In 1986, I had a hole-in-one at the Ames (IA) Country Club. As I was carrying on like a kid, my golf partner sat quietly in the golf cart. I thought maybe the ball hadn't actually gone in, but I could see the entire green and the ball wasn't on it. I asked him, “Did you see that?! It went in the cup, didn't it?!”

“Yes,” he replied, “But what were you trying to do?”

It was a good point — but it took some of the fun out of it! And, of course, this golf story ends with a round of drinks at the clubhouse — so my perfection had its price!

This story of perfection is far from my normal golf game. Like most recreational golfers, my greatest struggle with the game is consistency — 3 pars followed by a double bogey (2 shots over par).

Golf can serve as an analogy with pork production. The hole in one in pork production is the full-valued pig — the one that receives no discounts and hits most of the production performance targets.

Like the hole-in-one, the upside of variation shows the potential of swine production, and we may think, “that's what we're trying to do” — but it can be costly.

Clearly the low end of variation — the double bogies — may be eliminated fairly easily by managing the golf round or pork production a bit more carefully.

### What is Variation?

To discuss variation, we need a couple of statistical definitions:

A statistical population is a collection of all possible observations in a defined space. For example, a single barn has a population of 1,200 pigs.

A sample is a subset of the population. A pen in a barn or a truckload of pigs hauled out of a barn represents a sample of the pig population in the barn.

The individual pig on the truck is the observation within the sample of the truck, drawn from the population in the barn.

I often think of the “mean” or average as a sample level statistic. It tells us very little about the individual pig. In other words, they all look the same. They look like the mean.

In contrast, I think of variation as an observation-level statistic that gives us at least a fuzzy picture of what individual pigs look like.

Variation is a measure of dispersion of a variable's observations. Statistically, variation can be measured in several different ways:

• Range is the distance from the high value to the low value of all observations.

• Mean deviation is the average difference between repeated samples of two observations.

• Standard deviation is a measure of the “deviation” around a “standard” observation — the standard usually being the mean or average of the observed values.

• Coefficient of variation, or CV, is a unitless measure of variation (quantity without physical units) relative to the mean. It is the standard deviation divided by the mean, usually reported in terms of percentages.

Standard deviation is the most commonly used measure of variation. Its value has the same unit as the variable measured.

A large standard deviation implies a large dispersion of individual observations around the mean (a large range). A small standard deviation implies a small dispersion of individual observations around the mean.

The coefficient of variation is very useful for comparing the size of variation between two different samples.

For example, one finishing barn is closed out with an average weight of 275 lb. and a standard deviation of weights of 25 lb. A second barn closes out with an average weight of 260 lb. and a standard deviation of 24 lb. Which barn has more variable pigs? The 275-lb. finishing barn has a higher standard deviation, but its coefficient of variation (CV), standard deviation divided by mean, is 9.1%, while the CV for the 260-lb. barn is 9.23%.

So the barn with lighter average weights and a lower standard deviation actually has more relative variation than the other barn.

### Production Variation

If you view the pigs in a barn, or pull a truckload of pigs from a barn, you will have a snapshot of the variability in that barn.

The truckload is the most common economic snapshot because it's when pigs are weighed and priced. It shows the impact of the production variation on revenue (price sold x quantity).

The only way to observe the true variability in a barn would be to dump the whole barn at once. When you pull truckloads over a period of time, or sort pigs going into the truck, you are changing the sampling of the barn's population with respect to time. Therefore, you do not observe a true cost of variation.

If you're good at sorting, your truckload will be less variable than your overall barn. And, if you pull loads, you're measuring the variation of the pigs left in the barn at a different time than the pigs marketed earlier. Consequently, you never see a real cost of variation in an operation unless you very carefully measure weights and feed intake of all pigs through time.

This analysis considers the impact of variation on profitability through time. It's more of a video clip of pig growth and value than a snapshot.

### Modeling Variation in Growth

To demonstrate the economic value of reduced variation, a simulation model of pig growth and marketing is developed. The model requires only three components:

• A pig growth function accounting for production variation.

• Daily feed intake estimates for pigs to incorporate key variable costs.

• A packer's pricing matrix to evaluate the revenue impacts of variation.

The pig growth function is adapted from data collected by Alan Schinckel in Purdue University research trials on lean growth and body composition. These data were used to estimate a model of variation in body weight and growth using mixed, non-linear regression methods. This equation is used to simulate the body weight of 180 pigs in the finishing stage — from 49 to 205 days of age — and allows each pig to be grown individually within the sample distribution.

Figures 1 and 2 show the growth and average daily gain curves for the range of lightweight, median and heavyweight pigs. Other pigs fall within this range.

The growth curves possess the stylized S-shaped growth curve. As the pigs grow, the range in the high and low pig weight for a given age increases. However, for the original simulation model, the coefficient of variation remains constant (CV = 8%). In other words, relative variability does not change in relation to the pigs' weight.

