Thursday, December 10, 2015

A comparison of Weight Watcher's Points Plus Values and SmartPoints

Given that I like to use my own software to calculate points (don't worry WW intellectual property police, I don't actually distribute the formulas — I just calculate it on my home machine), I sat down today to dig into the new Smart Points calculations. It turns out the formula is not yet on Wikipedia (in fact, the old formulas are gone — you have to dig through revision history to find them) so I had to sit down with a spreadsheet and reverse engineer the new SmartPoints formula myself.1

As I did so, I realized the formulas gave me a chance to dig into what's behind the numbers. I'm going to present the numbers in terms of points-per-hundred-calories because that's a nice way to see how Weight Watcher's is going beyond simple calorie counting to try to nudge our behavior in certain directions.

PPV/100 calSmartPoints/100 cal
Saturated Fat2.96.1
*Alcohol numbers I've inferred by creating foods w/ a calorie count but no information for other nutrients. That is to say, they could also be taken as a "generic calorie" count -- what WW gives you if you provide it calorie information but no other nutrients. WW doesn't provide an input to enter grams of alcohol into their calculators. I haven't taken the time to check my numbers against actual values for foods with alcohol in the WW database.

**Fiber has no calories of course. I've put here instead the values-per-100 grams. In PPV, grams of fiber offset points from other nutrients. In SmartPoints, as far as I can see fiber has no impact, which makes me thoroughly confused why they still include it in the nutrition calculator...

Digging in a bit more detail

You can't quite trust the above chart as an apples-to-apples comparison, because a point-plus value is not the same as a smart point.

To get a baseline comparison, I thought it would be useful to compare the PPV-per-100-calories for each nutrient to an "average" value2, which I calculated to be:
Average SmartPoints/100 calories: 3.7 (or, if you prefer, 27 calories per average SmartPoint)
Average PPV/100 calories: 2.8 (or, if you prefer, 35 calories per average PPV)
I used the "average" points-per-100-calorie value to calculate the "deltas," which is to say, how WW is skewing their numbers to be different from a pure calorie counting system. Below are the differences between the PPV-per-100-calories of a nutrient and the baseline.  Values in this chart that are negative are those foods WW is incentivizing you to eat more of; the positive ones are those that are penalized, and the values give you the size of the penalty or incentive.

PPV DeltaSmartPoint Delta
Carbohydrates-4% (0.1)-16% (-0.6)
Sugar-4% (0.1)+65% (+2.4)
Fat+4% (0.1)-19% (-0.7)
Saturated Fat+4% (0.1)+65% (+2.4)
Protein-18% (-0.5)-84% (-3.1)
Alcohol*-4% (-0.1)-16% (-0.6)
*Alcohol numbers should be taken with a heavy grain of salt — see above.

So, what does all this mean?

Well, it makes it clear what WW has set out to do: help us eat less sugar and saturated fat, and get us eating more protein. I have no idea how strong the science is supporting those recommendations, but those are the recommendations they're making. My own not-that-informed sense is that there is strong consensus on the recommendations against added sugars and saturated fat. I'm not at all sure how much sense it makes to be eating protein as much as they seem to be pushing. We may all be eating like the Rock soon if we follow this advice.

I think WW does a good job tilting our hands in the right direction, but we have to be careful not to try to game the system too much. In the end, there's probably some truth to the idea that a calorie is a calorie, and I have great faith in my own ability to overeat even when adhering to the healthiest of food choices (I have faith I could get fat eating anything... I just love food too much).

One thing that concerns me is how much stronger the "tilt" is with the new points. If you look at the deltas above, you'll see that with points-plus, you were pretty close to counting calories, with a slight tilt of the formula toward lean proteins and fiber. With the new SmartPoints, the skew is much more dramatic, and that's not something I love.

