# The Math of Scoring First, from Russ Sears

May 27, 2011 |

Looking for some stats to put on the table for Basketball I found this analysis of actual to predicted wins in hockey.

Ties occur more than predicted. It does not appear the method is adjust to consider the power play at the end raise the chance that a tie occurs than the poisson distribution would. That is more goals are scored at the end of a 1 point difference game than throughout the rest of the game.

Other low scoring games like baseball do not follow the poisson distribution. In Baseball for example the time is unknown and each team takes same number of chances to reach a base. The more on base you have the more chances you have to score. (the past events effect your chance of scoring.

After reading this blog, the question I asked was how would you best simulate a model of a basketball game. I suspect those that control the ball and control the pace, (the time) the best win more than the teams have a good night shooting, because the law of large numbers smooths out the out come.

What is the W/L stats for those teams that steal the ball first?

## Phil McDonnell writes:

We have discussed the arc sine distribution here before. It is that U shaped distribution where the major probability of occurrence is in the tails. But it can apply to the question of how often the first team to score wins as well. The idea is that a surprisingly large proportion of the time in a random walk the walk will go positive or negative and never look back The arc sine distribution comes into play in looking at how many times you will cross a given level (including the zero level).

The idea would be to look at the first team to score as creating a point differential of +n. Then the arc sine predicts that a surprisingly many games will turn out with the point differential never going below zero.

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