The Law of Large Numbers
The Law of Large Numbers
The Odds… The Odds…
Like gamblers in Vegas, ball python breeders sit at the table each and every year and play the odds. And each year we bet on increasingly long one’s. We have to. Competition is increasing, prices are fickle and our desire to make something magical is insatiable. In many ways the designer morph business is a competitive sport and the release of the second edition of John Berry’s book has put all of us on notice. The first time I sat down and flipped through its pages all I could think was, “I’m gonna’ need a bigger boat.” More so than ever I see the heights to which I need to elevate my game. All that and there are several existing combos that didn’t make it into the book and photographic contributions from a few of the bigger names in the business were missing. We can only imagine the things they produce and don’t share with the world. Playing catch-up with the morph-producing leaders of this business is forever difficult. The dollars required remain ridiculous and their production helps them stay in front. I’m feel like I’m sitting in the fourth or fifth row, doing my best to leverage a modest but potential-rich collection of animals.
My opportunity to jump forward in the pack hinges largely on one thing: hitting the odds. It has to be. I don’t have the kind of money necessary to buy my way to the front. Each year I spend just enough on new morphs to make my finances constantly uncomfortable and each year I hold back a large number of animals that I should be turning into cash. People who have painful addictions often behave in such irrational ways. Doing the best I can with money I try to fill in the gaps by breeding my way forward in the pack. It’s a slow, uncertain and sometimes painfully frustrating process. The breeders I am trailing have either been around a lot longer than me or they have the finances available to buy themselves the pole position.
Because we are almost always trying to increase the genetic diversity of the animals we produce we seldom do pairings that provide a 100% guarantee on the odds. Every clutch has a desired sweet spot, a moving variable that we are shooting for. Not many people breed super pastel to super pastel or albino to albino even though doing so provides genetically guaranteed results. There wouldn’t be any measurable excitement when the eggs pipped because the results are already known. Genetically speaking, there also would be no forward progress. For many years people have been breeding albino males to het albino females. Meanwhile, albino females are busy being bred to albino spiders or albino black pastels or something else that still leaves some piece of the genetics to chance (while you may be hitting 100% on the albino you’re betting on 50/50 or longer odds for some other morph being added to the equation). Those of us who have eyes set on distant future prizes are breeding albinos to other simple-recessive animals, producing double or triple hets that are not visually exciting. While they are rich in potential they are quite normal in appearance. The payday comes a few years from now …maybe …when you hit on the 1:16 or 1:32 odds.
When you breed single-gene albino to single-gene albino you aren’t doing anything to advance the quality of your collection. More to the point, it’s a waste of a female albino. When combined with another morph the hets you could produce from an albino female are worth more (financially and genetically) than the albinos you can guarantee in a homozygous pairing. Because at least one of the genes is left to chance the results are almost always incomplete and intermediate. Lesser het albino, spinner het albino, albino black pastel, the list goes on. It seems we are always producing things that are visually one thing and het for something else. Once mature these animals are likely to be paired with mates that also do not give us a guaranteed returns on the odds. The lesser het albino might be bred to an albino pinstripe, the spinner het albino could be bred to an albino female and the albino black pastel will be bred to another albino black pastel. All of these pairings offer opportunity but they do not offer certainty. You could miss on the odds, leaving that pairing’s pinnacle of genetic achievement frustratingly unrealized. The odds are long to hit on the albino kingpin, the albino spinner and the albino super black pastel. Hitting on the odds is a magical moment but missing on the odds means your production is not much better than that of a person who is much less invested and breeding albino male to het albino female. Such is the nature of betting on long odds; win big …or lose big.
Pretty much every person who breeds ball pythons has lamented their mistreatment at the hands of The Odds. Friends and colleagues console them by offering assurances that the odds will come back around for them next time. But is it true? Does missing the odds on one clutch earn you the right to have the odds work in your favor on the next one? Is getting brutalized on the odds a way of earning some reptile breeder’s form of karma credit?
In short, no.
When you flip a coin there is a 50/50 chance it will land on heads. The odds are equal for tails. If the first coin flip lands on heads what influence does that exert over the second flip? Do the 50/50 odds shift to favor tails? Of course not. Each flip of the coin is independent of and unrelated to the preceding flip(s). The same is true with ball python genetics. To the best of our knowledge all of the morphs available in the market place are determined at the moment of fertilization and do not change. Whatever genetic code is carried in the haploid cells prior to their union is what determines what type of morph you are producing.
Every year I know, hear or read about a breeder getting miraculous results on the odds. You know who I’m talking about. The guy who breeds het albino to het albino and hatches nothing but albinos. The guy who breeds double het axanthic pied to double het axanthic pied and gets two male axanthic pieds from 7 eggs. The guy who breeds pastel het ghost to spider het ghost and produces 4 ghost bumble bees (humble bee’s). We can go on forever. I console myself by remembering that they are not telling me about all the clutches they had with results that were on par (or under). How the odds work is not foreign to me and while Mr. Punnet’s square tells me how things statistically should go I know from countless times at bat that they frequently don’t. The ratios illustrated by the Punnet square show us the likelihood that certain genes will come together but in no way does it guarantee that the genes will cooperate. So how much stock can you put in the square? A lot if you are producing a lot. Not much if you are only producing a little. Let’s explore some numbers to see what I’m saying.
