# What a flow score means

A note on the **flow index** from the Week 2 activity sheet (page 2) and the Gap Flow demo.

## How it is worked out

Each player rates three statements from 1 (not at all) to 7 (completely):

| Item | Statement | Direction |
|---|---|---|
| F1 | The challenge matched my skill. | higher = more flow |
| F2 | I lost track of time. | higher = more flow |
| F3 | I was aware of what was going on around me. | **reversed**: higher = *less* flow |

F3 is reversed, so it is flipped before averaging (8 − F3 turns a 7 into a 1 and a 1 into a 7):

**Flow index = (F1 + F2 + (8 − F3)) ÷ 3**

## Highest and lowest

| | F1 | F2 | F3 | Flow index |
|---|---|---|---|---|
| **Highest possible** | 7 | 7 | 1 | (7 + 7 + 7) ÷ 3 = **7** |
| **Lowest possible** | 1 | 1 | 7 | (1 + 1 + 1) ÷ 3 = **1** |
| Neutral midpoint | 4 | 4 | 4 | (4 + 4 + 4) ÷ 3 = **4** |

So the scale runs **1 to 7**, with **4** as the middle.

## Is high good or bad?

**High is more flow.** A score near 7 means the player felt the challenge matched their skill, lost track of
time and stopped noticing the room: the absorbed state Csikszentmihalyi describes. A score near 1 means the
opposite: a mismatch between challenge and skill (too hard or too easy), time dragging, and the room
getting in the way.

For this module, when we are designing for engagement, higher is what we are aiming for. Three cautions:

- **It is a feeling, not performance.** A player can score high flow and still sit down early, or play well
  and score low. That is why the sheet also records time in and the recorder's times.
- **Low is not always a design failure.** A horror game may want you anxious and aware; a menu screen does
  not need flow. Ask whether the score matches the experience you intended.
- **Compare, don't grade.** The useful number is the change for the same person between rounds (B against C),
  not one player's score against another's. People use rating scales differently.

As a rough rule of thumb for class discussion (not validated norms): about **5 and above** is strong flow,
**3 to 5** is mixed, and **below 3** means something is breaking it.

## The related numbers

- **Time distortion = estimated time ÷ actual time.** Below 1 = time flew (a sign of flow); above 1 = it dragged.
- **Distraction cost = (B − C) ÷ B**, using the flow index from Round B (ramp) and Round C (ramp + distractors).
  A positive result means the distractors cost flow; we write it as a drop, e.g. 0.59 → "flow −59%".

**Worked example (P01 on the slides):** Round B = 6, 5, 2 → (6 + 5 + 6) ÷ 3 = **5.7**.
Round C = 3, 2, 6 → (3 + 2 + 2) ÷ 3 = **2.3**. Distraction cost = (5.7 − 2.3) ÷ 5.7 = 0.59, so **flow −59%**.

## In the Gap Flow demo

The demo's results page uses the same formula and scale from the one-button card after each round. It also shows
**time in channel**, the share of the round (0–100%) that the game's own model placed you inside the flow channel.
That is the game's estimate from your play, not your self-report, so it is worth comparing the two.

*The flow index is a teaching shortcut, not a validated instrument. For real studies use the Flow Short Scale
(Rheinberg et al., 2003), the IEQ (Jennett et al., 2008) or the GEQ (IJsselsteijn et al., 2013).*