The Value of Leads

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

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.

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