# USTA tiebreak match score distributions

#### beernutz

##### Hall of Fame
This came up in one of the endless USTA NTRP threads and I'd never really thought about it very much so I spent a half hour trying to figure out the various possible score outcomes of a USTA match that would be input into a dynamic NTRP calculation.

Unless I'm way off it looks there there are 168 unique score outcomes if the first and second set scores are interchangeable. By interchangeable I mean that a 6-0, 6-1 win looks the same to the computer as a 6-1, 6-0 win.

I think it is interesting that there are 13 of these 168 scores, for each player, where even though that player wins the match, he or she will lose more games than they win. I am assuming a tiebreak counts as one game and if that is wrong then my differential calculation is wrong.

Feel free to pick it apart.

Anyway, here goes:
Code:
``````	Set 1			Set 2			Tiebreak                Player 1 Game	P2 lose more
#	Player 1Player 2        Player 1 Player 2       Player 1 Player 2 Winner Differential	games but win	Differentials	Count
1	0	6		0	6				Player 2        -12	no	       -12	       1
2	1	6		1	6				Player 2	-10	no	       -11	       1
3	2	6		2	6				Player 2	-8	no	       -10	       2
4	3	6		3	6				Player 2	-6	no	       -9	       2
5	4	6		4	6				Player 2	-4	no	       -8	       4
6	5	7		5	7				Player 2	-4	no	       -7	       4
7	6	7		6	7				Player 2	-2	no	       -6	       5
8	6	0		6	0				Player 1	12	no	       -5	       6
9	6	1		6	1				Player 1	10	no	       -4	       9
10	6	2		6	2				Player 1	8	no	       -3	       10
11	6	3		6	3				Player 1	6	no	       -2	       12
12	6	4		6	4				Player 1	4	no	       -1	       21
13	7	5		7	5				Player 1	4	no	       0	       14
14	7	6		7	6				Player 1	2	no	       1	       21
15	0	6		7	6		1	0	Player 1	-4	no	       2	       12
16	0	6		7	6		0	1	Player 2	-6	no	       3	       10
17	1	6		0	6				Player 2	-11	no	       4	       9
18	2	6		1	6				Player 2	-9	no	       5	       6
19	3	6		2	6				Player 2	-7	no	       6	       5
20	4	6		3	6				Player 2	-5	no	       7	       4
21	5	7		4	6				Player 2	-4	no	       8	       4
22	6	7		5	7				Player 2	-3	no	       9	       2
23	6	0		6	7		1	0	Player 1	6	no	       10	       2
24	6	0		6	7		0	1	Player 2	4	yes	       11	       1
25	6	1		6	0				Player 1	11	no	       12	       1
26	6	2		6	1				Player 1	9	no
27	6	3		6	2				Player 1	7	no		               168
28	6	4		6	3				Player 1	5	no
29	7	5		6	4				Player 1	4	no
30	7	6		7	5				Player 1	3	no
31	0	6		7	5		1	0	Player 1	-3	no
32	0	6		7	5		0	1	Player 2	-5	no
33	1	6		7	6		1	0	Player 1	-3	no
34	1	6		7	6		0	1	Player 2	-5	no
35	2	6		0	6				Player 2	-10	no
36	3	6		1	6				Player 2	-8	no
37	4	6		2	6				Player 2	-6	no
38	5	7		3	6				Player 2	-5	no
39	6	7		4	6				Player 2	-3	no
40	6	0		5	7		1	0	Player 1	5	no
41	6	0		5	7		0	1	Player 2	3	yes
42	6	1		6	7		1	0	Player 1	5	no
43	6	1		6	7		0	1	Player 2	3	yes
44	6	2		6	0				Player 1	10	no
45	6	3		6	1				Player 1	8	no
46	6	4		6	2				Player 1	6	no
47	7	5		6	3				Player 1	5	no
48	7	6		6	4				Player 1	3	no
49	0	6		6	4		1	0	Player 1	-3	no
50	0	6		6	4		0	1	Player 2	-5	no
51	1	6		7	5		1	0	Player 1	-2	no
52	1	6		7	5		0	1	Player 2	-4	no
53	2	6		7	6		1	0	Player 1	-2	no
54	2	6		7	6		0	1	Player 2	-4	no
55	3	6		0	6				Player 2	-9	no
56	4	6		1	6				Player 2	-7	no
57	5	7		2	6				Player 2	-6	no
58	6	7		3	6				Player 2	-4	no
59	6	0		4	6		1	0	Player 1	5	no
60	6	0		4	6		0	1	Player 2	3	yes
61	6	1		5	7		1	0	Player 1	4	no