A daily feed intake equation was needed to estimate the feed costs for the gain achieved in the growth model. The feed intake of pigs over time is shown in Figure 3. On any given day, all pigs, regardless of their weight on that day, are assumed to have the same feed intake. All variation arising in costs originates only from the differing growth rates of the pigs.

The marginal cost of gain for a light pig is higher than the marginal cost of gain for a heavy pig. In reality, feed intake and growth are likely to be correlated. As feed intake increases, growth increases. It would be very interesting to consider what these covariate relationships might mean, but the complexity is beyond what is necessary for simulation purposes.

An equation relating backfat to bodyweight was used to estimate the lean composition of the pigs. The equation is very rudimentary and based on calibration to USDA Agricultural Marketing Service (AMS) reports of lean percent. As with the earlier example, quite a bit of work could be done on modeling the relationship of weight, age and lean percent or backfat.

The simulated model estimates that pigs average 265 lb. at 161 days of age for a lifetime average daily gain of approximately 1.65 lb./day. The backfat at this weight averages 0.71 in. For comparison, AMS reported (LH_HG201, 3/13/08) that negotiated pigs sold averaged 265 lb. and averaged 0.71 in. backfat.

Beyond the base model described above, which is the low-variation model (CV = 8%), two other models were simulated: a middle-variation model (CV = 10%) and a high-variation model (CV = 20%). Figure 4 shows the distribution of the pigs under the three levels of variation.

It's difficult to say which level of variation is most representative. Most CVs are reported for pigs marketed. It is safe to assume pigs marketed have already been sorted, thus lowering the CV to 8 or 10%.

However, Dewey, de Grau and Friendship, in an observation study of pig variation on commercial farms, reported at a 2001 London Swine Conference (Ontario, Canada) that over the life of pigs, the CV remains remarkably stable and varies between 20% and 31%, with 20% being the CV at 20 weeks of age (140 days).

This observed result is consistent with the growth function simulated with a CV of 20% for weights as the baseline of high variation. While nowhere near the complexity of the real world, the model will suffice to give some grainy video of the economic tradeoffs.

### Simulating the Economic Impact of Variation

The primary economic impact of variation is the impact on revenue of the variation. This occurs through the combination of weight (pounds of pork sold), and price affected by packer premiums or discounts for weights and leanness of the pigs.

Figure 5 shows a representative packer grid. This is a surface plot that represents the revenue tradeoff in three dimensions — weight, backfat and premium level or price. To the left side, lightweight pigs are discounted; to the right side, heavy pigs are discounted. At the front edge of the box, pigs are discounted because of low backfat, and to the back of the box, pigs are discounted because of high backfat. The base hog price used is a \$40/cwt., live equivalent price, and different values would affect absolute levels, but relative changes would be consistent.

The steps indicate where a premium/discount changes based on weight or backfat measures. You can market a pig anywhere on the surface or tread of the step and get the same price. The highest plateau is the highest possible value for a pig. Assuming costs are constant, ideally you would like to have all pigs priced at this plateau.

Figure 6 shows the high-variance pigs (CV = 20%) marketed through the packer grid, but not including feed costs or sort premiums. Notice how small the highest plateau is. Only 26% of the pigs meet the highest-revenue objective. Other pigs are discounted either because of weight or backfat measures. This is compared to Figure 7, which are the medium-variation pigs (CV = 10%). Not only are there more pigs on the plateau (37%), but 1.3% of pigs are now at the lowest possible price, whereas 2.7% of the higher-variance pigs are at the lowest value of \$16.40/cwt.

Figures 8 and 9 take the analysis one step further to include feed costs. Feed costs are based on feed intake and growth described earlier and a corn price of \$3.55/bu. and a soybean meal price of \$275/ton.

Again, higher feed prices will affect the level of costs, but not the relative impacts of variation. These figures are shown as gross profit over feed costs/head. The distinguishing feature of these charts is the dark blue peak, which signifies pigs that are very near their “full value.”

At the lower left of Figure 8, a large number of high-variation pigs that are low weight and low backfat are actually sold at a loss. From an economic perspective, these pigs should simply be culled as not covering variable costs. With mid-variation (CV = 10%, Figure 9), there are no pigs sold at a loss; therefore, all pigs should be retained.

Now let's look at what's happening over time and levels of variation. Figures 10 and 11 show the gross profit over feed costs of marketing at the “optimum profit day/weight” for the medium- and high-variation examples. As a comparison to the surface charts, this chart is a slice of one day of a surface chart, and the day chosen is the day that the pigs, on average, have their highest value.

Figure 10 shows the value of each of the pigs marketed on Day 157 in a high-variance case (CV = 20%). Earlier, this was suggested as the variation one might observe in an unsorted barn or truckload sampled from that barn.

