diff --git a/src/ecs/Components.ts b/src/ecs/Components.ts
index 3860231..90d79fa 100644
--- a/src/ecs/Components.ts
+++ b/src/ecs/Components.ts
@@ -2,11 +2,23 @@
 import { Layer, SpriteSheet } from "../applet/Render";
 import { Component, copyDense, copySparse, EntityState, StateForSchema, Store } from "./Data";
 
+/**
+ * Nominal type used to remind users to enforce some level
+ * of quantization on numbers kept in game state. This reduces
+ * physics precision in theory, but lets us feel more comfortable
+ * about determinism for rollback physics.
+ */
+export type FixedPoint = number & {_type: "fixed point"};
+
+export function Floor(x: number): FixedPoint {
+    return Math.floor(x) as FixedPoint;
+}
+
 export class Box {
     constructor(
-        public x: number, public y: number,
-        public w: number, public h: number
-    ) {};
+        public x: FixedPoint, public y: FixedPoint,
+        public w: FixedPoint, public h: FixedPoint
+    ) { };
 };
 
 /**
@@ -14,7 +26,7 @@ export class Box {
  */
 export function Approach(source: number, target: number, speed: number): number {
     const delta = target - source;
-    if(Math.abs(delta) <= speed) {
+    if (Math.abs(delta) <= speed) {
         return target;
     } else {
         return source + Math.sign(delta) * speed;
@@ -25,10 +37,10 @@ export function Approach(source: number, target: number, speed: number): number
  * pairs of vertex coordinates in ccw winding order
  */
 export interface Polygon {
-    points: number[];
+    points: FixedPoint[];
 }
 export class PolygonComponent extends Component<PolygonComponent> {
-    points: number[];
+    points: FixedPoint[];
     constructor(from: Partial<PolygonComponent>) {
         super(from);
         this.points = from.points?.slice() ?? []
@@ -39,16 +51,16 @@ export class PolygonComponent extends Component<PolygonComponent> {
 }
 
 export class Location extends Component<Location> {
-    X: number;
-    Y: number;
+    X: FixedPoint;
+    Y: FixedPoint;
     Angle: number;
     VX: number;
     VY: number;
     VAngle: number;
     constructor(from: Partial<Location>) {
         super(from);
-        this.X = from.X ?? 0;
-        this.Y = from.Y ?? 0;
+        this.X = from.X ?? (0 as FixedPoint);
+        this.Y = from.Y ?? (0 as FixedPoint);
         this.Angle = from.Angle ?? 0;
         this.VX = from.VX ?? 0;
         this.VY = from.VY ?? 0;
@@ -90,7 +102,7 @@ export class RenderSprite extends Component<RenderSprite>  {
     public index: number;
     public offsetX: number;
     public offsetY: number;
-    constructor(from: Partial<RenderSprite> & {sheet: SpriteSheet}) {
+    constructor(from: Partial<RenderSprite> & { sheet: SpriteSheet }) {
         super(from);
         this.sheet = from.sheet;
         this.layer = from.layer ?? 1;
diff --git a/src/ecs/Location.ts b/src/ecs/Location.ts
index 9189867..7d87b36 100644
--- a/src/ecs/Location.ts
+++ b/src/ecs/Location.ts
@@ -1,4 +1,4 @@
-import { Data, Location, Polygon } from "./Components";
+import { Data, Floor, Location, Polygon } from "./Components";
 import { Join } from "./Data";
 
 export function TransformCx(cx: CanvasRenderingContext2D, location: Location, dt = 0) {
@@ -9,20 +9,20 @@ export function TransformCx(cx: CanvasRenderingContext2D, location: Location, dt
 export function TfPolygon({points}: Polygon, {X, Y, Angle}: Location): Polygon {
     const sin = Math.sin(Angle);
     const cos = Math.cos(Angle);
-    const result = {points: new Array(points.length)};
+    const result: Polygon = {points: new Array(points.length)};
     for(let i = 0; i < points.length; i += 2) {
         const x = points[i];
         const y = points[i+1];
-        result.points[i] = x*cos - y*sin + X;
-        result.points[i+1] = x*sin + y*cos + Y;
+        result.points[i] = Floor(x*cos - y*sin + X);
+        result.points[i+1] = Floor(x*sin + y*cos + Y);
     }
     return result;
 }
 
