Bruce Bennett

Warning: Numbers! A 5-4 lead may be better than a 2-0 lead.

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

 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

 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:

 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.

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