62	6	1		5	7		0	1	Player 2	2	yes
63	6	2		6	7		1	0	Player 1	4	no
64	6	2		6	7		0	1	Player 2	2	yes
65	6	3		6	0				Player 1	9	no
66	6	4		6	1				Player 1	7	no
67	7	5		6	2				Player 1	6	no
68	7	6		6	3				Player 1	4	no
69	0	6		6	3		1	0	Player 1	-2	no
70	0	6		6	3		0	1	Player 2	-4	no
71	1	6		6	4		1	0	Player 1	-2	no
72	1	6		6	4		0	1	Player 2	-4	no
73	2	6		7	5		1	0	Player 1	-1	no
74	2	6		7	5		0	1	Player 2	-3	no
75	3	6		7	6		1	0	Player 1	-1	no
76	3	6		7	6		0	1	Player 2	-3	no
77	4	6		0	6				Player 2	-8	no
78	5	7		1	6				Player 2	-7	no
79	6	7		2	6				Player 2	-5	no
80	6	0		3	6		1	0	Player 1	4	no
81	6	0		3	6		0	1	Player 2	2	yes
82	6	1		4	6		1	0	Player 1	4	no
83	6	1		4	6		0	1	Player 2	2	yes
84	6	2		5	7		1	0	Player 1	3	no
85	6	2		5	7		0	1	Player 2	1	yes
86	6	3		6	7		1	0	Player 1	3	no
87	6	3		6	7		0	1	Player 2	1	yes
88	6	4		6	0				Player 1	8	no
89	7	5		6	1				Player 1	7	no
90	7	6		6	2				Player 1	5	no
91	0	6		6	2		1	0	Player 1	-1	no
92	0	6		6	2		0	1	Player 2	-3	no
93	1	6		6	3		1	0	Player 1	-1	no
94	1	6		6	3		0	1	Player 2	-3	no
95	2	6		6	4		1	0	Player 1	-1	no
96	2	6		6	4		0	1	Player 2	-3	no
97	3	6		7	5		1	0	Player 1	0	no
98	3	6		7	5		0	1	Player 2	-2	no
99	4	6		7	6		1	0	Player 1	0	no
100	4	6		7	6		0	1	Player 2	-2	no
101	5	7		0	6				Player 2	-8	no
102	6	7		1	6				Player 2	-6	no
103	6	0		2	6		1	0	Player 1	3	no
104	6	0		2	6		0	1	Player 2	1	yes
105	6	1		3	6		1	0	Player 1	3	no
106	6	1		3	6		0	1	Player 2	1	yes
107	6	2		4	6		1	0	Player 1	3	no
108	6	2		4	6		0	1	Player 2	1	yes
109	6	3		5	7		1	0	Player 1	2	no
110	6	3		5	7		0	1	Player 2	0	no
111	6	4		6	7		1	0	Player 1	2	no
112	6	4		6	7		0	1	Player 2	0	no
113	7	5		6	0				Player 1	8	no
114	7	6		6	1				Player 1	6	no
115	0	6		6	1		1	0	Player 1	0	no
116	0	6		6	1		0	1	Player 2	-2	no
117	1	6		6	2		1	0	Player 1	0	no
118	1	6		6	2		0	1	Player 2	-2	no
119	2	6		6	3		1	0	Player 1	0	no
120	2	6		6	3		0	1	Player 2	-2	no
121	3	6		6	4		1	0	Player 1	0	no
122	3	6		6	4		0	1	Player 2	-2	no
123	4	6		7	5		1	0	Player 1	1	no
124	4	6		7	5		0	1	Player 2	-1	no
125	5	7		7	6		1	0	Player 1	0	no
126	5	7		7	6		0	1	Player 2	-2	no
127	6	7		0	6				Player 2	-7	no
128	6	0		1	6		1	0	Player 1	2	no
129	6	0		1	6		0	1	Player 2	0	no
130	6	1		2	6		1	0	Player 1	2	no
131	6	1		2	6		0	1	Player 2	0	no
132	6	2		3	6		1	0	Player 1	2	no
133	6	2		3	6		0	1	Player 2	0	no
134	6	3		4	6		1	0	Player 1	2	no
135	6	3		4	6		0	1	Player 2	0	no
136	6	4		5	7		1	0	Player 1	1	no
137	6	4		5	7		0	1	Player 2	-1	no
138	7	5		6	7		1	0	Player 1	2	no
139	7	5		6	7		0	1	Player 2	0	no
140	7	6		6	0				Player 1	7	no
141	0	6		6	0		1	0	Player 1	1	no
142	0	6		6	0		0	1	Player 2	-1	no
143	1	6		6	1		1	0	Player 1	1	no
144	1	6		6	1		0	1	Player 2	-1	no
145	2	6		6	2		1	0	Player 1	1	no
146	2	6		6	2		0	1	Player 2	-1	no
147	3	6		6	3		1	0	Player 1	1	no
148	3	6		6	3		0	1	Player 2	-1	no
149	4	6		6	4		1	0	Player 1	1	no
150	4	6		6	4		0	1	Player 2	-1	no
151	5	7		7	5		1	0	Player 1	1	no
152	5	7		7	5		0	1	Player 2	-1	no
153	6	7		7	6		1	0	Player 1	1	no
154	6	7		7	6		0	1	Player 2	-1	no
155	6	0		0	6		1	0	Player 1	1	no
156	6	0		0	6		0	1	Player 2	-1	no
157	6	1		1	6		1	0	Player 1	1	no
158	6	1		1	6		0	1	Player 2	-1	no
159	6	2		2	6		1	0	Player 1	1	no
160	6	2		2	6		0	1	Player 2	-1	no
161	6	3		3	6		1	0	Player 1	1	no
162	6	3		3	6		0	1	Player 2	-1	no
163	6	4		4	6		1	0	Player 1	1	no
164	6	4		4	6		0	1	Player 2	-1	no
165	7	5		5	7		1	0	Player 1	1	no
166	7	5		5	7		0	1	Player 2	-1	no
167	7	6		6	7		1	0	Player 1	1	no
168	7	6		6	7		0	1	Player 2	-1	no``````

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