Playing The Odds

Using statistics to recognize if a management change offers the highest payback.The extra nickels and dimes you save (or spend) with everyday management decisions could easily be the difference between red or black ink at the bottom of your accounting ledger in 1998.If you made a management decision today that improved daily gain by .10 lb./pig/day, what would it mean to your bottom line?If you trimmed

Using statistics to recognize if a management change offers the highest payback.

The extra nickels and dimes you save (or spend) with everyday management decisions could easily be the difference between red or black ink at the bottom of your accounting ledger in 1998.

If you made a management decision today that improved daily gain by .10 lb./pig/day, what would it mean to your bottom line?

If you trimmed your feed cost/lb. of gain by $.015, but the change also caused a .05 lb./pig/day slippage in daily gain, how would that affect your bottom line?

Or, perhaps, you invest a dime per pig in a product that boosts daily gains by .02 lb./day - does the payback justify your investment?

Producers and their advisors make similar decisions every day, often without a thought about how the decision could affect their marketing strategy and/or the price they receive from a packer when pigs are sold.

Extension Swine Specialist Mike Brumm has researched the effects of some management changes, then considered how the resultant shifts in pig performance might affect the price received under various packer buying programs.

The University of Nebraska researcher admits such a distinction was often difficult to make in the past. Continuous-flow operations where pigs were constantly removed to market and more pigs brought into the system made it nearly impossible to define groups. As pigs reached desired weights or more space was needed for the next group coming in, pigs were often moved and mixed making it almost impossible to keep track of ages, origin or other pertinent inputs. Commonly applied statistical tools that could help understand the impact of management changes simply do not apply.

But much of that changed as producers increasingly embraced all-in, all-out (AIAO) production methods. With AIAO, facilities are stocked, groups are identified and remain constant from the start of the growing period until they leave finishing facilities for market.

"At the time of stocking, pigs are often from one to three farrowing sources, of common genetics, and often within two weeks of age of each other," Brumm notes. Barrows and gilts are often penned separately in grow-finish buildings. In larger operations, entire buildings may be stocked by gender.

"The clear defining of a population - by room, barn, farm, etc. - means that producers and their advisors can now employ common statistical methods to describe each population of pigs," Brumm notes.

Statistical methods! Yikes! Don't let the reference to "statistics" spook you, says Brumm. Much of the mathematics is already done and, he adds, there is a payoff.

Here's Brumm's bottom line: If your records can supply the information needed to drive modern day "what if" models, time-tested statistics can shed new light on the impact and the profit potential of your management decisions. It's not necessary to understand the statistical methods and formulas precisely, only their application.

Understanding The Bell Curve Most people have been exposed to something called "the bell curve," which simply reflects the normal distribution of a trait or measurable component in a population. In general terms, the curve shows how a population is distributed. Examples might be the distribution of height among men in your hometown. Or, the weight of all third parity sows in your gestation barn. Or, the range of daily gains recorded on a group of nursery pigs.

If you recorded the weights of all pigs in an AIAO facility, barring any unusual management orhealth problems that could cause unusual shifts in the population's distribution, Brumm notes that the distribution of weights over the curve will follow the pattern shown in Figure 1 - the bell curve.

The distribution of points along the curve is commonly described by two statistical terms - "mean" and "standard deviation."

The "mean" - often called the "average" - identifies the peak or center of the distribution curve.

"Standard deviation" simply reflects the variation along the curve - defining the shape of the curve. Deviations affect how flat (wide) or peaked (narrow) the shape of the curve will be.

Keep The Faith If you're not a statistician, read the next couple of paragraphs on faith - a practical example will follow.

Brumm explains: "The mathematical formulas used to calculate standard deviation for a normally distributed population result in 68.26"percent" of the population being +1 standard deviation of the mean. Two standard deviations from the mean includes 95.4"percent" of the population."

The Nebraska extension specialist explains that years of tracking and defining "normal" distribution curves have given rise to something statisticians call "Z" tables. About all you really have to understand about these tables is that they help determine the number of samples meeting criteria for a population defined by a mean and standard deviation.

In everyday terms, this example using grow-finish pigs should help: We have a grow-finish unit, operated AIAO, stocked with 100 pigs/room. The mean (average) weight of the pigs is 210 lb. The standard deviation is 21 lb. Now, through the use of the Z table, we can accurately describe the distribution of the weights of the 100 pigs across the bell curve.

Brumm starts with the simplified Z table (Table 1, page 24). The Z values listed provide the multiplier of the standard deviation. So, with Z=1, for the 100 pigs in the room with a mean weight of 210 lb., a +1 standard deviation (21 lb.) would have pigs weighing in at 231 lb. (210+21). Now, the value associated with Z=1 in Table 1 is .3413. This means that 34.13"percent" of the 100 pigs would weigh between 210 and 231 lb. Rounding off, we can put 34 pigs in that range. Likewise, since the normal population curve (the bell curve) is distributed equally on both sides of the mean (center), there would also be 34 pigs (34.13"percent") between 189 and 210 lb. (210-21). We now know that 68 of the pigs weigh between 189 and 231 lb.

