As reference, over the past week or so there has been a bit of a back and forth from Tango and the Basketball Analytics crowd. There are four main blog posts that have touched on this subject:

1. The Myth of the Free Replacement-Level Player from Boxscore Geeks (and comments form Dave Berri)
2. Myth of “Myth of Replacement Level” from Tango
3. Wins Above Replacement (WAR): What is it good for? (not “absolutely nothing”) from Dave Berri
4. What is a replacement level NBA player? from Tango

This is all great, but in particular the last blog post of finding a replacement level NBA player has me lost in the trees. I need to get back to seeing the forest before I can figure out my confusions.

Where is an actual description of this Replacement Level Theory that I hear so much about? I haven’t seen it defined in any of the blogs or comments. I’d like to know more about this other than “think of it like fantasy sports”. That particular example may help me better understand the theory after I know the theory, but there are an infinite number of theories that the example could apply to. I can’t learn this stuff only from examples.

And once I can get a hold of Replacement Level Theory and how it is calculated, what is it’s application to the NBA? Is the goal to be another measure of productivity? Or is the goal to eventually translate a player’s production to a dollar amount? This is what I’d really like to get back to in this entire discussion, but I’ve lost sight of what this discussion is about.

This thread:

http://tangotiger.com/index.php/site/comments/why-war-and-not-waa

Post #5 in particular

And finally this article:

http://www.baseballprospectus.com/article.php?articleid=18790

Hi Tango, thanks for the response. I’ve read through your links, but I am still lost. I think part of this is that I was not clear on where I am lost, so maybe I can be clearer on that.

What I do not understand about Replacement Level Theory is the basic assumptions built into the theory and its main objective. In other words, what is it that replacement level is attempting to measure? I know that it is literally taking a hypothetical baseline of a replacement level player and then subtracting this away from the production of your player of interest. I do not have a problem following the different ways to measure the replacement level player and I am not trying to get an idea of why replacement level is the chosen baseline instead of others. My confusion is a step before that.

My guess at this point as to Replacement Level Theory is that one is attempting to figure out the market value of a player (not the productivity). It is going about this by looking at the productivity of a player and then subtracting away the team’s alternative of a low-cost and easily acquirable player (which sounds similar to marginal/opportunity cost). It appears to assume a few things such as a roughly linear relationship between wins and payroll, that the productivity of a player does not depend on teammates, and the distribution of player talent can also be approximated by distribution of observed salaries. There may be more assumptions, but they don’t seem to be evident to me at the time.

I am not sure if my idea of replacement level theory is the same as what the sabermetrics community has in mind. I don’t have a clue if I am in the ballpark, but I’m trying to figure out what the ballpark is.

That’s pretty much it!

Well that is comforting that I have an OK grasp on the reasoning behind Replacement Level Theory. I’ll have to think about this application a bit more as it relates to the NBA, but there is one philosophical question behind replacement level that already confuses me. And that is the market value definition.

I realize that in MLB there are a few contract restrictions (minimum salary, pre-arbitration and arbitration players). Saber appears to handle this by not using the salary disbursement involved with these players, but only the disbursement to Free Agents. So Saber knows to focus their market valuation in the context of “if Mike Trout were a Free Agent, then based on X WAR he should command $Y”. This is clever and clear to me. It also adheres to one who does not wish to extrapolate their results beyond what it can tell you. Here, this appears to be a good first approximation and gives replacement level standing within MLB.

The NBA has vastly more contract restrictions and it is something I think about a fair amount. There is a total salary restriction (BRI to all players), team salary restrictions (soft salary cap), and individual salary restriction (a specific value). So what is the context of market value for the NBA? If one tells an answer that LeBron James can be worth $40 million, well your $40 million is an estimate of a hypothetical situation that does not exist. That $40 million is from a different economic environment and LeBron cannot make more than ~$21 million. Market value in this context is not helpful from what my impression of the goal of replacement level. In this context, LeBron with $40 million valuation is not a market valuation. It would be better thought of as a productivity measure. And if we are thinking of this as a productivity measure, then the extra step of estimating the replacement level adds more complication to estimating productivity. I’m also not sure if the measure of productivity changes.

