First R program run.

> nams(x=ncaa2[,1:19],y=ncaa2[,20],B=4000,seed=34)->out
   var   pval  pvmax
1    2 0.0000 0.0000
2    3 0.0001 0.0001
3    5 0.0116 0.0116
4    4 0.0053 0.0116
5    7 0.0025 0.0116
6   17 0.0433 0.0433
7   15 0.0527 0.0527
8    6 0.1056 0.1056
9    9 0.0826 0.1056
10   8 0.0536 0.1056
11  12 0.2350 0.2350
12  10 0.2864 0.2864
13  13 0.3163 0.3163
14  18 0.2697 0.3163
15  11 0.4953 0.4953
16   1 0.6326 0.6326
17  14 0.7056 0.7056
18  19 0.8605 0.8605
19  16 0.9032 0.9032
   m  n    B seed      tau ng   alphahat
1 19 94 4000   34 6.847734 74 0.03802676

Variables Selected = x2 x3 x5 x4 x7

The program selected alpha=.038 because there is a local max
at alpha index=20, and alpha[21]=.038. The first 30 slopes 
and alphas are below and confirm that.

Here is the same run and seed using the second program. We
suppress the printing of p-values.

> nams2(x=ncaa2[,1:19],y=ncaa2[,20],B=4000,seed=34,print=F)->out
   m  n    B seed      tau ng   alphahat alpha.index
1 19 94 4000   34 6.847734 74 0.00966541          16

Variables Selected = x2 x3
 
So this second program chooses an alpha that is too small because it does
not consider local maxima.  In Monte Carlo runs, this problem seems to
be fairly minor.

Some alphas and slopes:

> data.frame(alpha=round(out$alpha,3),slope=out$slope)[1:30,]
   alpha    slope
1  0.000 46.80076
2  0.000 46.80076
3  0.000 46.80076
4  0.000 46.80076
5  0.000 46.80076
6  0.000 46.80076
7  0.000 46.91300
8  0.000 47.32895
9  0.000 47.69292
10 0.000 47.96412
11 0.000 48.16979
12 0.002 49.06924
13 0.004 48.12386
14 0.006 47.61976
15 0.008 47.17240
16 0.010 46.94845
17 0.017 46.72706
18 0.022 46.77776
19 0.027 46.88092
20 0.033 46.97705
21 0.038 46.92536
22 0.045 46.81071
23 0.046 46.81524
24 0.048 46.77506
25 0.050 46.72071
26 0.051 46.69242
27 0.062 46.46548
28 0.070 46.15943
29 0.079 45.79370
30 0.088 45.56822
> data.frame(alpha=round(out$alpha,3),slope=out$slope)[74,]
   alpha    slope
74     1 46.97743