Friday, March 19, 2010

The Rules of Bowling: Tax Brackets and Bowling Awards

Is it possible to get a raise and take home less money as a consequence? If this has ever happened to you, you understand why the structure of the federal income tax can be a cruel beast. This can occur if your raise pushed you into the next tax bracket. The term "bracket" in this context refers to discrete categories of income. Here is an example, if you had $33,949 of taxable income in 2009, you were taxed at a rate of 15%, or a total tax of $5,092. If you received a raise of $1,000, so you are now making $34,949. Now, you are taxed at a rate of 20%, or a tax of $6,989. When your salary was $1,000 less, you had a net income that was $897 greater.

Aside from the standard arguments about progressive taxation versus "flat" taxes, I'm not sure why rates of taxation are applied this way. If I had to guess, it is to ease the burden on analytically anxious people who prepare their own taxes. This type of bracketing penalty could easily be avoided if we simply got rid of the categorical treatment of income and instead used a smooth function that relates income to tax rate, but I'm going a little overboard here. The reason why I bring this up is because the structure of awards in USBC bowling is analogous to federal tax bracketing, and moving from one bracket to the next may mean that you are not going to receive an award for a while. It can function as a punishment.

In the 2009-2010 USBC rulebook, there were changes made to the award system. In this post, I want to focus on "Single Game Awards" in adult bowling. Here is how the rulebook reads:

There are a number of changes from the prior edition. For example, awards were granted for single games that were 75 and 100 pins over average. Those have been eliminated. Also, the categories of awards have changed. Awards used to be granted for scores of 80, 100, 120, 140, 160, 180, 200, 250, and 300. It is unclear why these award categories have changed, but from my perspective, the addition of the 225 game category is very welcome because the difference between scores of 200 and 250 is huge, particularly for bowlers with low averages.

The graph below shows the relationship between average and the number of pins above average you have to bowl in order to earn an award.

The first thing to notice is that as your average improves, it becomes "more difficult" to earn awards. For example, if your average is between 100 and 145, you need a game that is 40 to 60 pins above average to get your patch. If you average 180 to 200, you need to exceed your average by 70 to 90 pins. Although you have to exceed your average by a greater number of pins, I'm not sure that you are less likely to merit award when you are a better bowler. Bowlers with higher averages are much more likely to string together strikes which will result in the occasional very high game score. My hunch is that the upward climbing nature of the award structure takes into account this property of skill and scoring.

The other property of this graph of which to take note is its sawtooth quality. This results from the bracketed nature of averages in the award structure. When you enter a new average category, assuming you are improving, your chances of winning an award are minimized. For example, if your average climbs from 160 to 161, the minimum game award for which you are eligible is the is the "250". You remain eligible for the 250 award until your average exceeds 180. I can tell you from personal experience that bowling a 250 game with a 161 average is a herculean feat. It is much easier to do if you average 180, both because you are a better bowler and because you only have to bowl 70 pins over average in comparison to 89.

I am actually not advocating any changes to this system. Unlike my feelings about the federal tax code and rules about youth apparel, I like the USBC awards system as it is, and I like the recent revisions to it. My point is that when you are in the bottom of a bowling "tax bracket", your chances of earning an award are fairly slim. When you approach one of the thresholds in average, you should really take advantage of the opportunity to win an award because that is when your chances are best, and soon you won't even qualify. And just think of all the stuff you could stick to your fridge with that new magnet.


  1. you're saying my 300 game is just around the corner?

  2. Just around the corner, Kafka. Just around the corner.


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