These are just my initial thoughts, and I need to think through these some more. Until I have a better grasp on this, I know I need to take a step back from thinking about NBA Replacement Level. I may end up coming back to Replacement Level, but I’m not willing to dive right in at this time.

In your illustration, Lebron generates 40 million$ of additional revenue, at cost of 21 million$ in cash, and I presume 21 million “units” against the cap and 21 million “units” against the floor.

(I wouldn’t use “dollars” in cap/floor cases, because it’s not actually costing you money.  You are paying salaries and that costs money.)

Hopefully that gives you enough to think about your next step.

Tango can feel free to disagree with me on this (it is his blog after all!) but personally I find it more confusing than helpful to bring salary into the picture when talking about player value and “replacement level”. There are just so many complicating factors in different leagues: maximum salaries, minimum salaries, different contract lengths, team and player options, guarantees and opt-outs, signing bonuses, etc. I think once you have a clear understanding of player value in terms of performance (e.g. WAR or WAA or whatever alternative framework you think makes sense), then you can try to translate that performance to economic value based on how players get paid in the league in question. Then you can see if the framework provides any explanatory value.

The “cost” of a replacement level player is irrelevant to this particular discussion, IMO. In some alternate universe all baseball players would be paid a uniform salary of 1 peppercorn. In that alternate universe Mike Trout would still be the standard-bearer for a player’s contribution to winning, Chris Parmelee would still be a reasonable example of someone who no team would miss tremendously (no offense, Chris - you are immeasurably better at baseball than I could ever hope to be), and there would still be the whole range of players in between.

It doesn’t matter if the actual cost of hiring Chris Parmelee is 1 peppercorn or $1 million or $100 million. His contribution to winning baseball games over the next 1B/OF guy waiting on a call-up from AAA is still the same - approximately zero. Thus he is a good example of what “replacement level” means in practice, regardless of what his contract says he is due to be paid.

As an aside, I do think “replacement level” is harder to define in sports that have more complicated team interactions than baseball. E.g. a no-defense, dead-eye 3 point shooter in the NBA might be worthless on some teams or the missing piece of the championship puzzle on others.

Well, the DEFINITION of replacement level is the level of performance that a team can expect of a player readily available at the most minimal cost.

If you like, you can call replacement level as the level of performance that a team can expect from the best players who have played MLB in the past but are not on an MLB roster today.  That gets you all those guys who signed minor league free agent contracts, but it also gets you all those rookies who have been sent down this year.  But it excludes those guys who are one game away from being cut or traded for almost nothing.

Now what do you do?  Add in another qualifier that he was a free agent at some point as well?  All you are doing is dancing around the “minimal cost” stipulation.  And we can all understand what “minimal cost” means and its implication.  We know it doesn’t include the young guys tied to teams.

I guess I’m arguing that no such appeal to the cost of the player is necessary - introducing it just emboldens smart but ill-informed people to focus on the wrong thing, coming up with what they think is a brilliant critique of the cost side (as in the economist’s terrible analogy about the auto dealership in the first article - sports, like all entertainment and unlike almost any other industry, is built on a tournament model of compensation) rather than focusing on the performance side, which is what actually matters.

If we can all agree on what a replacement level [blah] looks like in terms of performance, the economic discussion can follow rather than lead. E.g. you might define a replacement level movie as one that you won’t stop watching if you can’t find anything better (e.g. you’d rather watch it than watch nothing), but that you would never switch to watching if you were already watching something else. If you can get agreement on that, then you can have a discussion with people about whether movies are priced rationally within your framework. But framing the discussion in terms of cost first just muddies the issue for anyone who can’t get past the baggage they bring to the discussion.

I think that’s just theoretical.

Practically speaking, I think the evidence shows we’ve made great inroads in explaining replacement level as we have.

The few that haven’t been able to grasp it are really being obstinate about it.

Tangotiger - 15 August 2014 02:33 PM

The few that haven’t been able to grasp it are really being obstinate about it.

Yes, I definitely agree with that…

And you can’t worry about the obstinate.

You lead the charge, and you take care of those willing to take those steps, and make sure they aren’t derailed.