The table below (which does not display correctly if you are reading this from Facebook) shows the results of pairing a pinstripe to a normal ball python. The Pinstripe gene is a dominant trait and, according to the Punnet Square, there is a 50/50 chance that the babies will be Pinstripes. In the first analysis I assumed that ten females all laid ten eggs each. I then flipped a coin ten times to represent the 50/50 odds of pinstripe:normal. The results are in the right-hand column. Only two of the ten pairings produced results that match what the Punnet Square says they should be. Female #1 and #7 had odds very much in favor of Pinstripes but Female #6 only had one Pinstripe in the 10-egg clutch. As you look over the results you can see that they are quite varied. Such is the nature of the odds when viewed on a small scall. Now notice that the total ratio of Pinstripes to Normals is 47:53. That’s pretty darn close to the 50/50 odds the Punnet square promised: 47% of the babies are Pinstripes and 53% of the babies are Normals. What can we learn from this? As the data set increases (e.g. you hatch more eggs with the potential to produce a certain morph) you are more likely to produce at a level consistent with the Punnet square. If you only produce one or two clutches you are more likely to be the recipient of wild swings in the odds. For example, look at the results of just producing with two females (Females #1 & #2); you would have produced 13 pinstripes and 7 normals. Nice! But now look at Females #9 & #10. If theses were your two girls you would have had the exact opposite results; only seven Pinstripes and 13 normals. If Pinstripes are worth $200 each that is a swing of $1,200; one breeder walks away with $2,600 and the other earns only $1,400. This is part of what makes it so difficult to make a living as a reptile breeder. No matter how hard you work you are always at the mercy of a coin toss. There is neither financial nor mental stability in that.
|# of eggs||Female||Ratio (Pinstripe:Normal)|
The table above is interesting but what happens when you adjust the number of eggs to more realistic values (after all, every girl doesn’t lay ten eggs)? In the table below I counted the number of eggs laid by ten of my females and flipped a coin again. The results are shown in the table below. Similar to the previous table there are few pairings that did exactly what the Punnet Square said would happen. Female #4 was the only girl who produced 50/50 odds. And just like before we can see that there are some wild swings in the odds from one clutch to the next. Female #1 produced 5 Pinstripes and 1 Normal. Female #3 did even better with 6 Pinstripes and 1 Normal. But Female #6 and Female #7 did more poorly with a combined ratio of 3 Pinstripes and 7 Normals. When you look at the average from the ten pairings you see that the final ratio was 32:28 which is pretty close to the 50/50 odds we were expecting. 53% of the babies are Pinstripes and 47% are normals. What am I learning from this? I can only put faith in the Punnet Square and The Odds when I am working with larger and larger data sets. If you want to increase the ability to predict that rate at which you will produce a certain morph you have to attempt to produce an increasingly large number of them. If you rely on small groups of animals to produce statistical results you can expect results across the board. If you are trying to make a living out of doing this you are setting yourself up for failure. When I was in college I worked as a waiter. Anybody who has ever waited tables knows a few truths: 1) Virtually all of your income comes from tips and 2) while the standard gratuity is 15% you can count on a lot of variation. When I went to work to wait tables on a Friday night I knew I was going to make some money but it was never consistent. Some nights I would leave with $80 and others I would leave with over $200. It’s tough to control your finances when your income is so variable. Such is the nature of breeding a particular morph on a small scale.
|# of eggs||Female||Ratio (Pinstripe:Normal)|
As a final bit of proof for the predictability associated with ever-larger numbers I did ten trials of 1,000 eggs that had 50/50 odds of producing Pinstripes. After 10,000 coin flips (er, eggs hatching) we can see that 49.33% of them were Pinstripes and 50.67% of them were normals.
|# of eggs||Ratio (Pinstripe:Normal)|
Part of the reason I sat down to write this is that I, like many other ball python breeders, am a perpetual Punnet Square optimist. With every clutch laid I convince myself that the odds are going to be in my favor. And it simply isn’t true. I produce a few hundred baby ball pythons each season. And that production represent all of my projects and the overwhelming majority of my production is geared toward hitting on longer than 50/50 odds. It’s no wonder that I get depressed when eggs start to hatch. As the incubator fills I begin to mentally count morphs that haven’t even pipped yet. And it hurts when the odds don’t pan out the way I planned. This morning, as a 10-egg clutch of pastel x black pastel spider hatched and I saw that not one baby carried the pastel gene I was reminded yet again that missing on the odds is a constant companion. It will deflate you and kill your motivation more than anything else. In the business world you will often hear people say, “Under promise, over deliver.” The idea is to set expectations lower and then wow people with the service or product your provide. Ball python breeders like me would do well to take a page from this script. Unless you are producing large numbers you need to underestimate what the Punnet Square says is possible. This way you stand a better chance of being happy when little heads start poking out of eggs.