Two reasons I did WW instead of trying Atkins or South Beach or Paleo or any of the other trendy diets is that (1) I wanted to be able to keep eating real food of all varieties and more importantly (2) I have great faith in my ability to overeat any food category; I don't have one "weak point" when it comes to this stuff; it's all a weak point. For that reason, I'm worried that if WW is relying more on skewing our food choices toward certain categories and away from others, they could end up moving closer to a trendy diet and further from what I've always valued about the program: rather than a particular diet, WW always presented a sensible system to help people figure out how best to manage (and enjoy!) food in their lives. It's not as clear to me they're doing that now.

I know that I found that after my first 40 pounds lost, I could no longer trust myself to eat as much fruit as I wanted and still lose. I never actually counted fruit as "points," but I did have to watch myself with it; obviously the fact that fruit has significant caloric value but no points was catching up to me. I imagine people who binge on lean proteins will run into similar problems with the new system.

On the bright side, if you're one of the lucky human beings who can successfully eat saturated fats and sugar without overeating, you'll probably find the reverse is true: I suspect that there isn't real evidence to back up the enormous penalties WW gives these foods on a caloric basis alone. My suspicion is that the real problem with eating high-sugar high-sat-fat foods is that they tend to make you overeat. I'm not saying I think WW is wrong to penalize these foods — the three pounds I put on last week with a friend's cookie party in the mix is evidence they're right — but still, I'm guessing that the numbers meant to nudge us toward better behavior could also end up misleading if we take them too slavishly.

In the end, I have faith WW is doing their best to present the best calculations to nudge us toward a sustainable relationship with food. That said, it's not a gameable system; it's a program you have to work at. There will be no shortcuts.

Put another way, although a look at the math of the new SmartPoints shows that, eating nothing but protein, I could take in nearly 6,000 calories a day and stay in my budget eating, I'm certain I would gain and gain fast doing that. In the end, though, that kind of absurd hypothetical is besides the point: the real value of points is how they interact with real people making real choices. It's too soon to tell how they work, but I can only hope SmartPoints will work out for the best.


[1] If you want to get this right, sit down with a spreadsheet and the WW calculator, but here's my initial formula rounded to two significant figures -- all nutrients are in grams:
0.24*Sugar + 0.55*Saturated Fat + 0.27 * (Fat-Sat Fat) + 0.12 * (Carb - Sugar) + 0.024 * Protein + Alcohol * 0.18.

Note, it was pointed out in the comments that someone said you should be able to calculate the points from calories, sat fat, sugar and protein alone. Indeed, you can get very close. The following formula is, in my tests, slightly less accurate but perfectly serviceable:
(0.0305 * calories) - (0.098*protein) + (0.12*sugar)+(0.275*sat fat)
[2] If you're curious how I calculated an "average" calorie, here's what I did. At first I thought I'd just average out the points-per-100cal values, but that's not really fair since you shouldn't eat equal amounts of all those nutrients. So I looked up recommended dietary intake at the Mayo Clinic and used those recommendations to put together these numbers:
Sugar ValSat Fat ValNon-Sat-Fat ValNon-Sugar CarbProteinFiber
Recommended calories100171378128844831
Recommended Grams25194232211231

Of course that's a full man's diet -- far less than someone trying to lose weight eats -- but nonetheless it still gives me the proportions I needed to calculate out a weighted average number of points-per-100 calories. Another important note is that to do this rigorously, I would have had to try to take into account the weight of 0-points foods — all those calories from fruits and carrots and squash we're not counting here. There wasn't a simple way for me to go from the Mayo Clinic recommendations to calculating how many calories we all should be taking in in "zero points" ways each day, so I didn't bother trying.


  1. Dear Thomas, thank you for sharing this in-depth analysis. I create my own spreadsheet workbook for tracking and analysis and I love having a formula to work with. I believe there is science to support significantly negative results of excessive sugar consumption by humans (beyond fat) but I'm not convinced about saturated fat being worse than unsaturated. Too much evidence of healthy cultures eating lots of cheese/kefir/yogurt for example.

