I looked at the probability that scoring a given goal led to a win in regulation. I am using the RTSS files to pull the various leads. I went through every game from 200708 through 201213. Winning teams scored 24565 of the 36804 total goals, or 0.6674546. However, the probability that winning teams scored any particular goal goes down as the total score goes up:
Goal 
Won 
Lost 
Prob 
1 
4658 
2147 
0.684 
2 
4532 
2126 
0.681 
3 
4133 
2033 
0.670 
4 
3639 
1831 
0.665 
5 
2768 
1501 
0.648 
6 
2054 
1080 
0.655 
7 
1273 
699 
0.646 
8 
774 
408 
0.655 
9 
393 
218 
0.643 
10+ 
341 
196 
0.636 
So the notion that the winning team scores 66.7% of every goal goes out the window. Why?
Let's define the "value" of a goal as the amount it increases your chance of winning. Not all goals have equal value. There are 4 basic types of goals: goals that break ties, goals that extend leads, goals that create ties, and goals that cut deficits. Graphically, the value of a lead looks like:
The most valuable goals break ties or create ties. The other goals are less valuable. Goals scored in blowouts, whether scored by the leading team or the trailing team, are essentially valueless.
Here are the various leads from these games, with the probability of winning. Leading score is the columns, trailing score is the rows:

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
0 
0.685 
0.862 
0.955 
0.993 
0.992 
1.000 
1.000 
1.000 
1.000 
#DIV/0! 
1 

0.733 
0.907 
0.976 
0.992 
1.000 
1.000 
1.000 
1.000 
1.000 
2 


0.794 
0.944 
0.992 
1.000 
1.000 
1.000 
1.000 
1.000 
3 



0.827 
0.973 
1.000 
1.000 
1.000 
1.000 
1.000 
4 




0.871 
0.993 
1.000 
1.000 
1.000 
#DIV/0! 
5 





0.889 
0.952 
1.000 
1.000 
#DIV/0! 
6 






0.778 
1.000 
1.000 
#DIV/0! 
7 







1.000 
#DIV/0! 
#DIV/0! 
8 








1.000 
#DIV/0! 
9 









#DIV/0! 
Computing the Values
The first goal always breaks a 00 tie. It always creates a 10 lead. A 10 lead gives you a probability of winning of 0.684. The first goal has a value of 0.184.
After the first goal, the game has to be 10. The second goal can be scored by the leading team, creating a 20 lead, or by the trailing team, creating a 11 tie. A 20 lead increases the probability of winning from 0.684 to 0.862. It has a value of 0.178. Moving from down 01 to tied 11 increases the probability of winning from 0.316 to 0.500. It has a value of 0.184. So the calculated value of the second goal is
(0.184 + 0.178) / 2 = 0.181
The probability of winning if you score the second goal is 0.500 + 0.181 = 0.681. Exactly the observed value from the table above.
There are 4 possibilities for the third goal. The team leading 20 scores to make it 30, the team trailing 02 scores to make it 12, one team can break a 11 tie, or the other team can break a 11 tie. The calculated value of the third goal is
(0.093 + 0.129 + 0.233 + 0.233) / 4 = 0.172.
The probability of winning if you score the third goal is 0.500 + 0.172 = 0.672. The observed value is 0.170.
Powers of 2 and the Binomial Theorem
For a game of n goals, there are 2^n possible sequences of goals. For 1 goal, there are 2 sequences: 10 and 01. For 3 goals, there is one way to get to 30, 3 ways to get to 21, 3 ways to get to 12, and 1 way to get to 03. As we go up in n:
N 
Scenarios 
Distribution of Scores 
1 
2^1=2 
11 
2 
2^2=4 
121 
3 
2^3=8 
1331 
4 
2^4=16 
14641 
5 
2^5=32 
15101051 
6 
2^6=64 
1615201561 
7 
2^7=128 
172135352171 
The right column is "Pascal's Triangle" which derives from the Binomial Theorem. The number of high value goals is the middle term(s).
N 
Scenarios 
High Value Goals 
Probability 
1 
2 
2 
1.000 
2 
4 
2 
0.500 
3 
8 
3 
0.375 
4 
16 
6 
0.375 
5 
32 
10 
0.313 
6 
64 
20 
0.313 
7 
128 
35 
0.273 
8 
256 
70 
0.273 
9 
512 
126 
0.246 
10 
1024 
252 
0.246 
11 
2048 
462 
0.226 
So as n goes up, the value of the nth goal goes down. The probability of a goal being "High Value" goes down faster than the value of a "High Value" goal goes up. Calculating Pascal’s Triangle says that for n=17, the probability that a goal is "High Value" is 0.185, so the value of the 17^{th} goal is at most 0.093. For n=21, the probability that a goal is "High Value" is about 0.168, so the value of the 21^{st} goal is at most 0.084. The limit of the value of a "High Value" goal is 0.500. At the limit, the probability approaches 0.00. 0.00 x 0.500 = 0.
As an example, suppose the score is 100. What is the value of scoring the 11^{th} goal here? Zero either way. What is the probability that the winning team scores the 11^{th} goal in this scenario? 0.500.
Retrospective versus Prospective
All of this is retrospective. Looking closely at my data, I see that the team scoring the 17^{th} goal won 100% of the 17 goal games (1 out of 1). Does that mean that the 17^{th} goal is actually the most valuable? Uh, no. Prospectively, we have to not only look at the value of each goal, but the probability that each goal will happen. Let's call this importance. The first goal has the most importance.
Goal 
Value 
Probability 
Importance 
Relative 
1 
0.184 
1.000 
0.184 
1.000 
2 
0.181 
0.978 
0.177 
0.958 
3 
0.170 
0.906 
0.154 
0.836 
4 
0.165 
0.804 
0.133 
0.720 
5 
0.148 
0.627 
0.093 
0.505 
6 
0.155 
0.461 
0.072 
0.388 
7 
0.146 
0.290 
0.042 
0.229 
8 
0.155 
0.174 
0.027 
0.146 
9 
0.143 
0.090 
0.013 
0.070 
10+ 
0.135 
0.079 
0.011 
0.058 
Value of a Goal and Average Goal Total
The value of a goal is a function of average total score. In one extreme, if the average total score was 1, the first goal would have a value of 0.500 and winning teams would score 100% of the first goal. At the opposite extreme, the total score in NBA games is up around 200 so the first point in an NBA game has a value close to zero and winning teams score the first point almost exactly 50% of the time.
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