CoolData blog

7 July 2014

Mine your donor data with this baseball-inspired analysis

I’ve got baseball analytics on my mind. I don’t know if it’s because of the onset of July or because of a recent mention of CoolData on Nate Silver’s FiveThirtyEight blog, but I have been deeply absorbed in an analysis of donor giving behaviours inspired by Silver’s book, “The Signal and the Noise.” It might give you some ideas for things to try with your own database.

Back in 2003, Silver designed a system to predict the performance of Major League Baseball players. The system, called PECOTA, attempts to understand how a player’s performance evolves as he ages. As Silver writes in his book, its forecasts were probabilistic, offering a range of possible outcomes for each player. From the previous work of others, Silver was aware that hitters reach their peak performance at age 27, on average. Page 81 of his book shows the “aging curve” for major league hitters, a parabola starting at age 18, arcing smoothly upwards through the 20s, peaking at 27, and then just as smoothly arcing downwards to age 39.

My immediate thought on reading about this was, what about donors? Can we visualize the trajectory of various types of donors (major donors, bequest donors, leadership annual fund donors) from their first ten bucks right after graduating, then on into their peak earning years? What would we learn by doing that?

In baseball, the aging curve presents a problem for teams acquiring players with proven track records. By the time they become free agents, their peak years will have passed. However, if the early exploits of a young prospect cause him to resemble one of the greats from the past, perhaps he is worth investing in. The curve, as Silver notes, is only an average. Some players will peak far earlier, and some far later, than the average age of 27. There are different types of players, and difference types of curves, and every individual career is different. But lurking in all that noise, there is a signal.

Silver’s PECOTA system takes things further than that — I will return to that later — but now I want to turn to how we can visualize a sort of aging curve for our donors.

What’s the payoff? Well, to cut to the chase: It appears that some donors who go on to give in six figures (lifetime total) can be distinguished from the majority of lower-level donors at a very early age. Above-average giving ($200 or $250, say) in any one year during one’s late 20s or early 30s is a predictor of very high lifetime value. I have found that when big donors have started their giving young, they have started big. That is, “big” in relation to their similarly-aged peers – not at thousands of dollars, but at $100 or $500, depending on how old they were at the time.

Call it “precocious giving”.

Granted, it sounds a bit like plain common sense. But being analytical about it opens up the possibility of identifying a donor with high lifetime value when they’re still in their late 30s or early 40s. You can judge for yourself, but the idea appealed to me.

I’m getting ahead of myself. At the start of this, I was only interested in getting the data prepared and plotting the curve to see what it would look like. To the extent that it resembled a curve at all, I figured that “peak age” — the counterpart to baseball player performance — would be the precise age at which a donor gave the most in any given year while they were alive.

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I wrote a query to pull all donors from the database (persons only), with a row for each year of giving, summing on total giving in that year. Along with Year of Gift, I pulled down Year of Birth for each donor — excluding anyone for whom we had no birthdate. I included only amounts given while the donor was living; bequests were excluded.

The next step was to calculate the age the donor was at the time of the gift. I added a column to the data, defined as the Year of Gift minus Year of Birth. That gave me a close-enough figure for age at time of giving.

As I worked on the analysis, I kept going back to the query to add things I needed, such as certain donor attributes that I wanted to examine. Here are most of the variables I ended up pulling from the database for each unique combination of Donor ID and Age at Time of Gift:

  • ID
  • Age at Time of Gift (Year of Gift minus Year of Birth)
  • Sum of Giving (total giving for that donor, at that age)
  • Donor Category Code (Alum, Friend, etc.)
  • Total Lifetime Giving (for each donor, without regard to age)
  • Deceased Indicator (are they living or dead as of today)
  • Current Age (if living, how old are they right now)
  • Year of Birth
  • Year of Gift

