Sir Francis Galton, Blaise Pascal and Where You End Up in Life

There was a mathematical genius that lived in 19th century Victorian England named Galton. There was a triangle invented by Paschal a 17th century French mathematical genius. The work of these two don’t define reality but it completely informs reality. Paschal invented his famous triangle:

You can read about the magic of Paschal’s Triangle here

It turns out the first reference was by the Chinese in the early 14th century and was used as a calculating machine. Francis Galton invented a means to animate Paschal’s triangle  It’s worth watching the progress of the balls as they settle from the collection bin into the distribution. The distribution of course is the famous Gaussian distribution described by mathematicians and gamblers Gauss and Adrain in the 19th century but hinted to by Galileo in the 16th century. Galileo noticed errors were distributed. Small errors more likely than large errors which then leads one to ask what is error accumulation and how does error accumulation effect things? The answer of course is the effect can be massive or indiscernible since errors can be of either sign and can add or cancel. This is the concept of sequence of return risk from the 16th century.

David Byrne et. al. put it this way:

And you may find yourself 
Living in a shotgun shack
And you may find yourself 
In another part of the world
And you may find yourself 
Behind the wheel of a large automobile
And you may find yourself in a beautiful house
With a beautiful wife
And you may ask yourself, well
How did I get here?

Where you end up is a function of a normal distribution of millions of decisions.

Notice that one lone ball way out in the right tail. How the hell did he get there and what is the probability? (the answer is 2^14) This assumes the board is level and gravity is acting equally on each ball and there is a 50/50 probability of a ball bouncing left or right at any given peg. Tilt the board the odds change. Here is the story of how you got there. This is how life works in a probabilistic universe, and you can use that to qualify your risk and effect where you end up. If you constantly make rightward choices you end up in right bins. Left choices, left bins. This example belies the silliness of the expression “you can’t beat the market so invest in low cost mutual index funds” . What that statement defines is the 50% bin. Clearly A LOT of balls beat the 50% bin. So the next time you hear someone quacking that party line tell ’em “you’re a clueless dumb ass” because they are. The way you end up on the left of the 50% bin is to make leftward choices. The next time you hear someone quacking about 4% x25 understand it depends. In a 50/50 portfolio counting from the left that puts you in bin 6 or so (98% chance of success). 80/20 moves you to bin 7 from the left. 99/1 gets you to maybe bin 8. Yes you can beat the market but the market can also beat the hell out of you by rightward decisions instead of leftward decisions. People do this all the time, claim you can’t beat the market and then proceed to try and beat the market by using real estate or by taking monstrous equity risk in their portfolio. People sit around with cash in the bank which they intend to invest but just can’t bring themselves to invest “waiting for a pull back”. This is called market timing and market timing can be a leftward decision, except you have to know when an event leans left which implies you need rules for trading that force leftward decisions. An example of leftward market timing is re-balancing to a predetermined portfolio risk level every so often. The mechanical nature of re-balancing forces leftward decisions. Sitting around waiting for a pull back merely means your portfolio is not risked correctly and money you intend to put at risk to procure some profit is not doing the job, a decidedly rightward decision cloaked in a leftward delusion. Lets say you choose to “MAX OUT YOUR PRETAX accounts” ever hear that one? Is that a leftward or rightward decision? How did you get here? You let the days go by. What that means is you wind up with a huge pretax pile some of which is owned by the government and at age 70 is wholly controlled by the government. RMD is progressive and taxes are progressive so the government by law is going to take a (progressive)^2 tax bite. Here is what happen in a (progressive)^2 scenario:

The red line is the ever evolving tax bite eaten by the government in retirement. The black line is money already taxed. Over time black beats red. Betting red was a rightward decision, black a leftward decision. It just took some time to manifest itself, yet people quack that nonsense all day long. A better tactic (and the leftward decision) is some of each and to optimize that ratio along the way. To understand that you need to understand what each account will be used for in funding retirement and the rules of taxation for each account going in and coming out, so you can make leftward decisions. Do not just let the days go by or it will be the same as it ever was.

I took a little break from the blog to live my life. I bought some Udemy courses on various topics on black Friday for $10 each, topics heavy into computer programming, micro controller programming, excel programming and a few others. Udemy is a little better choice than Youtube since you can correspond with the lecturer. I also completed my CME to keep my medical license active and I’ve been doing stuff in the yard since it’s FL and 70 degrees outside. It’s a great time to make some vitamin D in FL. I’ve really started to whittle down my blog involvement especially other blogs since the information contained is often useless if not actually wrong. Some sites are so agenda and marketing driven as to be unreadable. Some sites conflate ideas into a miss mash of gobbledygook and then dole it out in “10 Bullet Points of Nonsense”. If if the adage is “it’s 20% content and 80% marketing”, that’s another way of saying “you can rely on 80% of what I say to be BS!” Who needs it? I started working on an outline for a non Bogglehead approach along the above lines of processing probabilities in making financial plans. We’ll see where that goes. May be worth while may be a piece of junk.

