Match count (byte)

Fit to analytical expectation

Expected distribution assumes MD5 acts like a random function. The matching-byte count is Binomial(16, 1/256): each of the 16 output bytes matches its input byte independently with probability 1/256.

Expected (now) scales that analytical distribution to the hashes computed so far; Expected (end) scales it to the full 2¹²⁸ keyspace. Residual is the Pearson residual (Observed − Expected) / √Expected in units of σ. A p-value near 1 means the observed distribution is consistent with random; near 0 means it is statistically surprising.

Distribution moments

	Observed	Expected
Mean	0.062	0.063
Std. deviation	0.250	0.250

Pearson χ² test

Samples	6,074,724,434,051,072
Reduced χ²	0.146
Degrees of freedom	7
p-value	0.994

Per-bucket detail

Bucket	Observed	Expected (now)	Expected (end)	Residual
0	5,705,977,103,804,776	5,705,977,093,983,813	319,626,579,315,078,477,702,860,203,058,987,532,288	+0.13σ
1	358,022,084,304,181	358,022,092,171,535	20,055,001,055,063,831,456,466,004,705,206,599,680	−0.42σ
2	10,530,059,607,397	10,530,061,534,457	589,852,972,207,761,198,416,652,048,739,074,048	−0.59σ
3	192,706,994,338	192,707,008,474	10,794,694,916,220,392,661,616,333,793,787,904	−0.03σ
4	2,456,059,896	2,456,069,716	137,579,445,010,652,283,251,277,038,616,576	−0.20σ
5	23,113,256	23,115,950	1,294,865,364,806,139,908,717,484,703,744	−0.56σ
6	166,300	166,193	9,309,489,550,893,809,600,699,564,032	+0.26σ
7	926	931	52,154,003,086,240,170,526,113,792	−0.17σ
8	2	4	230,091,190,086,352,270,000,128	−1.04σ
9	0	0	802,060,793,329,338,155,008	−0.12σ
10	0	0	2,201,735,511,100,130,816	−0.01σ
11	0	0	4,709,594,676,149,986	−0.00σ
12	0	0	7,695,416,137,500	−0.00σ
13	0	0	9,285,570,000	−0.00σ
14	0	0	7,803,000	−0.00σ
15	0	0	4,080	−0.00σ
16	0	0	1	−0.00σ