The result was a data set with more than 200,000 rows. Notice, of course, that a donor ID can appear on multiple rows — one for each value of Age at Gift. The key thing to remember is that I didn’t care what year giving occurred, I only wanted to know how old someone was when they gave. So in my results, a donor who gave in 1963 when she was 42 is much the same as a donor who gave in 2013 he was the same age.

pecota1

Now it was time to visualize this data, and for that I used Tableau. I connected directly to the database and loaded the data into Tableau using custom SQL. ‘Age at Gift’ is numerical, so Tableau automatically listed that variable in the Measures panel. For this analysis, I wanted to treat it as a category instead, so I dragged it into the Dimensions panel. (If you’re not familiar with Tableau, don’t worry about these application-specific steps — once you get the general idea, you can replicate this using your tool of choice.)

The first (and easiest) thing to visualize was simply the number of donors at each age. Click on the image below to see a full-size version. Every part of the shape of this curve says something interesting, I think, but the one thing I have annotated here is the age at which the largest number of people chose to make a gift.

pecota2

This chart lumps in everyone — alumni and non-alumni, living donors and deceased donors — so I wanted to go a little deeper. I would expect to see a difference between alumni and non-alumni, for example, so I put all degree and non-degree alumni into one category (Alumni), and all other donor constituents into another (Non-alumni). The curve does not change dramatically, but we can see that the number of non-alumni donors peaks later than the number of alumni donors.

pecota3

There are a number of reasons for analyzing alumni and non-alumni separately, so from this point on, I decided to exclude non-alumni.

The fact that 46 seems to be an important age is interesting, but this probably says as much about the age composition of our alumni and our fundraising effort over the years as it does about donor behaviour. To get a sense of how this might be true, I divided all alumni donors into quartiles (four bins containing roughly equal numbers of alumni), by Birth Year. Alumni donors broke down this way:

  1. Born 1873 to 1944: 8,101 donors
  2. Born 1945 to 1955: 8,036 donors
  3. Born 1956 to 1966: 8,614 donors
  4. Born 1967 to 1991: 8,172 donors

Clearly these are very different cohorts! The donors in the middle two quartiles were born in a span of only a decade each, while the span of the youngest quartile is 24 years, and the span of the oldest quartile is 71 years! When I charted each age group separately, they split into distinct phases. (Reminder: click on the image for a full-size version.)

pecota4

This chart highlights a significant problem with visualizing the life cycle of donors: Many of the donors in the data aren’t finished their giving careers yet. When Nate Silver talks about the aging curves of baseball players, he means players whose career is behind them. How else to see their rise, peak, and eventual decline? According to the chart above, the youngest quartile peaks (in terms of number of donors) at age 26. However, most of these donors are still alive and have many years of giving ahead of them. We will turn to them to identify up-and-coming donors, but as long as we are trying to map out what a lifetime of giving looks like, we need to focus on the oldest donors.

An additional problem is that our donor database doesn’t go back as far as baseball stats do. Sure, we’ve got people in the database who were born more than 140 years ago, but our giving records are very sparse for years before the early 1970s. If a donor was very mature at that time, his apparent lack of giving history might cause us to make erroneous observations.

I decided to limit the data set to donors born between 1920 and 1944. This excludes the following donors who are likely to have incomplete giving histories:

  • Anyone who was older than 50 in 1970, when giving records really started to get tracked, and
  • Anyone who is currently younger than 70, and may have many years of giving left.

This is a bit arbitrary, but reasonable. It trims off the donors who could never have had a chance to have a lifetime of giving recorded in the data, without unduly reducing the size of my data set. I was left with only 20% of my original data, but still, that’s more than 6,000 individuals. I could have gotten fussier with this, removing anyone who died at a relatively young age, but I figured the data was good enough to provide some insights.

The dramatic difference made by this trimming is evident in the following two charts. Both charts show a line for the number of donors by age at time of gift, for each of three lifetime giving levels: Under $1,000 in blue, $1,000 to $10,000 in orange, and over $10,000 in purple. What this means is that all the donors represented by the purple line (for example) gave at least $10,000 cumulatively over the course of their lifetime.

