The Stats Behind 0 for 27

For those who are not aware, last night in game 7 of the Western Conference finals, the Rockets combined to shoot 0 for 27 on three point attempts from midway through the second quarter into the fourth quarter (including James Harden shooting 0 for 10).

What are the odds of that?! Let's use this as an opportunity to utilize some basic statistics.

The math behind determining the probability of shooting 0 for 27 from three is easy enough, but requires a basic assumption. Each shot needs to be considered one "trial" with a certain success rate. The 27 missed three point attempts were taken by the following players with their season three point field goal percentages in parentheses:

• 10 - James Harden (36.7%)
• 7 - Eric Gordon (35.9%)
• 6 - Trevor Ariza (36.8%)
• 2 - PJ Tucker (37.1%)
• 1 - Joe Johnson (27.9%)
• 1 - Gerald Green (36.9%)

The probability of any single player missing "x" number of shots in a row can be calculated by successively multiplying the complement of their three point percentage. For example, the probability of PJ Tucker missing two three point shots in a row can be calculated as follows:

P(PJ Tucker 0 for 2) = (1 - 3FG%)(1 - 3FG%) = (1 - 0.371)^(2) = 39.6%

What about James Harden missing 10 successive shots?

P(James Harden 0 for 10) = (1 - 3FG%)^10 = (1 - 0.367)^(10) = 1.03%

There was about a 1% chance for James Harden to miss 10 shots in a row. In order to calculate the total probability of the Rockets shooting 0 for 27, the probability of each individual player missing their number of successive shots must be calculated. After the probabilities have been calculated for each player then the probability of 0 for 27 can be calculated by multiplying the probabilities:

P(Rockets 0 for 27) = P(J. Harden 0 for 10)*P(E. Gordon 0 for 7)*P(T. Ariza 0 for 6)*P(PJ Tucker 0 for 2)*(J. Johnson 0 for 1)*P(G. Green 0 for 1)

The probability of the Rockets shooting 0 for 27 was 0.00053% or 1 in 190,220! As a somewhat helpful point of reference, the odds of getting struck by lighting in your lifetime are about 1 in 3,000 (Nat. Geographic).