I looked at the probability that creating a given lead led to a win in regulation. I am using the RTSS files to pull the various leads and when the goals were scored. I went through every game from 2007-08 through 2012-13. First the count of how many times the lead occurred (column is leading score, row is trailing score):
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
0 |
6802 |
3295 |
1608 |
680 |
250 |
97 |
33 |
8 |
2 |
0 |
1 |
|
4557 |
2709 |
1390 |
521 |
199 |
80 |
26 |
9 |
1 |
2 |
|
|
2629 |
1524 |
721 |
218 |
72 |
26 |
10 |
3 |
3 |
|
|
|
1019 |
547 |
233 |
57 |
16 |
5 |
1 |
4 |
|
|
|
|
278 |
144 |
61 |
13 |
1 |
0 |
5 |
|
|
|
|
|
45 |
21 |
8 |
1 |
0 |
6 |
|
|
|
|
|
|
9 |
6 |
1 |
0 |
7 |
|
|
|
|
|
|
|
2 |
0 |
0 |
8 |
|
|
|
|
|
|
|
|
1 |
0 |
9 |
|
|
|
|
|
|
|
|
|
0 |
Next the probability of winning:
|
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! |
So, looking at one goal leads:
Lead |
Probability |
Number |
1 to 0 |
0.685 |
6802 |
2 to 1 |
0.733 |
4557 |
3 to 2 |
0.794 |
2629 |
4 to 3 |
0.827 |
1019 |
5 to 4 |
0.871 |
278 |
6 to 5 |
0.889 |
45 |
And two goal leads:
Lead |
Probability |
Number |
2 to 0 |
0.862 |
3295 |
3 to 1 |
0.907 |
2709 |
4 to 2 |
0.944 |
1524 |
5 to 3 |
0.973 |
547 |
6 to 4 |
0.993 |
144 |
Finally, three goal leads:
Lead |
Probability |
Number |
3 to 0 |
0.955 |
1608 |
4 to 1 |
0.976 |
1392 |
5 to 2 |
0.992 |
723 |
6 to 3 |
1.000 |
235 |
So a one goal lead is not the same as a one goal lead. The value of a lead goes up as total goals go up. In fact, holding a 5 to 4 lead gives you a higher probability of winning the game than holding a 2 to 0 lead. This came as a surprise to me. I expected a trend upward, but nothing this dramatic. The effect of time is much stronger than I thought.
When you score matters
Let's look at 2 to 0 and 5 to 4 leads and let's break them down by periods.
Lead |
First |
N |
Second |
N |
Third |
N |
2 to 0 |
0.833 |
1661 |
0.861 |
2171 |
0.933 |
942 |
5 to 4 |
0.000 |
1 |
0.724 |
29 |
0.877 |
268 |
So a 5 to 4 lead looks better than a 2 to 0 lead because most 5 to 4 leads happen in the Third Period. If you control for time, a 2 to 0 lead is always better.
Logistic Regression
So let's look at a model of the probability of winning being a function of time and lead size. Time is the time a goal gets scored and LeadVal is the size of the lead (1 goal, 2 goals, 3 goals, etc.)
Call:
glm(formula = LeaderWon ~ Time * LeadVal, family = binomial(logit),data = LeadVal2)
Coefficients |
Estimate |
Std. Error |
z value |
Pr(>|z|) |
Significance |
(Intercept) |
2.259e-02 |
8.088e-02 |
0.279 |
0.78 |
|
Time |
-4.654e-06 |
4.582e-05 |
-0.102 |
0.919 |
|
LeadVal |
4.915e-01 |
6.394e-02 |
7.688 |
1.5e-14 |
*** |
Time:LeadVal |
3.410e-04 |
3.535e-05 |
9.648 |
2e-16 |
*** |
LeadVal is highly significant. The bigger the lead, the more likely you are to win. Time a goal gets scored, in and of itself, is not significant. There is a strong interaction between Time and LeadVal. A lead late in the game is worth more than a lead of the same magnitude early in the game.