8 Replies to “Sir Francis Galton, Blaise Pascal and Where You End Up in Life”

  1. Yep. Our real lives are way more interesting than the online world. I have started to read more of the white papers available about retirement income planning. I am becoming more confident in my approach with respect to our situation.

    The problem of offering advice to others is that what would work for me would not work for others. That’s the part most people do not think about.

    That’s what I am seeing more and more. I agree that those who offer blanket sing song simple advice is frankly dangerous and extremely unsophisticated. And all those who unwittingly follow them may not see the errors until they are decades out.

    1. The very first thing to do with retirement planning is to start at your death and work backward. It’s not till you understand your need from death going back to the day of retirement that you understand the real meaning of need. That amount is the amount the portfolio plus other sources like SS HAS TO SUPPORT. Included in that number is taxes, medical care cost, and inflation, beside normal cost of living. So if you spent 3M reaching age 65 your going to need at least 3M inflation adjusted to reach 95. If you analyze like this instead of just pulling a number out of thin air you stand a better chance of “leaning left” in your portfolio disbursement. All of those decisions during accumulation are dictated by the end just like the final position of any ball is dictated by its sequence on the way down. Like Galileo found errors, are cumulative and tend to compound in the same way interest compounds except errors carry the additional risk of a sign, they can add to the end or subtract from it. This is why leaning left is so important good choices can make up to some extent for bad SOR.

  2. That graph with the red and black line of how tax deferred and taxable account behave with time is striking and one I am going to have to actively work on myself to avoid the RMD. I have bookmarked your strategy of roth conversions and once I retire hopefully will have a couple of decades to make the transfers in the most tax advantageous way possible

    1. The reality of that graph was derived from some professional estate planning software specifically tailored to doing tax optimization over decades in retirement. It is software used by my adviser. The software advised 100% TIRA to Roth conversion at the top of the 24% bracket but I’m converting less. To pay for conversion I have to sell brokerage stocks which are growing nicely. The difference between the top of the 24% and what I am doing is about 100K in taxes so that’s 100K that grows and already has been taxed so it’s growth would be on a line that bisects the 2 curves. Given my particular situation I calculate leaving a $500K to 600K residual in TIRA keeps you in the 12% bracket for over a decade, longer if that money is in bonds, so just RMD and turn it into an annuity and let the Roth grow unmolested and keep the 100K tax saving growing in the brokerage. Growth on the 100K should more than pay for the equivalent small tax burden of keeping some money in the TIRA. If tax law changes or the need arises the TIRA can be drawn at a higher than RMD rate to provide some extra cash flow in the short term or for something like a recession to keep from selling stocks low. Otherwise live off SS + the TIRA RMD + some from the brokerage mixed with TLH for a nice life. All of that money is tax advantaged. SS is taxed at 85% and has a built in inflation component, the TIRA has funding that was post tax money so I pay taxes on only 94 cents/dollar on that money, and the brokerage is coupled with TLH so I pay no cap gains on that money till the TLH runs out. By then I should be 85. It’s a little complicated but provides the government with the least amount of my money going forward and is conservatively legal.

  3. I like the graph! I have intuitively thought that was true ever since 2010 when Roth conversions were born. However it seemed like a lot of effort to figure a way to estimate the crossover point. Nevertheless, I have become a Roth fanboy. Given my typical spending pattern and plugging my pre-tax account into the Schwab RMD calculator, I’m fairly certain my RMD will easily exceed my spending if I do nothing. So I get to take out money I don’t need and pay extra income tax on top of that and it gets progressively worse as I grow older. What a deal! For now I’m taking advantage of the 24% bracket; since it’s so wide I can fill it to the max by rolling over some pre-tax 401k into its Roth partner. I appreciate all the ideas and considerations you’ve brought up in this blog and I’m trying to wrap my head around them. To use a med school analogy, this is like trying to get a sip of water from a fire hydrant.

