If your smoothing constant is 0.1, I think that’s *waaay* too smooth. If you want *N* previous values to be included in a moving average, you set your smoothing constant to 2/(N+1). A smoothing constant of 0.1 means

0.1 = 2/(N+1)

0.1N + 0.1 = 2

0.1N = 1.9

N = 19

so nearly three weeks are being averaged into each datapoint.

If you want to include 7 days, set ⍺ = 0.25, or if you want it to include 14 days, set ⍺ = 0.13.

### Why ⍺ = 0.25 is better for these purposes

With an EWMA, if you have a constant rate of change, the change in the moving average should eventually converge on the raw rate of change. So if you have a goal to lose 0.1 lbs per day and you lose exactly 0.1lbs per day, eventually, the value of any day’s EWMA should be 0.1 less than the previous day’s value.

If you are 200lbs on *Day 0* and you lose 0.1lb every day after that, we’ll have these values with `⍺ = 0.1`

:

```
| Day | Weight | Wt. Δ | EMA Value | EMA Δ
| 75 | 192.5 | -0.1 | 193.39967 |
| 76 | 192.4 | -0.1 | 193.29970 | -.09997
| 77 | 192.3 | -0.1 | 193.19973 | -.09997
```

But with `⍺ = 0.25`

, we’ll have:

```
| Day | Weight | Wt. Δ | EMA Value | EMA Δ
| 30 | 197.0 | -0.1 | 197.29994 |
| 31 | 196.9 | -0.1 | 197.19995 | -.09999
| 32 | 196.8 | -0.1 | 197.09996 | -.09999
...
| 39 | 196.1 | -0.1 | 196.40000 |
| 40 | 196.0 | -0.1 | 196.30000 | -.10000
```

What this means is that with a smoothing constant of 0.1, we don’t even hit convergence to five decimal points after 77 days; with 0.25, we hit it after 40.

This also has further implications for what the graph will look like. With a smoothing rate of 0.25 and a constant weight loss of 0.1lbs per day, the EWMA would always be 0.3lbs above any day’s datapoint past the 40 day mark. In contrast, a smoothing constant of 0.1 and weight loss of 0.1lbs per day will have an EWMA graph that’s 0.9lbs above the datapoint each day.

So, in conclusion, 19 days is a lot of datapoints to factor into a moving average, and a 75+ day lag for the EWMA rate of change to converge on the raw rate of change is a *reeeeeally* long time.