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May 21, 2012, 01:16 PM ET
A Note on Championship Leverage Index

by Neil Paine

I’ve used the concept of “Championship Leverage” a lot over the past year or so, but I realize that I’ve never really explained it very well. Here’s an attempt to correct that…

Championship Leverage obviously owes its name to the baseball stat invented by Tom Tango to measure the cruciality of a given base-out-inning situation. It starts with the win probability of each team in a series, given the current “state” of the series (home team in Game 4 up 2-1, road team in Game 6 down 3-2, etc.). The state of the series not only tells you how often each team can expect to win (assuming evenly-matched opponents with true .500 talent levels and a .600 home-court advantage), but also how much that probability can swing based on the outcome of the next game of the series, which in turn tells you the most important games in the series.

Here’s a table for a 2-2-1-1-1 best-of-7 series (”Exp Δ” means the expected swing in series win probability for the game, based on the home team having a 60% chance of winning the game):

Game # Home W Home L Home SerW% Swing w/ W Swing w/ L Exp Δ
1 0 0 0.532 0.128 -0.192 0.154
2 1 0 0.660 0.132 -0.199 0.159
2 0 1 0.340 0.122 -0.182 0.146
3 2 0 0.843 0.100 -0.150 0.120
3 1 1 0.539 0.154 -0.231 0.185
3 0 2 0.207 0.100 -0.150 0.120
4 3 0 0.942 0.058 -0.086 0.069
4 2 1 0.693 0.163 -0.245 0.196
4 1 2 0.307 0.141 -0.211 0.169
4 0 3 0.058 0.038 -0.058 0.046
5 3 1 0.904 0.096 -0.144 0.115
5 2 2 0.552 0.208 -0.312 0.250
5 1 3 0.144 0.096 -0.144 0.115
6 3 2 0.760 0.240 -0.360 0.288
6 2 3 0.240 0.160 -0.240 0.192
7 3 3 0.600 0.400 -0.600 0.480

Here is the same table, but for a 2-3-2 best-of-7 series:

Game # Home W Home L Home SerW% Swing w/ W Swing w/ L Exp Δ
1 0 0 0.532 0.128 -0.192 0.154
2 1 0 0.660 0.132 -0.199 0.159
2 0 1 0.340 0.122 -0.182 0.146
3 2 0 0.843 0.100 -0.150 0.120
3 1 1 0.539 0.154 -0.231 0.185
3 0 2 0.207 0.100 -0.150 0.120
4 3 0 0.942 0.058 -0.086 0.069
4 2 1 0.693 0.163 -0.245 0.196
4 1 2 0.307 0.141 -0.211 0.169
4 0 3 0.058 0.038 -0.058 0.046
5 3 1 0.856 0.144 -0.216 0.173
5 2 2 0.448 0.192 -0.288 0.230
5 1 3 0.096 0.064 -0.096 0.077
6 3 2 0.840 0.160 -0.240 0.192
6 2 3 0.360 0.240 -0.360 0.288
7 3 3 0.600 0.400 -0.600 0.480

And finally, a 2-2-1 best-of-5 series:

Game # Home W Home L Home SerW% Swing w/ W Swing w/ L Exp Δ
1 0 0 0.539 0.154 -0.231 0.185
2 1 0 0.693 0.163 -0.245 0.196
2 0 1 0.307 0.141 -0.211 0.169
3 2 0 0.904 0.096 -0.144 0.115
3 1 1 0.552 0.208 -0.312 0.250
3 0 2 0.144 0.096 -0.144 0.115
4 2 1 0.760 0.240 -0.360 0.288
4 1 2 0.240 0.160 -0.240 0.192
5 2 2 0.600 0.400 -0.600 0.480

Using these numbers, you can measure how important a game is within a series. However, the “Championship” part of Championship Leverage involves also taking into account the playoff round in which the game took place. Again assuming each team is morally a .500 ballclub, your generic probability of a title before the 1st round would be 6.3% (1/16), which goes to 12.5% if you win, then 25%, then 50%, then 100% if you win the championship.

That’s where a table like this comes from:

Date Game # Home Pts Road Pts Winner hW rW Hm p(Ser) Hm p(Champ) Leverage
4/29/2012 1 MEM 98 LAC 99 LAC 0 0 53.2% 6.7% 0.75
5/2/2012 2 MEM 105 LAC 98 MEM 0 1 34.0% 4.2% 0.71
5/5/2012 3 LAC 87 MEM 86 LAC 1 1 53.9% 6.7% 0.90
5/7/2012 4 LAC 101 MEM 97 LAC 2 1 69.3% 8.7% 0.95
5/9/2012 5 MEM 92 LAC 80 MEM 1 3 14.4% 1.8% 0.56
5/11/2012 6 LAC 88 MEM 90 MEM 3 2 76.0% 9.5% 1.40
5/13/2012 7 MEM 72 LAC 82 LAC 3 3 60.0% 7.5% 2.33
5/15/2012 1 SAS 108 LAC 92 SAS 0 0 53.2% 13.3% 1.49
5/17/2012 2 SAS 105 LAC 88 SAS 1 0 66.0% 16.5% 1.55
5/19/2012 3 LAC 86 SAS 96 SAS 0 2 20.7% 5.2% 1.16
5/20/2012 4 LAC 99 SAS 102 SAS 0 3 5.8% 1.4% 0.45

That’s the Clippers’ first 2 rounds of the playoffs. From “Hm p(Ser)”, you can see what the home team’s probability of winning the series was going into any given game (derived from the charts I listed above), which is multiplied by the generic probability of a championship if they won the series in question to arrive at “Hm p(Champ)”. Using that stat and the possible swings in Championship Probability with a win or a loss, you can calculate an “Exp Δ” stat at the championship level (rather than at the series level as we did before).