The first chart is based on ALL the data, before trimming according to birth year. The second chart is based on the 6,000 or so records I was left with after trimming. The first chart seems to offer an interesting insight: The higher the lifetime value of donors, the later in life they tend to show up in great numbers. But of course this just isn’t true. Although the number of donors with lower lifetime giving peaks at earlier ages, that’s only because that whole group of donors is younger: They’re not done giving yet. (I have added ‘Median Current Age’ to the high point of each curve to illustrate this.) Remember, this chart includes everyone — it’s the “untrimmed” data:

pecota5
Contrast that three-phase chart with this next one, based on “trimmed” data. The curves are more aligned, presumably because we are now looking at a better-defined cohort of donors (those born 1920 to 1944). The oldest donor is 24 years older than the youngest donor, but that’s okay: The most important concern is having good data for that range of ages. Because the tops of these curves are flatter, I have annotated more points, for the sake of interest.

pecota6

These curves are pretty, but they aren’t analogous to “performance curves” for baseball players — we haven’t yet looked at how MUCH donors give, on average, at each age. However, what general observations can we make from the last chart? Some that come to my mind:

  • Regardless of what a donor finally ends up giving lifetime, there are always a few (a very few) who start giving while they are in their 20s, and a few who are still around to give when they are in their late 80s and early 90s.
  • The number of donors starts to really take off at around age 40, and there is steady growth until about age 50, when the growth in number of donors begins to slow or plateau.
  • Donors start to drop out rapidly at around age 70. This is due to mortality of course, but probably the steepness of the drop is exaggerated by my trimming of the data at the older end.

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Here is where things really get interesting. The whole point of this exercise was to see if we can spot the telltale signs of a future major donor while they are still relatively young, just as a baseball scout looks for young prospects who haven’t peaked yet. Do donors signal unusual generosity even when they are still in their 20s and 30s? Let’s have a look.

I zoomed in on a very small part of the chart, to show giving activity up until age 35. Are there differences between the various levels of donors? You bet there are.

As soon as a high-lifetime-value donor starts to give, the gifts are higher, relative to same-age peers who will end up giving less. The number of donors at these early ages is miniscule, so take this with a grain of salt, but a trend seems unmistakable: Up to the age of 30, donors who will end up giving in five figures and higher give about 2.5 to 3.5 times as much per year as other donors their age who end up giving $1,000 to $10,000 lifetime. AND, they give FIVE TIMES as much per year as other donors their age who end up giving less than $1,000 lifetime.

pecota7

Later on, at ages 35 and 40, donors who will finish their giving careers at the high end are giving two to three times as much per year as donors in the middle range, and 5.6 to 7 times per year (respectively) as donors who will finish on the lowest end.

It might be less confusing to chart each group of donors by average giving per year, rather than by number of donors. This chart shows average giving per year up until age 65. Naturally, the averages get very spiky, as donors start making large gifts.

 

pecota8

To temper the effect of extreme values, I log-transformed the giving amounts. This made it easier to visualize how these three tiers of donors differ from each other over a lifetime of giving:

pecota9

What do I see from this? These are generalizations based on averages, but potentially useful generalizations:

  • Upper-end donors start strong relative to other donors, accelerate giving after age 40, and continue to increase giving throughout their lifetimes.
  • Middle- and low-range donors start lower. They also increase their yearly giving until their late 40s, but after that, they plateau and stay at the same level for the rest of their lives.

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What’s the bottom line here? I think it’s this: Hundreds of donors were well on their way to being exceptional by the tender age of 40, and a few were signaling long before that.

