Labour economics: golf caddying edition

Radio Sport yesterday was consumed with a debate about whether Steve Williams, the caddy for Masters winner, Adam Scott, is worth the money he is paid.

For those who don't follow golf, here is the background. Steve Williams is a New Zealander who was the professional caddy for Tiger Williams in his heyday (1999-2011). They had an acrimonious break-up two years ago, and since then Williams has been caddying for the Australian, Adam Scott. Williams' contract sees him earning 10% of Scott's prize earnings, which I gather is a typical contract for a professional caddy. Obviously, if you can caddy for one of the greats, that is a very lucrative contract indeed. (The prize for winning the Masters this year was $1.44m USD.)

Now the debate on Radio Sport concerned whether any caddy is worth that amount of money. And for an economist, "worth" would typically mean what a caddy can contribute relative to the next best alternative. Is it really the case that a top caddy can improve a golfer's winnings by more than 10%, relative to what he would earn with one of the throng of enthusiastic golf fans who would be prepared to do the job for a normal kind of salary? While there has been much commentary on the advice that Williams gave Scott on his winning shot at the Masters this week, it seems unlikely that the best caddy is really that much better than the alternative.

There is a second labour-economics question that I did not hear addressed on Radio Sport: Why are caddies paid on a commission basis (percentage of income) rather than a flat rate? The standard answers to these questions from the contract literature would be that either the golfer is more risk averse than the caddy, or that this is a hidden-information problem and that the caddy needs a financial incentive to exert the effort needed to do a good job. The former hardly seems likely given the relative incomes of the golfer and his caddy. The second is even less likely to pass the sniff test: Does it really take additional costly effort to give good advice on which club to use and how a putt is likely to break?

Instead, maybe we should be looking to the efficiency wage literature which contains a number of different theories for why above-market-clearing wages can persist in the face of unemployment. My favourite model to explain caddy wages would be Shapiro and Stiglitz's classic model of shirking. In their model, the high ("efficiency") wage persists as a preference for employment over unemployment is needed to induce a fear of being fired and hence an incentive not to shirk in the face of costly monitoring of effort. The model I have in mind for caddies is similar. The top golfers are big superstars whose flaws and foibles would be fodder for the tabloids. A caddy who works closely with a golfer is likely to have considerable information that tabloids would love to get hold of. So why might one pay above the market-clearing wage for a caddy? So that the cost to the caddy of losing his job would not be dwarfed by payments he might be offered by a tabloid. And why pay caddies on a commission basis? Because the greater is a golfer's earnings, the greater is his stardom, the more a tabloid would be prepared to pay for information, and hence the greater would be the needed efficiency wage.

What other explanations explain the twin puzzle of high remuneration and a percentage-of-earnings contract. If I were teaching labour economics, I would set this as an essay question.

Cricket and the Wasp: Shameless self promotion (Wonkish).

In their coverage of the Wellington-Auckland game in the HRV cup last Friday, Sky Sport introduced WASP—the “winning and score predictor” for use in limited-overs games, either 50-over or 20-20 format. In the first innings, the WASP gives a predicted score. In the second innings, it gives a probability of the batting team winning the match.

I am very happy about this as it is based on research by my former doctoral student, Scott Brooker, and me. Not surprisingly, the commentators didn’t go into any details about the way the predictions are calculated, so I thought I would explain the inner workings in a wonkish blog post.

The first thing to note is that the predictions are not forecasts that could be used to set TAB betting odds. Rather they are estimates about how well the average batting team would do against the average bowling team in the conditions under which the game is being played given the current state of the game. That is, the "predictions" are more a measure of how well the teams have done to that point, rather than forecasts of how well they will do from that point on. As an example, imagine that Zimbabwe were playing Australia and halfway through the second innings had done well enough to have their noses in front. WASP might give a winning probability for Zimbabwe of 55%, but, based on past performance, one would still favour Australia to win the game. That prediction, however, would be using prior information about the ability of the teams, and so is not interesting as a statement about how a specific match is unfolding. Also, the winning probabilities are rounded off to the nearest integer, so WASP will likely show a probability of winning of either 0% or 100% before the game actually finishes, even though the result is not literally certain at that point.

The models are based on a database of all non-shortened ODI and 20-20 games played between top-eight countries since late 2006 (slightly further back for 20-20 games). The first-innings model estimates the additional runs likely to be scored as a function of the number of balls and wickets remaining. The second innings model estimates the probability of winning as a function of balls and wickets remaining, runs scored to date, and the target score.