    I really appreciate the comprehensiveness of your analysis too, related to the "average" calorie and alcohol, etc. Thank you again!

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  3. Dear Thomas, could You please check Your reverse Engineering? WW Claims to use calories, Protein, saturated fat and sugar for computing the smartpoints. Using These inputs there is not made a differenciation between (not saturated)fat and (non-sugar-)carbohydrates. And their Points-value should corrrespond to their contribution to the total calories, which is about twice as much for fat as for carbohydrates. so fat must have at least twice the Points of carbohaydrates.
    An other variant: WW did not tell us the truth about their formula.......

    thank You very much for Your Analysis of this formula. Your results are my only way to calculate the Points, as the printed materials in my Country are very very bad, a app (for which we WW-members will certainly have to pay additionally) might come sometime in 2016, and the apps in other countries are only available for the citizens of These countries.

    Yours sincerely

    Josef Hochmayr from medieval Austria

  4. Josef, take a look at my spreadsheet here and make a copy to play with if you like:

    At least for the tests I've put in, my calculated values appear to line up with the WW calculators pretty well, but if you find a set of values where my calculations are broken, please let me know.

    1. I need to go back to school and become an engineer to figure all of this out...guess I am really stupid!

  5. Just looking again at my spreadsheet. If you look at the per-100-cal column, you'll see that protein, non-sugar carbs and non-sat fat are all very close to 3 points per 100 calories.

    Given that, you could probably re-work the formula to be


    You'd just have to work out the values of A, B, C & D.

    I can work on that in a bit -- it was easiest to start by just giving the WW calculator numbers where all the calories coming from a given nutrient and start there, which is why my original approach to the formula was to calculate in terms of each nutrient (sugar, non-sugar carbs, sat fat, non-sat fat, protein and alcohol)

    1. Ok -- calculated those values pretty well. I seem to be a little less accurate with this version of the calculation, which leaves me thinking that WW is actually treating calories from fat and carbs slightly differently. That said, you can get very close to accurate with just those four numbers as follows:

      (0.03 * Calories) + (0.122 * Sugar) + (0.28 * Sat Fat) - (0.096 * Protein)

    2. Slight correction: this one does even better.
      (0.0305 * calories) - (0.098*protein) + (0.12*sugar)+(0.275*sat fat)

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    4. Hello Thomas, I have tested Your numbers: Results ok only for values in Your spreadsheet, because calories not computed correctly in Excel spreadsheet: 4 instead of 4,1 for prot and carb as well as 9,0 instead of 9,3 for fat.

    5. Not sure I follow.

      I originally calculated calories just so I could create and test values with the new system, since it requires calories + the nutrients. I just have the standard 4*protein + 4*carbs + 9*fat for calories.

      As far as the calculated points, did you find a set of values where my formulas fail?

    6. Hello Thomas!

      If You buy Food with 100g fat per 100g as in Line 2 of Your Excel-sheet, the declaration is as follows:

      100 g fat, 0 g Carbohydrates, 0g Protein... BUT: 930 calories instead of 900! Using the 900 calories in a formula wil result in wrong values, except in Your table, as the formula is built for 900cal per 100g fat. the same is valid for Protein and carbohydrates (4,1 instead of 4)

    7. Got it -- you're saying that 4/4/9 are inaccurate and 9.3 and 4.1 are the real numbers for fat and protein? I'm having trouble finding clear documentation of anything other than the 4/4/9 rule.

      I just did a calculation for a stick of butter to see if 9.3 was a better estimate, but I actually found my calorie estimate was *high*, not low -- with a value of 9kcal/gram, I got 1664 calories but the actual nutrition label shows 1627. Using the real calorie number vs. the calculated makes a difference of 1 point (81 v 82). My nutrient-based calculation (the longer formula) gets the right value (81.4 -- round to 81) whereas my calorie-based shorter formula gets it one point off (rounds to 82 vs. 81).