Once you’ve done that, calculate the average Exp Δ for every game in a given playoff season (the average in 2012 so far is 0.026; last year’s average was 0.047) and divide the game’s Exp Δ by the average Exp Δ across all games that year. The result is Championship Leverage Index, where 1.00 represents a game with an average impact on the championship (going back to our example, Game 7 of the Clippers-Grizzlies series had 2.3 times as much impact as the average game). Here are the highest-leverage games since the NBA went to a 16-team playoff in 1984:

Date Game # Home Pts Road Pts Winner Leverage
6/17/2010 7 LAL 83 BOS 79 LAL 9.24
6/23/2005 7 SAS 81 DET 74 SAS 9.00
6/12/1984 7 BOS 111 LAL 102 BOS 8.24
6/22/1994 7 HOU 90 NYK 84 HOU 7.43
6/21/1988 7 LAL 108 DET 105 LAL 7.25
6/12/2011 6 MIA 95 DAL 105 DAL 6.18
6/9/1985 6 BOS 100 LAL 111 LAL 5.69
6/20/2006 6 DAL 92 MIA 95 MIA 5.60
6/15/2010 6 LAL 89 BOS 67 LAL 5.54
6/14/1998 6 UTA 86 CHI 87 CHI 5.31
6/13/2003 5 NJN 83 SAS 93 SAS 5.11
6/2/1996 7 SEA 90 UTA 86 SEA 5.10
6/20/1993 6 PHO 98 CHI 99 CHI 4.96
6/9/2011 5 DAL 112 MIA 103 DAL 4.94
6/2/2002 7 SAC 106 LAL 112 LAL 4.80
5/30/1987 7 BOS 117 DET 114 BOS 4.70
6/3/2001 7 PHI 108 MIL 91 PHI 4.66
6/4/2000 7 LAL 89 POR 84 LAL 4.62
6/3/1990 7 DET 93 CHI 74 DET 4.56
6/7/1985 5 LAL 120 BOS 111 LAL 4.55
6/4/1995 7 ORL 105 IND 81 ORL 4.55
6/6/2005 7 MIA 82 DET 88 DET 4.50
6/18/2006 5 MIA 101 DAL 100 MIA 4.48
6/19/1994 6 HOU 86 NYK 84 HOU 4.46
6/13/2010 5 BOS 92 LAL 86 BOS 4.43

By using Championship Leverage Index, you can weight team and player performances by the importance of the game itself. For instance, here are the team PPG margin leaders in this year’s playoffs, both raw and weighted by leverage:

Rank Team Games Raw MOV Rank Team Lev Gm Lev MOV
1 SAS 8 13.8 1 SAS 7.0 15.3
2 MIA 9 7.2 2 OKC 8.2 7.5
3 OKC 8 7.1 3 IND 10.5 4.8
4 IND 9 6.6 4 MIA 9.6 4.0
5 BOS 10 3.5 5 BOS 11.8 3.6
6 MEM 7 0.7 6 PHI 11.8 -0.1
7 DEN 7 0.4 7 DEN 6.7 -1.8
8 PHI 10 0.3 8 MEM 7.6 -1.9
9 CHI 6 -1.7 9 CHI 5.3 -2.3
10 LAL 11 -3.1 10 LAL 12.6 -2.8
11 LAC 11 -4.6 11 LAC 12.3 -4.0
12 ATL 6 -4.7 12 ATL 5.3 -5.4
13 DAL 4 -6.5 13 DAL 2.3 -5.9
14 ORL 5 -10.8 14 ORL 3.7 -10.7
15 NYK 5 -14.0 15 NYK 2.9 -16.8
16 UTA 4 -16.0 16 UTA 2.3 -18.7

San Antonio leads both, but below them you see differences that are explained by the timing of each team’s good/bad performances. By playing better in less important games, Miami ranks lower in the leveraged MOV rankings than the raw ones, while teams like Oklahoma City and Indiana move up because more of their PPG differential was accrued in games that had more crucial implications. The difference between raw and leveraged MOV can even be turned into a “clutch” metric:

Rank Team Raw MOV Lev MOV Clutch
1 SAS 13.8 15.3 1.5
2 LAC -4.6 -4.0 0.6
3 DAL -6.5 -5.9 0.6
4 OKC 7.1 7.5 0.4
5 LAL -3.1 -2.8 0.3
6 BOS 3.5 3.6 0.1
7 ORL -10.8 -10.7 0.1
8 PHI 0.3 -0.1 -0.4
9 CHI -1.7 -2.3 -0.6
10 ATL -4.7 -5.4 -0.7
11 IND 6.6 4.8 -1.8
12 DEN 0.4 -1.8 -2.3
13 MEM 0.7 -1.9 -2.6
14 UTA -16.0 -18.7 -2.7
15 NYK -14.0 -16.8 -2.8
16 MIA 7.2 4.0 -3.2

There are a lot of cool things you can do with a stat like this, and hopefully this served as a primer for those wanting to learn more about the Championship Leverage concept and how it’s calculated.

Email Neil at np@sports-reference.com. Follow him on Twitter at @Neil_Paine.

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