By Brian Burke
I'll first air the assumptions and limitations. This analysis is based on contract/salary data provided by Spotrac.com. I've limited the years of analysis to only 2010 and '11 because that was the sample of data made available. More years of data could always be added to refine the results. +Expected Points Added per Game (regular season only) is used as the basis of performance because although it's far from perfect, it captures the impact of individual contribution to game outcome without sensitivity to situational variables beyond the control of the player. It also happens that +EPA/G fits best with the salary data, so it is the measure player performance for the purpose of this analysis. Lastly, due to the complexity of contract incentives, bonuses, guarantees, and duration, I have chosen annual 'cap hit' as the measure of contract cost.
That's a lot of assumptions, I realize. But the real world is messy, and the purpose here is to establish the general market--a starting point for further adjustments. As you'll see, the relationship between +EPA/G and cap hit is fairly strong, suggesting the assumptions aren't unreasonable. We should also recognize the distinction between observing what players tend to be paid and what they ideally should be paid.
The chart below plots the cap hit according to the +EPA/G of safeties from the 2010 and 2011 seasons. The correlation between cap hit and +EPA/G is 0.6, which is remarkably strong given that there is always a disconnect between expected and actual performance. Plus, there is all the randomness of a short, 16-game season.
The above chart includes all the safeties for whom I had contract data. But you'll notice a very large cluster of players in the lowest salary range, comprising mostly rookies or other players under minimum contracts. There's a wide dispersion of performance in this range, indicating performance and salary are not closely coupled for these players.
The original premise of this analysis is interested in top free agent players, so it probably makes sense to ignore the low end of the market. From this plot, we can see that about the rookie minimum of about $400k/yr buys you an average +EPA of about 1.0 points per game. But if you up the salary just a little, to about $700k/yr, you can buy a lottery ticket for anywhere between 0.5 to 2.5 +EPA per game. These are probably your mid-round draft picks or bargain basement veterans. This wide range shouldn't be surprising because of the uncertainty in expected performance of rookies, plus the fact that rookies are artificially underpaid while veterans have a higher minimum salary. Replacement level at safety is probably somewhere near the midpoint of that range, at about +1.5 EPA/G.
Above this cluster, there appears to be a clearer linear connection between salary and performance. Removing all players with cap hits below $1.5 million per year results in the chart below. The correlation increases to 0.68, and more importantly, it better represents the free agent market for top safeties.
It appears teams are willing to annually pay $2 million per +EPA/G - $170k. So a player like Troy Polamalu, who has averaged 3.2 +EPA/G since his sophomore season, should be worth an annual cap hit of 2 * 3.2 - .17 = $6.2 million. His actual hit is about $9 million. That's not to say he's overpaid. His full performance is certainly not captured by +EPA/G, however, that's true of all safeties. His share of un-captured performance would need to be far greater than other top starting safeties for that to explain the discrepancy. And that's a case that could be made on several fronts, including dependability, health, age effects, team needs, off-field marketing value, etc.
But a reasonable starting point for a safety of his expected performance should probably be close to $6.2 million, and adjustments can be made upward or downward from there.
There are several additional considerations. In addition to things like age and health, there are concepts like discount rates. Teams, like people, are usually willing to pay later for services rendered now. The league's new TV contract ensures payrolls will expand, so there is salary cap inflation to consider. There is also the Gladiator Effect. Defenses usually want only two safeties on the field at a time, so a single great safety can't be replaced by four or five average ones.
Improvements to the methodology would include a more rigorous analysis of who the players are, what their contract types are, adding more years of data for better context, and possibly correcting for the heteroskedastic relationship between salary and performance.
Anyway, I know this is wrong. I just hope it's not all wrong, and it's close enough to correct that some smart people can help refine it.