    1. People tend to want the “best” plan and remain inactive while “figuring it out”, when in reality since this is a time dominant thing in that it has to be done and the cost of doing it has to be born and completed before age 70 the “best” plan is to do something towards the goal, and tweak if you can as you go. My analysis is the government owns some of that money and at age 70 assumes control of disbursement, no ifs ands or buts so give them their money and get on with your life owning YOUR money. It’s the bargain you made when you got into bed with them. I think my plan is about as close as to “have your cake and eat it too” as you can get. The thing about the graph is Roth conversion acts like a poor SOR on the front end and therefore takes a while to recover from If you can stand converting to the top of the 24% bracket you pay about 19 cents on the dollar for conversion, not the best but not bad either and if your still working the W2 covers the extra expense so the portfolio is closed and the risk remains low. Instead of diverting W2 money into growing the portfolio, you divert a little to getting the government out of your bed, which is a good deal IMHO. You remove the risk of tax rates increasing and the govt could accelerate the rate of RMD disbursement as well. In addition when you die your spouse will get killed in increased taxes. If you wait you get a bad SOR when you are old. So it’s pay me with certainty now or pay me later and suffer decades of uncertainty. There’s a chance paying now is a rightward decision but given 22 trillion in debt there is a better chance it’s a leftward decision. Homey likes to control his risk and even more his ol’ lady’s risk when he’s dead. Glad my ideas bear a little fruit for you GF

  4. I find that trying to calculate the Roth conversion is the part that always makes my head spin.

    We pulled off a large (for us) Roth conversion during a “big year” where we maximized contributions to 401k, corporate profit-sharing and maxed out our defined benefit plan. We had lots of conversion space and a low taxable burden at that time.

    I’m looking for someone who can provide fee-based advice on a Roth conversion plan, factoring in the uncertainty of a stop work date.

    I’ve always thought you’d be the guy to design this software, Gasem, but I’m all ears if you have a specific recommendation.

    Enjoy being in your math class,


    1. I set out once to write a program but the problem is to decide what problem to optimize. You can optimize least taxes going forward or least taxes paid for conversion or somewhere in between and its affected by the ROI in the left over TIRA. Least taxes going forward cost the most in taxes in the present and moves the crossover point far in the future like 18 years. Least taxes in the present doesn’t get enough money out to make a difference. In 5 years you’re back to square one. This is why I think you have to specifically designate your goal by ear marking each account by purpose like WR or insurance or bank. If the Roth is to be insurance and legacy then convert a smaller amount, probably around half of the TIRA unless the TIRA is huge. If you expect to live off the Roth a bigger conversion is the ticket, but then again “HUGE” is defined by your budget and cash flow need. 2M is not huge if you’re pulling out 200K/yr so it’s a super individualized process about what to optimize. The other problem with a program this complex is validating the data aka nightmare. What I did was write separate excel modules that optimized one thing so I could make sure the data was valid at each step and then iterated by hand to achieve various goals and scenarios. The validation step was beyond my pay grade for writing a one step solution. Also as tax law changes and if RMD disbursement changes or someone dies and filing status changes. the whole thing becomes invalid. It was project enough for me to figure out my particular situation but a more generalized solution is not how I want to spend my retirement, but I learned a ton about the science in the process. There is commercial accountant grade software available with accountant grade pricing which I was able to compare my numbers with that programs numbers and the numbers between my analysis and the program compared very favorably but the conclusions were somewhat different because the object of optimization was different based on where my conversion money was coming from during conversion, a level of complexity not anticipated by the program It’s likely only a AUM account manager with a quant bent is going to be able to purchase such a package. That is the advantage of a good AUM manager, you pay a little on the front end and save a s*** load on tax efficiency the back end. People are always quacking about the cost but for a 5M+ portfolio the cost may be around 300 bp NOTHING LIKE 1000. They charge 1% on small accounts because it’s a lot of work to manage any account big or small so you’re better off as a manager with 10 BIG accounts than 1000 small ones. If you save 1000 to 2500 bp on tax efficiency over 20 years you’re WAY ahead compared to the dumb assed bogglehead DIY argument. My AUM has saved me a ton because he knows all or can figure out the leftward leaning choices and all of those choices compound over time. You get what you pay for. Pay Larimore $15, you get 15 bucks worth of bogglehead rap. Nothing more nothing less. Pay him another $15 you get the same rap in a different book. For the rest of your success and all of those million correctly executed leftward decisions, YOYO. Jack Bogel wrote the same book 15 times. Jack Bogel may get you toward the center of the distribution if you follow through and do things pretty much perfectly by the book. Invest every month in a 50/50 fund for 30 years. Start messing around with your own “improved version” all bets are off.

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