Information like this would be interesting to Annual Fund as they work to identify prospects for leadership-level giving. But $10,000 in a lifetime is a little too low to make the Major Gifts folks take notice. Can we carve out the really big donors from the $10K-plus crowd? And can we also identify them before they hit 40? Have a look at this chart. For this one, I removed all the donors who gave less than $10,000 lifetime, and then I divided the high-end donors into those who gave less than $100,000 lifetime (green line) and those who gave more than $100,000 (red line).

pecota10

 

The lines get a bit jagged, but it looks to me like the six-figure lifetime donors pull away from the five-figure donors while still in their 40s. And notice as well that they increase their giving after age 65, which is very unusual behaviour: By 65, the vast majority of donors have either long plateaued or are starting to wind down. (You can’t see this in the chart, but that post-65 group of very generous donors numbers about 50 individuals, with yearly average giving ranging around $25,000 to $50,000.)

When I drill down, I can see about a hundred donors sitting along the red line between the ages of 30 and 45, whom we might have identified as exceptional, had we known what to look for.

With the benefit of hindsight, we are now able to look at current donors who were born more recently (after 1969, say), and identify who’s sending out early signals. I have those charts, but I think you’ve seen enough, and as I have said many times in the past: My data is not your data. So while I can propose the following “rules” for identifying an up-and-comer, I don’t recommend you try applying them to your own situation without running your own analysis:

  • Gave more than $200 in one year, starting around age 28.
  • Gave more than $250 in one year, starting around age 29.
  • Gave more than $500 in one year, starting around age 32.

Does this mean I think we can ask a 32-year-old for $10,000 this year? No. It means that this 32-year-old is someone to watch out for and to keep engaged as an alum. It’s the donors over 50 or so who have exhibited these telltale patterns in their early giving that might belong in a major gift prospect portfolio.

Precocious giving certainly isn’t the only indicator of a good prospect, but along with a few other unusual traits, it is a good start. (See: Odd but true findings? Upgrading annual donors are “erratic” and “volatile”.)

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Where do you go from here? That is completely up to you. I am still in the process of figuring out how to best use these insights.

Coming up with some rules of thumb, as above, is one way to proceed. Another is rolling up all of a donor’s early giving into a single score — a Precocity Score — that takes into account both how much a donor gave, and how young she was when she gave it. I experimented with a formula that gave progressively higher weights to the number of dollars given for younger ages. For example, $100 given at age 26 might be worth several times more than $200 given at age 44.

Using my data set of donors with a full life cycle of giving, I tested whether this score was predictive of lifetime value. It certainly was. However, I also found that a simple cumulative sum of a donor’s giving up to age 35 or 40 was equally as predictive. There didn’t seem to be any additional benefit to giving extra weight to very early giving.

I am shying away from using giving history as an input in a predictive model. I see people do this all the time, but I have always avoided the practice. My preference is to use some version of the rules above as just one more tool to use in prospect identification, distinct from other efforts such as predictive modelling.

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That’s as far as I have gotten. If this discussion has given you some ideas to explore, then wonderful. I doubt I’m breaking new ground here, so if you’ve already analyzed giving-by-age, I’d be interested in hearing how you’ve applied what you’ve learned.

Incidentally, Nate Silver went on to produce “similarity scores” for pairs of hitters. Using baseball’s rich trove of data, he compared players using a nearest-neighbour analysis, which took into account a wide range of data points, from player height and weight to all the game stats that baseball is famous for. A young prospect in the minor leagues with a score that indicates a high degree of similarity with a known star might be expected to “age” in a similar way. That was the theory, anyway.

One can imagine how this might translate to the fundraising arena. If you identified groups of your best donors, with a high degree of similarity among the members of each group, you could then identify younger donors with characteristics that are similar to the members of each group. After all, major gift donors are not all alike, so why not try to fit multiple “types”?

I would guess that the relatively small size of each group would cause any signal to get drowned out in the noise. I am a little skeptical that we can parse things that finely. It would, however, be an interesting project.

A final note. The PECOTA system had some successes and for a time was an improvement on existing predictive tools. Over time, however, pure statistics were not a match for the combination of quantitative methods and the experience and knowledge of talent scouts. In the same way, identifying the best prospects for fundraising relies on the combined wisdom of data analysts, researchers and fundraisers themselves.

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