09/17/2014 3:12PM

Fornatale: Payoffs affect scores far more than field size

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Dear Pete:

I played in both of the NHCQualify.com free contests last week and I was wondering: how do you expect scores to change when you’re playing in a field of 1,000 versus 100?

Signed,

Curious

Dear Curious:

Thanks for the excellent question. To answer it, I called an old friend of the blog and our resident math whiz, PublicHandicapper.com editor and NHC Players’ panel member Chris Larmey.

Larmey was quick to point out that the number one factor affecting final scores isn’t field size; it’s the specific run of races in any given contest. If a contest is full of longshot winners, the average score is higher and the winning score is higher. 

“To use an apt metaphor, all boats float higher with the rising tide,” Larmey explained. “The key point to keep in mind is that higher win-place prices tend to drive up all scores, not just the winning score.”

But what about the effect of field size? That’s a different story.

“Field size is not like the rising tide,” Larmey said. “It does not raise the average or median score. However, it does tend to raise the winning score.”

Asked why this is, Larmey presented a different analogy that’s worth sharing in full:

“Let’s imagine that we want to compare two typical U.S. cities near each other with similar demographics, but one is very small, with a population of only 100, and one is very large, population over 1 million. We will compare them by looking at the average or median height of all adults in each city and the tallest adult in each city. Because the large city has over 1 million people, we would expect to find some very tall people; in fact, we are likely to find a ‘one-in-a-million’ person who is over seven feet tall and destined for a lucrative career in the NBA. We also would expect to find some very short people, a few of whom may even be destined for lucrative careers as jockeys. In other words, we are likely to find more people at the extremes of both tall and short. Conversely, because the small city only has 100 people, we would not expect to find many people at the extremes. Of course, we would expect some variability in height and some taller people but we would be surprised to find someone over seven feet tall. However, and this is a key point, we would expect the ‘average’ or median height to be about the same in both cities. This is because in the bigger city, the extremes at both ends, tall versus short, tend to cancel each other out, so the average and median height stay about the same even though the tallest person is much taller in the larger city.”

 Contest size has a similar effect on contest scores. Larmey illustrated this by imagining two simultaneous contests using the same 12 mandatory races. One contest has 100 entries, the other 1 million.

“Regardless of the average $2 win-place payouts for the 12 races being used by both contests, we would expect the average and median scores in both contests to be about the same,” Larmey explained – this perfectly mirrors the analogy about average height in the two cities mentioned above. Larmey continued, “But we would expect the winning score to be higher in the larger contest,” – a la the seven-foot t tall person in the big city above. Larmey completed his thought by saying, “In other words, you would expect the difference or ‘spread’ between the median score and the winning score to be greater in the larger contest.”

In fact, this spread will increase as contest size increases. That was the reasoning behind the new NHC Tour scoring system, which Larmey helped design. Under Larmey’s system, more points are awarded to the winners in larger contests.

What does this mean for the contest player in practical terms? That’s a complicated question we will save for the next edition of Ask Pete.