Sport biz: A game of regression

Playing golf requires many skills, and math is one of them. Before that first satisfying slice is launched from the tee box, there are handicaps to consider and calculations of estimated time remaining before the first beer cart appearance to be advanced.

The more progressive among you can go even deeper, taking into account slope ratings and total course yardage metrics to produce some sort of internal calculation of a theoretical personal score goal that will vanish after three thrashes from the weeds on No. 4 but that is useful nonetheless for modeling purposes.

A new bar has been established at the intersection of golfing and arithmetic by a group of economists and researchers from Colorado State University and the University of Idaho. They set out last summer to determine the relationship between the amount of money you’re willing to spend on a round, and the actual amount you shell out.

Their work, “A Hybrid Individual-Zonal Travel Cost Model for Estimating the Consumer Surplus of Golfing in Colorado” practically sings from the page with memorable one-liners and witticisms.

Here’s a suggestion: Next time you’re idly awaiting your call from the starter, ask your mates if they knew “That with the linear model, it is possible to calculate the price elasticity with respect to travel cost, and this is also price inelastic at the mean of the data at −0.4338, and identical to the semilog?”

Chances are they didn’t.

Or, while throwing down a cold one in the clubhouse, observe that “The golfer’s travel time can be included as a separate variable, avoiding the necessity of having to assign a particular fraction of the wage rate to monetize the opportunity cost of time to combine with the travel cost variable.” And that you’d like them to pass the pretzels.

These are indeed useful snippets of knowledge to throw into the conversation. But later, things get serious. There on page nine of the report, which was published last month in the Journal of Sports Economics, is the most shocking of all findings: “In preliminary regressions,” the report notes, “we tested for heteroskedasticity and found it to be present.”

Egads, golfers! Here you’ve been, casually boffing the ball around the course, completely oblivious to the fact that all around you is heteroskedasticity! We can only hope you washed your hands after the turn. (OK, truth is, it’s actually a tool statisticians use to root out potential misinterpretations of variances within data.)

In the end, the report offers some interesting takes.

The central finding is that golfers generally are game to spend around $75 for a day on the course – travel included. But the state’s golfers generally pay just $49 on average for greens fees, plus $8 on automobile travel. That means – and you knew there was going to be a catch here – golfers actually are spending $18 less for a round (and related travel) than they’re willing to spend.

The resulting inelasticity – or absence of a clear connection between price and demand levels – suggests golf courses could be leaving money on the table, and as the report chillingly suggests, “could … raise green fees somewhat.”

Aaargh!!! Do our state’s best and brightest economists have nothing better to do than to suggest that we pay more to golf?

In fact, there’s more to it. The authors, among other motivations, want to know whether golf courses represent a sound use of water, and determining the amount of “consumer surplus” around golfing can help get to an answer. Plus, they note, there are plenty of other activities – hiking and skiing are two – in which there is a high consumer surplus, or gap between perceived value vs. actual cost. (One caveat comes from the fact that the conclusions were drawn from data originally collected in 2003. Perceptions may have changed sharply since then.)

In any case, let’s try to keep these results mum, shall we? That way our consumer surplus of $18 per round will be more than enough to let us enjoy a cool one while comparing handicaps and scores in the clubhouse.

With a pencil and a card. 

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