The pigs are marketed at an average weight of 258 lb. with an average value of \$55.97/head. However, many pigs are marketed below this value and even in negative territory. The “full-valued pig” is marketed at 292 lb. and at a value of \$86.37/head. The full-valued pig is the absolute best to hope for; it assumes no variation in weights, time or quality. But the difference between the full-valued pig and the average market pig is \$30.40/head!

Achieving that optimum level for every pig is clearly not cost-effective. The only way I can imagine it is by selling each pig individually when it reaches that optimum — clearly beyond any reasonable management alternative. However, it does demonstrate the value of the “hole-in-one,” and we can improve by moving incrementally toward this full-value pig. Figure 11 demonstrates this.

Pigs in Figure 11 are drawn from a distribution of pigs with mid-variation (CV = 10%). This reduction in variation is similar to what is observed with sorting practices. The optimal date of marketing increases (164 vs. 157 days), average market weights are higher (271 vs. 258 lb.), and the average profitability increases (\$68.37 vs. \$55.97/head).

So reducing variation by approximately half results in an increase in profitability of about \$12.40/head. The full-valued pig is still at 292 lb., but now its value is reduced to \$82.52/head.

Why is the value reduced?

Because the full-value pig reaches market weight earlier with high variability, so it is reflected as having lower feed costs due to fewer days on feed. We would find a full-valued pig at Day 157 of marketing the medium-variance pigs, too, and it would have a value similar to the 157-day, full-valued pig for high-variation pigs.

The full-valued pig is showing that the heavier pigs pass through that point, and once they reach that point, the ideal would be to market them rather than reaching the point of decreasing returns as shown in these charts.

Figure 12 shows all three levels of variation, including the lowest variation sampled (CV = 8%). It is graphed on the day of the optimal marketing of the lowest-variation group, which is Day 167. The optimal marketing day is 10 days later than the high-variation pigs at 157 days, and the profit is much higher — \$72.96/head vs. \$55.97/head — a difference of nearly \$17/head!

The full-value pig still exists. Its weight is remarkably similar to the other full-valued pigs, not surprisingly, and its value is close to the medium-variation pigs marketed at 164 days.

Although it is difficult to see, if you took the high-variation pigs to this marketing date from 157 days, then the average value of the high-variance pigs would be \$54.73, a loss of another \$1.20/head.

Finally, Figure 13 shows the “video” of pigs' values over time and growth. I included only the value of the low, average and high-weight pig for the low-variance case. Heavy pigs should be marketed as soon as possible because they are losing value both from a cost and revenue perspective. Similarly, light pigs represent a tradeoff between costs and the price/premium steps.

Notice that the “treads” on the steps are always sloping downward. Once you hit a premium level, the pig loses value every day beyond that point until it gets to the next step. This occurs because of the lightest pigs' higher cost of feed. If there were no costs to monitoring and sorting these pigs, you would get rid of them exactly when they hit the grid premium and not a day longer. You can also infer what happens with higher feed prices — the treads between the steps get steeper, suggesting even greater cost to holding low-weight pigs longer. In the extreme price event, the step up may not even compensate for the feed costs between steps — increasing the cost of these pigs that are hidden in the averages.

### Conclusions

This analysis shows that the potential economic merits of reducing variation in pigs are significant. These benefits accrue for three fundamental reasons:

• Marketing more pigs near the full-valued pig.

• Increasing average weights possible at marketing, thus increasing total revenue by pushing more pounds through the system.

• Reducing marginal feed costs for reaching higher-valued pigs.

The obvious, unanswered question is, what's the most cost-effective method to reduce variation to capture these profit opportunities?

A paper by J.F. Patience and A.D. Beaulieu at the 2006 Manitoba Swine Seminar reviewed research suggesting several possibilities to reduce or manage variation. They concluded, as most others have, that it is difficult to identify any single production practice — other than sorting — that consistently and significantly reduces variation because of the interplay of genetics and environment in production.

However, we may be asking the wrong question. Rather than asking which production methods could reduce variation, perhaps we should be asking what incentives can be put in place to reward practices that meet a target level of variation.

This is essentially what the packer grid in this analysis does. Packers don't say, “sort pigs to reduce the variation in the plant.” They provide a grid that gives rewards and penalties to reduce variation to meet their grid. It allows for flexibility and creativity in meeting that goal.

The same idea can be applied to swine production by rewarding reductions in variation. What would happen if, instead of making payments on a “per-pig-space basis” or a “pigs-out-the-door” basis,” the payments were allocated based on the number of “full-valued” pigs out the door? How much creativity would occur in finding ways to reduce variation in production, besides just sorting?

This paper suggests the value of reduced variation is there. Perhaps we should consider a new avenue to incentivize a reduction in production-based variation rather than prescribing methods. In the long run, the correct incentives may provide the most potential to truly reduce variation and capture that value.