      The good news is that those errors are unlikely to matter for real quantities of real foods (I used big numbers in my table to make sure I was getting the right math out of the WW calculator, but hopefully we're not eating 27 or 28 point foods often...).

    8. Thank You, Thomas , for Your work on that formulas.

      Noe I use Your nutrient-based calculation and it works very fine. (Except for Christmas-cakes. They have soooo many Points! :-)...)

  6. Thank you Thomas.
    My Mistake: You wrote about SP per 100 CALORIES, not gramms!
    Next Time I will read your Posts more thoroughly.

    And besides discussion about numbers: If I had not found your blogpost about that Points, my wife and I had stopped dealing with WW tomorrow, lacking a tool to compute the Points for Food, that is not in printed lists of Ww.

  7. Nice work, any idea how to figure the daily/bonus point allowance?

    1. No -- I think they've done much more in terms of that because they don't even give everyone the same weeklies anymore. Obviously to reverse engineer that I'd need way more data -- a huge bank of information about people's ages, genders, weights, and allowances.

  8. Hi Thomas, thanks so much for the incredible blog post. Is there any chance you have a formula for the old PointsPlus calculation? I'm excited to use my new spreadsheet, but I'm also wondering if there's a way to compare points to the old model.

    Thanks so much!

    1. The old formula is available in the WW wikipedia page if you dig through the history. Here's what I used -- taken, I believe, from that.

      Sugar Sat Fat Non-Sat Fat Non-Sugar Carb Protein Generic Calorie->Point (Alcohol's implied value?) Fiber
      0.1086 x g. carb
      + 0.2571 x g. fat
      + 0.0914 x g. protein
      - 0.08 x g. fiber
      (+ 0.0271 x calories from alcohol)

      As I mention above, the old points were *much* closer to raw calorie counting, with only a slight tilt of the hand in favor of protein and away from fat.

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    2. Their formula is within a few decimal points of my second one if you just multiply my values by 33 ((0.0305 * calories) - (0.098*protein) + (0.12*sugar)+(0.275*sat fat)). The one that's different is sat fat, but I'm guessing that theirs will prove inaccurate if you multiply out by large amounts as I did to get my values.

      If you have found values where my formula doesn't work, please let me know what the values were -- for my test values, my numbers have held correct so far. Obviously fruits and veggies will be off -- I mean a food where you plug in the nutrient values and get a different value from the WW calculator.

      There is a slight chance WW is playing with the formula still and different people get different results. I sat at a meeting with someone who had a different value for an egg than I did on my calculator -- I don't know if that was a bug or an experiment on their side or if they're personalizing the points in some way (god help us if that's true)

  10. Although I am not a geek, my thanks go out to Thomas Mills Hinkle for his formula for SmartPoints. I've put it in a spreadsheet and am using it currently. My one concern at present is the (apparent) change to the daily point calculation using Gender, Age, Height and Weight. Did it change also? If so, what would be a good formula for that.

  11. Wow, Thomas, your formula (0.0305*calories) - (0.098*protein) + (0.12*sugar)+(0.275*sat fat)
    has worked on every test I've tried so far when comparing with the WW online calculator. BRILLIANT! Thank you!

  12. By any chance has anyone been able to calculate the number of activity points that are required.

    1. It would be great if i can calculate that goal, so i don't need to log onto the site. Great job on this. This is so nice to have.

  13. So I was playing around with your formula and the one on CalorieLab. For some things you two were only off by a decimal (but rounding evened it out). For others, you were off by a point. I have a spreadsheet in which I have both your formulas side by side and I'm comparing them with my WW online account (I want to write a FileMaker app to do this, eventually turning it into a recipe calculator). I tried a WaWa Sizzli, a Hershey bar, Shamrock Shake, and Wheetabix biscuit. You were generally off by only 1 point, but for the Shamrock Shake you were 2 less.

  14. thanks for the detailed analysis. i'm trying to find a formula for points plus that is as clear as the one you have above for smartpoints. (Y x carbs) + (Z x fat).... etc. Thanks!