If we extend to two standard deviations from the mean (2x21=42), we have defined the weight range at 210 to 252 lb. (210+42) and 168 to 210 (210-42). In other words, 47.72"percent" (from the Table 1, take .4472 x 100 pigs) of the pigs will fall to the left of the median on the bell curve and 47.72"percent" to the right. That leaves only 4.6"percent" of the pigs in this room (approximately 5 pigs) weighing less than 168 lb. or more than 252 lb.

Okay, so we now have a better idea of the weight range of the pigs in the barn. But, there's one more statistical linkage that needs to be made before we get to the payoff. Hang in there.

Brumm reinforces that describing a pig population using these common statistical terms has merit for producers and their advisors. Still, he acknowledges, few have the knowledge base needed to understand how typical pig populations vary in weight over a growout period.

Research work at many universities and company research farms reinforces that as mean weights increase, standard deviation likewise increases. Both measures are expressed in pounds, and therefore tend to change together. That means that a description of how a pig population varies requires both the mean and the standard deviation be given. It is meaningless to list the standard deviation of a group unless you know the mean or average it "deviates" from.

Brumm offers this final mathematical twist to solving the link between the standard deviation and the mean. This measure - called the coefficient of variation or "CV" for short - is often used to describe the variation in a population. Simply stated, CV is the standard deviation divided by the mean. The result is expressed as a percentage.

So, a CV of 10"percent" says the standard deviation is 10"percent" of the mean value. "Another way of stating this is that approximately 21/43 (68.3"percent") of the pigs have weights that are + 10"percent" of the average weight for all of the pigs."

Brumm's work with actual groups of pigs has shown that CV values in growing/finishing populations tend to be relatively stable - particularly toward the end of the finishing period. Therefore, the CV can be a useful indicator of how much weights vary in a finishing pen, room or barn.

What is normal CV? "Based on my experience at Concord (Experiment Station), I typically tell producers and their advisors to start with the 10"percent" or 11"percent" CVs in the table. Then as they gain experience, they can make adjustments up and down. An 8 (CV) would be very rare, but 12-14 might be common in some systems," he says Brumm also reminds us that disease challenges can have an impact on CV values. "These tables and the underlying math are based on normally distributed populations. They probably don't apply if a disease or management situation caused a lot of knotheads - which will skew the curve," he adds.

The Payoff The stage is now set to use Table 2. Using the population statistics we've just reviewed, we can now estimate pig weights within a normal distribution in the grow-finish population. Our starting point is at the 50th percentile column where the average weight is listed.

Brumm offers this example: Using experience, judgement or other means, a producer or consultant determines the CV for a group is 10"percent" and the average weight of all pigs is 220 lb. Brumm has done the math, thus generating Table 2, converting CVs to percentile distributions for the various CVs and average weights.

Looking at Table 2, you'll note that a group of pigs with an average weight of 220 lb. and a CV of 10"percent" has 20"percent" of the pigs weighing 201 lb. or less (20th percentile) and 20"percent" weighing 239 lb. or more (80th percentile).

Now that we have an estimate of how pig weights are distributed over the group, we can apply those weight distributions to a packer's payment matrix. Table 3 offers the payment matrix for IBP and Hormel & Co. as of Aug. 1, 1997.

You're now ready to measure the financial impact of how a management decision might affect your bottom line. "Knowing the weight distribution, producers and advisors can calculate packer discounts for sort loss when a variety of market options are considered," says Brumm. "With an estimate of sort loss versus fixed and variable costs associated with each additional 'pig day' in a facility, the financial consequences of various marketing decisions can be estimated."

Possibilities might include whether to "top off" pens in a finishing barn to capture a packer's premium and reduce crowding in the finishing pens. Brumm offers this scenario: 20"percent" of the heavier pigs in a finishing barn are sold with the next sale planned two weeks later. "If I know the average weight of the top 20"percent" and have some estimate of the CV, I can use the table to estimate the average weight of all pigs in the barn. Then I can do a rough feed/gain, cost of gain to date, etc. calculation. I can also use average daily gain projections and calculate how many discounted pigs I would have if I sold the remainder at various time intervals on various packer grids.

"This lets me balance facility costs vs. packer discounts for pigs not meeting the requirement," Brumm explains.

There are always tradeoffs. Topping off finishing pens means the hierarchy of the pen will have to be re-established, which has implications on growth and efficiency. The compromise might be to establish the weight distribution of the pen and, if warranted, match lighter hogs to one packer's payment matrix, heavies to the other so the barn can be emptied, cleaned and restocked.

Brumm also reinforces that the tables can be used to more accurately describe the impact of a management change on a pig population. "Rather than saying the use of a vaccine, feed additive, drip cooling system, etc. decreased the variation, it is more meaningful to say - 'the use of XYZ reduced the CV at marketing from 11 to 10. This number can now be used in conjunction with Table 2 to model the financial impact of that change on price received, barn flow, etc."

There is no doubt that the application of these common statistical methods to describe populations of grow-finish pigs nudges producers to the next level of precision when making management decisions, Brumm notes. These methods will help producers more clearly estimate the payback potential of a management or herd health change. And, these techniques shed new light on how a marketing decision and packer payment matrices interact with performance shifts caused by changes in management.