 export function DumbMotion(data: Data, interval: number) {
     Join(data, "location").forEach(([location]) => {
-        location.X += location.VX * interval;
-        location.Y += location.VY * interval;
+        location.X = Floor(location.X + location.VX * interval);
+        location.Y = Floor(location.Y + location.VY * interval);
         location.Angle += location.VAngle * interval;
     });
 }
diff --git a/src/ecs/test.ts b/src/ecs/test.ts
index 52f94c0..d41bb6f 100644
--- a/src/ecs/test.ts
+++ b/src/ecs/test.ts
@@ -7,6 +7,7 @@ import {
     CollisionClass,
     ComponentSchema,
     Data,
+    FixedPoint,
     Location,
     PolygonComponent,
     RenderBounds,
@@ -164,11 +165,11 @@ class LoopTest {
         // spinner box
         Create(this.data, {
             location: new Location({
-                X: 200,
-                Y: 200,
+                X: 200 as FixedPoint,
+                Y: 200 as FixedPoint,
                 VAngle: Math.PI
             }),
-            bounds: new PolygonComponent({points: [-50, 50, -60, 250, 60, 250, 50, 50]}),
+            bounds: new PolygonComponent({points: [-50, 50, -60, 250, 60, 250, 50, 50] as FixedPoint[]}),
             collisionTargetClass: new CollisionClass({ name: "block"}),
             renderBounds: new RenderBounds({color: "#0a0", layer: 0}),
         });
@@ -176,12 +177,12 @@ class LoopTest {
         // triangles
         [0, 1, 2, 3, 4, 5].forEach(angle => Create(this.data, {
             location: new Location({
-                X: 200,
-                Y: 200,
+                X: 200 as FixedPoint,
+                Y: 200 as FixedPoint,
                 Angle: angle,
                 VAngle: -Math.PI/10
             }),
-            bounds: new PolygonComponent({points: [70, 0, 55, 40, 85, 40]}),
+            bounds: new PolygonComponent({points: [70, 0, 55, 40, 85, 40] as FixedPoint[]}),
             collisionSourceClass: new CollisionClass({ name: "tri"}),
             renderBounds: new RenderBounds({
                 color: "#d40",
diff --git a/src/game/Death.ts b/src/game/Death.ts
index 25a16d8..318f558 100644
--- a/src/game/Death.ts
+++ b/src/game/Death.ts
@@ -1,5 +1,12 @@
 import { PlaySfx } from "../applet/Audio";
-import { Location, Polygon, PolygonComponent, RenderBounds } from "../ecs/Components";
+import {
+    FixedPoint,
+    Floor,
+    Location,
+    Polygon,
+    PolygonComponent,
+    RenderBounds,
+} from "../ecs/Components";
 import { Create, Id, Join, Lookup, Remove } from "../ecs/Data";
 import { Data, Lifetime, Teams, World } from "./GameComponents";
 
@@ -39,20 +46,20 @@ export function CheckLifetime(data: Data, world: World, interval: number) {
 export function SmokeDamage(data: Data, world: World) {
     Join(data, "hp", "location").forEach(([hp, {X, Y}]) => {
         // convert dealt damage to particles
-        const puffs = Math.floor(hp.receivedDamage / 3);
-        SpawnBlast(data, world, X, Y, 2, "#000", puffs);
-        hp.receivedDamage = Math.floor(hp.receivedDamage % 3);
+        const puffs = Floor(hp.receivedDamage / 3);
+        SpawnBlast(data, world, X, Y, 2 as FixedPoint, "#000", puffs);
+        hp.receivedDamage = Floor(hp.receivedDamage % 3);
     });
 }
 
-function SpawnBlast(data: Data, world: World, x: number, y: number, size: number, color: string, count: number) {
+function SpawnBlast(data: Data, world: World, x: FixedPoint, y: FixedPoint, size: FixedPoint, color: string, count: FixedPoint) {
     for(let puff = 0; puff < count; puff++) {
         const angle = Math.PI * 2 * puff / count;
         SpawnPuff(data, world, x, y, size, color, angle);
     }
 }
 
-function SpawnPuff(data: Data, world: World, x: number, y: number, size: number, color: string, angle: number): Id {
+function SpawnPuff(data: Data, world: World, x: FixedPoint, y: FixedPoint, size: FixedPoint, color: string, angle: number): Id {
     return Create(data, {
         location: new Location({
             X: x,
@@ -65,7 +72,7 @@ function SpawnPuff(data: Data, world: World, x: number, y: number, size: number,
             -size, size,
             size, size,
             size, -size
-        ]}),
+        ] as FixedPoint[]}),
         renderBounds: new RenderBounds({
             color,
             // TODO: work out standard layers
diff --git a/src/game/GameComponents.ts b/src/game/GameComponents.ts
index 74ce06a..59c623a 100644
--- a/src/game/GameComponents.ts
+++ b/src/game/GameComponents.ts
@@ -1,6 +1,6 @@
 import { KeyName } from "../applet/Keyboard";
 import { DrawSet, Layer } from "../applet/Render";
-import { ComponentSchema, Data as EcsData } from "../ecs/Components";
+import { ComponentSchema, Data as EcsData, FixedPoint } from "../ecs/Components";
 import { Component, copySparse, Join, StateForSchema, Store } from "../ecs/Data";
 import { DumbMotion } from "../ecs/Location";
 import { LockstepProcessor, TICK_LENGTH } from "../ecs/Lockstep";
@@ -14,8 +14,8 @@ export enum GamePhase {
 }
 export type RGB = [number, number, number];
 export class World {
-    width = 500;
-    height = 400;
+    width = 500 as FixedPoint;
+    height = 400 as FixedPoint;
 
