### How much influence is needed?

#### 4th June 2010

Tim Donaghy officiated 69 Regular season games in the 2006-2007 NBA Season. It is my belief that he bet nearly all of them. Assuming he actually biased his officiating based on the team he wagered on, why then have the NBA or others found it so difficult to assert that he actually fixed games?

One thing to note;

*Donaghy wagered exclusively on sides. I am not sure why this is the case and I think that totals are eminently more easy to influence than a side I’ll probably go into why this is (and why the not so bright Donaghy chose sides instead of totals in a future post). But for now just believe me when I say that they bet sides and not totals. I’ll also add that in all testimony Donaghy and his cohorts only mentioned betting on sides. *

So how then was Donaghy able to win such a high percentage ~70% or greater and do so without drawing any attention?

**1. The 50-50 Rule**

For the most part the people who make the line do a pretty good job of making a fair NBA full game side line. The “spread” in a game makes handicapping NBA sides without having a very specific approach (or putting in a lot of work) a roughly 50-50 proposition. 52.38% is the breakeven mark assuming you are betting at the industry standard 11 to win 10.

If Tim Donaghy flipped a coin and just officiated a game fairly he’d win roughly 50% of his selections. Disregarding issues of sample size roughly half of the time Tim Donagy placed a bet on a game he officiated he’d randomly win.

**2. 6 = 70%**

Assuming you were a rogue official and your goal was to hit around 70% how much influence would you need to exert? Or to put it differently how many points would you need to swing a 50-50 proposition into a 70% winner?

1 point = 53.28%

2 points = 56.91%

3 points = 60.64%

4 points = 64.14%

5 points = 67.51%

**6 points = 70.69%**

7 points = 73.63%

8 points = 76.34%

9 points = 79.21%

10 points = 81.73%

In other words if you possessed a magic wand (or whistle) that allowed you to add 6 points to the the team you bet on, (or subtract 6 few points from the team you bet against) you’d hit around 70% of your wagers.

*these numbers are based off of betting on the home team (the numbers vary slightly if you consider the visiting team but the win percentages are within~2%. For instance if you bet the away team and had 7 points in your favor you’d win about 74% of the time, 6 points gets you to 72%.

It can be a little tricky trying to determine the actual point value for a specific action so instead we deal with “ev” or expected value. Pretty much everything that happens on a basketball court has an expected value and it is important to account for this when we are trying to figure out how much Donaghy’s calls affected the outcome of a game.

My next post will explain and detail how a blown call can alter the ev of a possession.

## 6 Notes

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