Score! How a Basketball Fan Uses Actuarial Skills to Predict Ultimate Points
Zach Brogadir

Score! How a Basketball Fan Uses Actuarial Skills to Predict Ultimate Points

Which Method is Most Accurate - Jimmy “Buckets” Butler Example

Zach Brogadir May 26, 2015 Posted in: Blog Posts, General

Growing up I always dreamed of becoming an NBA player. When it became clear that I lacked height, athleticism and an ability to shoot a basketball, I decided to follow a new dream – to become an actuary, of course! While I haven’t been able to earn a living shooting hoops, I do find that the game of basketball can be a great analogy when explaining what are otherwise arcane actuarial concepts. For example, we can use basketball to illustrate some of the most common actuarial reserving methodologies.

As a Chicago Bulls fan, my favorite player is Jimmy “Buckets” Butler. In this example we’ll estimate Jimmy’s points total (or ultimate points) for Game 1 of the 2015 NBA Playoffs against the Milwaukee Bucks on April 18, 2015. We’ll make an estimate before the game begins and update that estimate after each quarter of the game using three methods comparable with actuarial methods: Initial Expected Points, Points Development Method and Bornhuetter-Ferguson (BF).

Prior to the beginning of the game we look at past experience to determine an initial expected estimate of Jimmy’s points total for Game 1. We first review Jimmy’s long-run production – he has averaged 20.0 points per game this season. We then look at Jimmy’s most recent trends – he averaged 18.7 points in his last seven games. Finally we look at an “industry” indication by reviewing how similar players have performed in a similar situation – NBA players at Jimmy’s position have averaged 21.4 points per game against Milwaukee this season. Considering these three indications, we make a judgmental selection of 20 as an initial estimate for Game 1. In the insurance world, we may look at loss ratios or loss costs from past policy periods to select an initial estimate of ultimate loss. Similarly to our basketball indications, the actuary must balance long-run indications, recent experience and industry indications.

The development method and BF method can only be used once the game has begun. These methods require an assumption regarding the development of losses (or points) over time. Actuaries generally evaluate loss development triangles to make this assumption. In this example we will assume that points are scored uniformly over each quarter. With this in mind, the points development pattern is as follows:

After one quarter of the game goes by, we calculate the three estimates of Jimmy’s ultimate points. This is similar to estimating an insurer’s ultimate loss one year after the beginning of a policy period. Jimmy scored 11 points in the 1st quarter. He’s off to a great start, already exceeding more than half our initial estimate. Let’s take a look at the projections from our three methods:

  • Initial Expected Points = 20
  • Points Development Method = 44
  • Bornhuetter Ferguson = 26
The initial estimate is not affected by experience within the game and therefore still estimates Jimmy will finish the game with 20 points. The development method believes Jimmy’s great 1st quarter will be followed by 3 equally great quarters based on our assumption of uniform point development ( 44 = 11 x 4.00 ). The BF method is not as responsive as the development method. It reflects Jimmy’s strong start but believes that the remainder of the game will develop similarly to our initial expectations ( 26 = 11 + [1 – 0.25] x 20 ).
We re-evaluate the game again after each quarter of the game. The results of our methods over time can be seen below.
Jimmy ended up scoring 25 points in the game. Here are some important takeaways that relate back to insurance:

  1. The development method over-reacted to an abnormally high scoring 1st quarter. As the game continued on and Jimmy’s output slowed, the development method estimate dropped significantly. For immature policy periods, the development method is very responsive and can over or under-react to initial reported losses. It becomes more reliable as a policy period matures.
  2. The initial estimate is based on indications from past experience and does not change over time. By the end of the 3rd quarter Jimmy had already exceeded the initial estimate. The initial expected method may not be a useful estimate of ultimate loss for mature policy periods because it does not reflect actual experience to date.
  3. The BF method balanced the development method and the initial expected method. It reflected a strong 1st quarter while also assuming the remainder of the game would develop similar to a more typical game. The BF method tends to produce more stable estimates although it is not as quick to respond to reported losses as the development method.
An actuary commonly uses these three basic methods (and potentially others) to estimate ultimate losses and IBNR. I hope this illustration helps you better understand how these common methods are calculated and where they are appropriate to use.

Now, if only I could use this to improve my jump shot!

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