     /*
      * Core Game Status
@@ -147,14 +147,14 @@ export class Boss extends Component<Boss> {
 }
 
 export class Message extends Component<Message> {
-    targetY = 0;
+    targetY = 0 as FixedPoint;
     layer: number;
     color: string;
     message: string;
     timeout = 3;
     constructor(from: Partial<Message>) {
         super(from);
-        this.targetY = from.targetY ?? 0;
+        this.targetY = from.targetY ?? (0 as FixedPoint);
         this.layer = from.layer ?? 1;
         this.color = from.color ?? "#000";
         this.message = from.message ?? "";
@@ -219,7 +219,7 @@ export class Engine implements LockstepProcessor<KeyName[], KeyName[][], Data> {
                 if (playerInput.indexOf("right") != -1) {
                     dir += 1;
                 }
-                location.VAngle = dir * 0.01;
+                location.VAngle = (dir * 0.01) as FixedPoint;
             }
         });
     }
diff --git a/src/game/Main.ts b/src/game/Main.ts
index c94790c..fa62977 100644
--- a/src/game/Main.ts
+++ b/src/game/Main.ts
@@ -3,7 +3,7 @@ import subscribe from "callbag-subscribe";
 
 import { KeyControl, KeyName } from "../applet/Keyboard";
 import { DrawSet } from "../applet/Render";
-import { Location, PolygonComponent, RenderBounds } from "../ecs/Components";
+import { FixedPoint, Location, PolygonComponent, RenderBounds } from "../ecs/Components";
 import { Create } from "../ecs/Data";
 import { RunRenderBounds } from "../ecs/Renderers";
 import { LockstepClient, Server } from "../net/LockstepClient";
@@ -46,10 +46,10 @@ export class Main extends LockstepClient<KeyName[], KeyName[][], Data> {
                 playerNumber: 0
             }),
             location: new Location({
-                X: 100,
-                Y: 200,
+                X: 100 as FixedPoint,
+                Y: 200 as FixedPoint,
             }),
-            bounds: new PolygonComponent({points: [-30, 0, 30, 0, 0, 40]}),
+            bounds: new PolygonComponent({points: [-30, 0, 30, 0, 0, 40] as FixedPoint[]}),
             renderBounds: new RenderBounds({
                 color: "#a0f",
                 layer: 0
@@ -61,10 +61,10 @@ export class Main extends LockstepClient<KeyName[], KeyName[][], Data> {
                 playerNumber: 1
             }),
             location: new Location({
-                X: 400,
-                Y: 200,
+                X: 400 as FixedPoint,
+                Y: 200 as FixedPoint,
             }),
-            bounds: new PolygonComponent({points: [-30, 0, 30, 0, 0, 40]}),
+            bounds: new PolygonComponent({points: [-30, 0, 30, 0, 0, 40] as FixedPoint[]}),
             renderBounds: new RenderBounds({
                 color: "#f0a",
                 layer: 0
diff --git a/src/game/Message.ts b/src/game/Message.ts
index 6f898b0..95801a8 100644
--- a/src/game/Message.ts
+++ b/src/game/Message.ts
@@ -1,4 +1,5 @@
 import { DrawSet } from "../applet/Render";
+import { Floor } from "../ecs/Components";
 import { Join, Remove } from "../ecs/Data";
 import { TransformCx } from "../ecs/Location";
 import { Data, GamePhase, World } from "./GameComponents";
@@ -22,23 +23,23 @@ export function ArrangeMessages(data: Data, world: World, interval: number) {
     const messages = Join(data, "message", "location");
     messages.sort(([{timeout: timeoutA}, {}], [{timeout: timeoutB}, {}]) => timeoutA - timeoutB);
 
-    let y = world.height / 3;
+    let y = Floor(world.height / 3);
     messages.forEach(([message, location]) => {
         message.targetY = y;
-        y += ADVANCE;
+        y = Floor(y + ADVANCE);
 
         const delta = message.targetY - location.Y;
         if(Math.abs(delta) < 100 * interval) {
             location.Y = message.targetY;
-            location.VY = 0;
+            location.VY = Floor(0);
         } else {
-            location.VY = Math.sign(delta) * 100;
+            location.VY = Floor(Math.sign(delta) * 100);
         }
 
         if(location.X >= world.width / 2 && message.timeout >= 0) {
-            location.X = world.width / 2;
+            location.X = Floor(world.width / 2);
             message.timeout -= interval;
-            location.VX = 0;
+            location.VX = Floor(0);
         } else if(world.phase == GamePhase.PLAYING) {
             location.VX = world.width;
         }