The estimates are constructed from a dynamic programme rather than just fitting curves through the data. To illustrate, in the first innings model to calculate the expected additional runs when a given number of balls and wickets remain, we could just average the additional runs scored in all matches when that situation arose. This would work fine for situations that have arisen a lot such as 1 wicket down after 10 overs, or 5 wickets down after 40 overs, etc.), but for rare situations like 5 wickets down after 10 overs or 1 wicket down after 40 it would be problematic, partly because of a lack of precision when sample sizes are small but more importantly because those rare situations will be overpopulated with games where there was a mismatch in skills between the two teams. Instead, what we do is estimate the expected runs and the probability of a wicket falling on the next ball only. Let V(b,w) be the expected additional runs for the rest of the innings when b (legitimate) balls have been bowled and w wickets have been lost, and let r(b,w) and p(b,w) be, respectively, the estimated expected runs and the probability of a wicket on the next ball in that situation. We can then write

V(b,w) =r(b,w) +p(b,w) V(b+1,w+1) +(1-p(b,w)))V(b+1,w)

Since V(b*,w)=0 where b* equals the maximum number of legitimate deliveries allowed in the innings (300 in a 50 over game), we can solve the model backwards. This means that the estimates for V(b,w) in rare situations depends only slightly on the estimated runs and probability of a wicket on that ball, and mostly on the values of V(b+1,w) and V(b+1,w+1), which will be mostly determined by thick data points. The second innings model is a bit more complicated, but uses essentially the same logic.

Now many authors have applied dynamic programming to analyse sporting events including limited overs cricket (see my previous post on this here), although I don’t know of any previous uses of such models in providing real-time information to the viewing public. Scott’s and my main contribution, however, is in including in our models an adjustment for the ease of batting conditions. I have previously blogged about our model for estimating ground conditions, here. Without that adjustment, the models would overstate the advantage or disadvantage a team would have if they made a good or bad start, respectively, since those occurrences in the data would be correlated with ground conditions that apply to both teams. Using a novel technique we have developed, we have been able to estimate ground conditions from historical games and so control for that confounding effect in our estimated models.

In the games on Sky, a judgement is made on what the average first innings score would be for the average batting team playing the average bowling team in those conditions, and the models’ predictions are normalised around this information. At this stage, I believe this judgement is just a recent historical average for that ground, but the method of determining par may evolve.

I gather that the intention is to unveil more graphics around the use of WASP throughout the season, with the system fully up and running by the time of the international matches against England. It’s going to be interesting listening to what the commentators make of the WASP. Last Friday’s game wasn’t the best showcase, since when Auckland came to bat in the second innings, their probability of winning was already at 92% and quickly rose higher. It was fun, though, hearing the commentators ask Wellington captain, Grant Elliot, who was wired for sound while fielding, what he thought their chances were given that WASP had the Auckalnd Aces at 96% at that point. Grant's reply was lovely: "Sometimes even pocket aces lose". This is worth remembering when (as will inevitably happen), a team has a probability of winning in the 90s but still goes on to lose.

Doing Well by Doing Good: Sports Edition

New Zealand play Argentina in the Rubgy Championship again this weekend, so there will likely be more discussion of the role that the immediate past New Zealand coach, Graham Henry, has as a coaching advisor to the Argentinian team.  When the two teams met a couple of weeks ago in New Zealand, the media commentary on this focused on patriotism (how dare Henry work for the opposition), industrial espionage (there should be a stand-down period between coaching stints for different teams, since Henry still has information about current NZ structures), and social policy (it is good for the game to provide help to the less-strong teams).

In contrast, no-one seems to have considered the possibility that Henry's assistance to Argentina could be good for New Zealand. File this one under Honours problem sets I would like to write if I were teaching an appropriate course. The model is as follows:

The Rugby Championship is a two-round, round robin tournament (home and away) involving four teams: New Zealand, Australia, South Africa and New Zealand. New Zealand is clearly currently the strongest of the four teams and Argentina the weakest. The disparity is not so great that any result is a foregone conclusion, but realistically the gap between New Zealand and Argentina is large.  The biggest threat to New Zealand in the competition, then, is not the prospect that they might lose to Argentina. It is that they might split their two-game series with the other two teams, and have the competition decided by bonus points.

Helping out Argentina, therefore, would be to our advantage, if it raised the probability of their beating the other two teams by more than if it raised the probability of their beating New Zealand. I have no idea just what assumptions would be needed to make this model work, which is why I think it would make a great problem set. There might even be a letters-style publication here. I'll put co-authorship out for tender!

RWC losses

Such are the measures of success in hosting international sporting events: The Herald calls the 2011 Rugby World Cup a success for having lost the country only $31.3 million, "$8 million less than they expected." Alas, the article seems not to be online. But as most of the APNZ story seems to come from the IRB press release, you can probably just read that.

I'd be interested in seeing what went into that final "cost to the country" tally. Is it just the cash transfer from the government to the RWC? Local government outlays as well? Costs of diverting a substantial part of the Wellington bureaucracy to supporting the RWC? Stadium expenditures, like Dunedin's mess, where the RWC push was a pretty explicit part of the case for building it?

RWC Minister Murray McCully comments:

"Without a doubt, RWC 2011 will generate significant economic benefits for this country for many years to come."

Sam Richardson points to some different results in Manawatu:

Far from producing a windfall, predicted to be worth between $750,000 and $2.2 million to the city, economic growth actually slowed during last year's tournament.

Proponents of the city's involvement, which included two matches, were "overly optimistic", said economic policy analyst Peter Crawford, and some city councillors are asking whether hosting large events is worth it.

The estimates process got it so wrong because it did not balance the likely benefits against the costs, he said.

One of the costs was the extent to which such a major event crowded out other activities.

I'll look forward to seeing Sam's paper at the NZAE meetings.

HT: Hamish Keith