 @@ static void test_throwing_player_versus(
         monster &mon = spawn_test_monster( mon_id, monster_start );
         mon.set_moves( 0 );
 
+        double actual_hit_chance = ranged::hit_chance(
+                                       dispersion_sources( p.throwing_dispersion( it, &mon ) ),
+                                       range, mon.ranged_target_size() );
+        if( std::fabs( actual_hit_chance - hit_thresh.midpoint ) > hit_thresh.epsilon / 2.0 ) {
+            CAPTURE( hit_thresh.midpoint );
+            CAPTURE( hit_thresh.epsilon / 2.0 );
+            CAPTURE( actual_hit_chance );
+            CAPTURE( range );
+            CAPTURE( mon.ranged_target_size() );
+            FAIL_CHECK( "Expected and calculated midpoints must be within epsilon/2 or the test is too fragile" );
+            return;
+        }
+
         auto atk = p.throw_item( mon.pos(), it );
         data.hits.add( atk.hit_critter != nullptr );
         data.dmg.add( atk.dealt_dam.total_damage() );
@@ -175,16 +190,16 @@ TEST_CASE( "basic_throwing_sanity_tests", "[throwing],[balance]" )
         test_throwing_player_versus( p, "mon_zombie", "rock", 5, lo_skill_base_stats, { 0.77, 0.10 }, { 5.5, 2 } );
         test_throwing_player_versus( p, "mon_zombie", "rock", 10, lo_skill_base_stats, { 0.27, 0.10 }, { 2, 2 } );
         test_throwing_player_versus( p, "mon_zombie", "rock", 15, lo_skill_base_stats, { 0.13, 0.10 }, { 1, 2 } );
-        test_throwing_player_versus( p, "mon_zombie", "rock", 20, lo_skill_base_stats, { 0.03, 0.10 }, { 0.5, 2 } );
+        test_throwing_player_versus( p, "mon_zombie", "rock", 20, lo_skill_base_stats, { 0.095, 0.10 }, { 0.5, 2 } );
         test_throwing_player_versus( p, "mon_zombie", "rock", 25, lo_skill_base_stats, { 0.03, 0.10 }, { 0.5, 2 } );
-        test_throwing_player_versus( p, "mon_zombie", "rock", 30, lo_skill_base_stats, { 0.03, 0.10 }, { 0.5, 2 } );
+        test_throwing_player_versus( p, "mon_zombie", "rock", 30, lo_skill_base_stats, { 0.06, 0.10 }, { 0.5, 2 } );
     }
 
     SECTION( "test_player_vs_zombie_javelin_iron_basestats" ) {
-        test_throwing_player_versus( p, "mon_zombie", "javelin_iron", 1, lo_skill_base_stats, { 0.95, 0.10 }, { 28, 5 } );
+        test_throwing_player_versus( p, "mon_zombie", "javelin_iron", 1, lo_skill_base_stats, { 1.00, 0.10 }, { 28, 5 } );
         test_throwing_player_versus( p, "mon_zombie", "javelin_iron", 5, lo_skill_base_stats, { 0.64, 0.10 }, { 13, 3 } );
         test_throwing_player_versus( p, "mon_zombie", "javelin_iron", 10, lo_skill_base_stats, { 0.20, 0.10 }, { 4, 2 } );
-        test_throwing_player_versus( p, "mon_zombie", "javelin_iron", 15, lo_skill_base_stats, { 0.03, 0.10 }, { 1.29, 3 } );
+        test_throwing_player_versus( p, "mon_zombie", "javelin_iron", 15, lo_skill_base_stats, { 0.11, 0.10 }, { 1.29, 3 } );
         test_throwing_player_versus( p, "mon_zombie", "javelin_iron", 20, lo_skill_base_stats, { 0.03, 0.10 }, { 1.66, 2 } );
         test_throwing_player_versus( p, "mon_zombie", "javelin_iron", 25, lo_skill_base_stats, { 0.03, 0.10 }, { 1.0, 2 } );
     }
@@ -195,7 +210,7 @@ TEST_CASE( "basic_throwing_sanity_tests", "[throwing],[balance]" )
         test_throwing_player_versus( p, "mon_zombie", "rock", 10, hi_skill_athlete_stats, { 1.00, 0.10 }, { 16.27, 6 } );
         test_throwing_player_versus( p, "mon_zombie", "rock", 15, hi_skill_athlete_stats, { 0.97, 0.10 }, { 12.83, 4 } );
         test_throwing_player_versus( p, "mon_zombie", "rock", 20, hi_skill_athlete_stats, { 0.82, 0.10 }, { 9.10, 4 } );
-        test_throwing_player_versus( p, "mon_zombie", "rock", 25, hi_skill_athlete_stats, { 0.64, 0.10 }, { 6.54, 4 } );
+        test_throwing_player_versus( p, "mon_zombie", "rock", 25, hi_skill_athlete_stats, { 0.58, 0.10 }, { 6.54, 4 } );
         test_throwing_player_versus( p, "mon_zombie", "rock", 30, hi_skill_athlete_stats, { 0.47, 0.10 }, { 4.90, 3 } );
     }
 
@@ -205,7 +220,7 @@ TEST_CASE( "basic_throwing_sanity_tests", "[throwing],[balance]" )
         test_throwing_player_versus( p, "mon_zombie", "javelin_iron", 10, hi_skill_athlete_stats, { 1.00, 0.10 }, { 34.16, 8 } );
         test_throwing_player_versus( p, "mon_zombie", "javelin_iron", 15, hi_skill_athlete_stats, { 0.97, 0.10 }, { 25.21, 6 } );
         test_throwing_player_versus( p, "mon_zombie", "javelin_iron", 20, hi_skill_athlete_stats, { 0.82, 0.10 }, { 18.90, 5 } );
-        test_throwing_player_versus( p, "mon_zombie", "javelin_iron", 25, hi_skill_athlete_stats, { 0.63, 0.10 }, { 13.59, 5 } );
+        test_throwing_player_versus( p, "mon_zombie", "javelin_iron", 25, hi_skill_athlete_stats, { 0.58, 0.10 }, { 13.59, 5 } );
         test_throwing_player_versus( p, "mon_zombie", "javelin_iron", 30, hi_skill_athlete_stats, { 0.48, 0.10 }, { 10.00, 4 } );
     }
 }
@@ -220,7 +235,7 @@ TEST_CASE( "throwing_skill_impact_test", "[throwing],[balance]" )
     // the throwing skill has while the sanity tests are more explicit.
     SECTION( "mid_skill_basestats_rock" ) {
         test_throwing_player_versus( p, "mon_zombie", "rock", 5, mid_skill_base_stats, { 1.00, 0.10 }, { 12, 6 } );
-        test_throwing_player_versus( p, "mon_zombie", "rock", 10, mid_skill_base_stats, { 0.86, 0.10 }, { 7, 4 } );
+        test_throwing_player_versus( p, "mon_zombie", "rock", 10, mid_skill_base_stats, { 0.92, 0.10 }, { 7, 4 } );
         test_throwing_player_versus( p, "mon_zombie", "rock", 15, mid_skill_base_stats, { 0.62, 0.10 }, { 5, 2 } );
     }