Analyzing diminishing returns to scale in marketing spend across channels on lead generation, and opportunities for reallocation of budget
Using a data set containing daily spend and leads generated by campaign for 2022 IFP open enrollment and special enrollment campaigns across 2 channels, SEARCH and PERFORMANCE_MAX, initial exploratory data analysis indicated that there may be opportunity to increase ROI under a constrained budget by re-allocating some spend from PERFORMANCE_MAX to SEARCH.
Starting with a log log elasticity analysis, the constant elasticity value for PMAX of .595 was about 45% less than the SEARCH value of .86 on average, showing Search to be more productive relative to Pmax
SEARCH
| Root MSE | 0.89768 | R-Square | 0.6825 | ||||||
| Dependent Mean | 4.88605 | Adj R-Sq | 0.6811 | ||||||
| Coeff Var | 18.37238 | ||||||||
| Parameter Estimates | |||||||||
| Variable | DF | Parameter Estimate | Standard Error | t Value | Pr > |t| | ||||
| Intercept | 1 | -1.80880 | 0.31226 | -5.79 | <.0001 | ||||
| l_tot_cst | 1 | 0.86044 | 0.03939 | 21.85 | <.0001 | ||||
PMAX
| Root MSE | 0.57181 | R-Square | 0.8177 | ||||||
| Dependent Mean | 3.96148 | Adj R-Sq | 0.8164 | ||||||
| Coeff Var | 14.43424 | ||||||||
| Parameter Estimates | |||||||||
| Variable | DF | Parameter Estimate | Standard Error | t Value | Pr > |t| | ||||
| Intercept | 1 | 0.42059 | 0.14566 | 2.89 | 0.0045 | ||||
| l_tot_cst | 1 | 0.59514 | 0.02318 | 25.67 | <.0001 | ||||
Adding a quadratic of log of cost to check non-constant elasticities, Search continues to outperform PMAX, but with diminishing effect. The Search linear term of 4.3874 is about 4x that of Pmax (1.1), indicating 4x return on a dollar invested relative to Pmax, but at lower spend levels, with a faster reduction in slope (negative quadratic term), so that it might make sense to re-allocate $ from PMAX to SEARCH at lower spend levels.
SEARCH
| Root MSE | 0.76667 | R-Square | 0.7695 | ||||||
| Dependent Mean | 4.88605 | Adj R-Sq | 0.7674 | ||||||
| Coeff Var | 15.69099 | ||||||||
| Parameter Estimates | |||||||||
| Variable | DF | Parameter Estimate | Standard Error | t Value | Pr > |t| | ||||
| Intercept | 1 | -16.19883 | 1.59853 | -10.13 | <.0001 | ||||
| l_tot_cst | 1 | 4.38739 | 0.38777 | 11.31 | <.0001 | ||||
| l_tot_cst_sq | 1 | -0.20764 | 0.02274 | -9.13 | <.0001 | ||||
PMAX
| Root MSE | 0.53587 | R-Square | 0.8409 | ||||||
| Dependent Mean | 3.96148 | Adj R-Sq | 0.8388 | ||||||
| Coeff Var | 13.52710 | ||||||||
| Parameter Estimates | |||||||||
| Variable | DF | Parameter Estimate | Standard Error | t Value | Pr > |t| | ||||
| Intercept | 1 | -0.89457 | 0.31551 | -2.84 | 0.0052 | ||||
| l_tot_cst | 1 | 1.10040 | 0.11142 | 9.88 | <.0001 | ||||
| l_tot_cst_sq | 1 | -0.04283 | 0.00926 | -4.62 | <.0001 | ||||
There’s a few methods to locate the optimal / maximal point for spend re-allocation. Here we used a quadratic in levels.
PMAX
| Root MSE | 84.44730 | R-Square | 0.3766 | ||||||
| Dependent Mean | 104.29336 | Adj R-Sq | 0.3681 | ||||||
| Coeff Var | 80.97093 | ||||||||
| Parameter Estimates | |||||||||
| Variable | DF | Parameter Estimate | Standard Error | t Value | Pr > |t| | ||||
| Intercept | 1 | 57.75747 | 8.53820 | 6.76 | <.0001 | ||||
| tot_cst | 1 | 0.03468 | 0.00402 | 8.62 | <.0001 | ||||
| tot_cst_sq | 1 | -9.53319E-7 | 1.484433E-7 | -6.42 | <.0001 | ||||
An extra dollar of spend, on average, for PMAX generates .0347 leads, for an average cost per lead of 28.835. The point of diminishing returns occurs at a daily spend level of about $18k (take first derivative of quadratic and set to zero).
SEARCH
| Root MSE | 211.19329 | R-Square | 0.7177 | ||||||
| Dependent Mean | 324.37036 | Adj R-Sq | 0.7151 | ||||||
| Coeff Var | 65.10869 | ||||||||
| Parameter Estimates | |||||||||
| Variable | DF | Parameter Estimate | Standard Error | t Value | Pr > |t| | ||||
| Intercept | 1 | 130.61622 | 16.48708 | 7.92 | <.0001 | ||||
| tot_cst | 1 | 0.02610 | 0.00145 | 17.97 | <.0001 | ||||
| tot_cst_sq | 1 | -1.17523E-7 | 1.484828E-8 | -7.91 | <.0001 | ||||
An extra dollar of spend, on average, for SEARCH generates .026 leads, for an average cost per lead of 38.31. The point of diminishing returns occurs at a daily spend level of about $111k. There may be outlier issues to investigate in another iteration.
Though average cost per lead for Search is higher, initially the cost per lead at lower levels is lower than PMAX.
So if we’re operating on a limited budget, we might recommend shifting dollars, on a daily basis, from PMAX to SEARCH up to the point of diminishing returns ($111k).
Graphs of the quadratic level functions highlight the point of diminishing returns.
SEARCH
PMAX
Next we pulled daily new ifp members for the same date range, and ran the same regressions. Elasticity for Pmax was .142 and Search was .3474, both with low r-square values (.07 and .2).
Regressing new members on total cost had same results – low significance, low r-square, pointing to the need to have better sales/channel data alignment in the database.
Lastly, the percentage split of leads across channels was applied as a weight on sales, to attempt to create a proxy for sales attribution. There was a modest improvement in R-square for elasticities, but levels fared worse, again corroborating the need for a tighter database. We did find some evidence of significance for a couple lags spend, so that could be incorporated in future work.