Important expectation-calibration note: I'm not making any claims about teacher performance, the usefulness of the value-added idea, or any lofty topics in general. I'm just trying to figure out how to recreate the first graph in the initial posting and get a closer look at the data behind it.

I grabbed the data set [1], loaded it into R, and tried to recreate the first graph in the original post. Observations:

1. The value-added scores are quantized so, as some people have suggested, it's hard to see the true density relationships in the original plot. There's a lot of overlapping data points.

2. I re-plotted the data using jittering to more accurately show the density distribution. I also added a GAM smoother to show the trend. Result: https://docs.google.com/file/d/0B2Tqdso8AsFNS3lWQTdPUGpHZlk/...

3. I also plotted the change in each teacher's value-added score from one year to the next. The resulting histogram: https://docs.google.com/file/d/0B2Tqdso8AsFNeUNiM3hHUGwzdlk/...

4. If we model the relationship as next_year_value_added = this_year_value_added + random_error, here's the fitted model:

    Call:
    lm(formula = va_0910 ~ va_0809, data = ds_cmp)

    Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
    (Intercept) 0.009157   0.002315   3.956 7.67e-05 ***
    va_0809     0.820085   0.017646  46.475  < 2e-16 ***
    ---
    Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

    Residual standard error: 0.2153 on 8691 degrees of freedom
    Multiple R-squared: 0.1991,	Adjusted R-squared: 0.199 
    F-statistic:  2160 on 1 and 8691 DF,  p-value: < 2.2e-16 

If you want to see exactly what I did, I threw my R code and the data sets up on GitHub: https://github.com/tmoertel/nyva-cursory

[1] http://www.ny1.com/content/top_stories/156599/now-available-...