When Should You Sign a Free Agent?

A couple posts ago I mentioned that we could use my logistic regression model to inform what kind of team should hire a free agent. In addition to the playoff model, we need to know what kind of point differential usually goes with each position in the standings. Over the course of the last seven years (the span my model covers), the average differentials are:

Seed East Average West Average
1          7                     6.6
2         5.2                  5.1
3         3.7                  4.5
4         1.1                  5.1
5         1.3                  4.4
6         1.1                  2.6
7         -.1                   2.5
8         -1                    2.1
9         -1.5                 .1
10       -2.7                -1.8
11       -2.7                 -2.6
12       -3.4                 -4
13       -4.4                 -4.2
14       -5.1                 -4.7
15       -7.4                 -8.2

One thing to note is that while the East and West are pretty even from 1 to 3 and 11 to 15, the West is much better from 4 to 10, so the typical view of the West being stronger or deeper seems to be true. So your decision as fake GM will depend on which conference you’re in. Remember that the question was, should you sign a free agent who could improve your team’s ability by 2 points (e.g., your point differential will go up 2) if it will kill your cap space for the next 5 years?
Let’s start with the lottery teams. Adding two points isn’t even enough to get you into the playoffs, except for maybe the 9th place team (maybe 10th in the East). If your goal is to win the playoffs, signing this guy isn’t really going to help. Yes, you’ll be in the playoffs, but the average 8th place team only has at best an 11% chance (in the West, where teams are closer) to just get out of the first round. So you’ll be mired at the bottom of the playoff teams, drafting ineffective rookies and unable to sign more help, for the next 5 years. Lottery teams would be better off sucking for a year or two, getting a big rookie who actually produces or signing cheap yet productive veterans, than making a big free agent splash.
Now let’s say you’re in the bottom half of the playoffs. Moving up 2 points is roughly enough to get you to the 4th seed, or getting home court. That moves you from underdog to favorite; the 5th seed should beat the 4th seed 43% of the time in the East, so the 4th seed should be favored and win 57% of the time. But, assuming the 4th seed wins and the 1 seed isn’t upset, the 4th seed then has to go on the road against the best team in the conference. In the East that puts you at 7% to move on, 28% in the West. Again, that doesn’t look so hot; people might think well of your team, you’ll be ‘scrappy’ and maybe a dark horse, but your chances aren’t great and again your free agent and draft prospects aren’t great. So if you’re 5 through 8 (excepting 5 in the West, where moving 2 would just about make you #1), you should look somewhere else as well.
Now we’re up to the money teams, 1 through 4. You already have home court advantage and you’re looking for that piece to put you over the top. The 1 and 2 seeds in the East have a 93% and 72%, respectively, chance of beating the 4 and 3 seeds; it’s only 72 and 64% in the West. So the 3rd and 4th seed teams should be pretty motivated to move into the top two positions, especially in the West. A 2 seed would become about even with the number 1 seed when they sign this free agent, which would obviously be desirable; if two even teams play, the team with home court should win 59% of the time. So it looks like signing the big free agent is worth it if you’re on the 1 through 3 seed in the East, and 1 through 5 in the West (in an average year; it’s more worth it the tighter you expect the teams to be the next year).
What are the probabilities of winning the championship for different seeds? Let’s assume the playoffs go smoothly; that is, the # 1 seed will beat #8, #4, #2, and then face the #1 seed in the other conference. For teams that aren’t #1, the only upsets are the ones you pull off; a #7 seed will upset #2, #3, #1, then #1 in the other conference. Here are your chances of winning the championship:

East #8   .002%  West #8   .034%
East #7   .003%  West #7   .069%
East #6   .013%  West #6   .079%
East #5   .035%  West #5   .57%
East #4   .038%  West #4   1.9%
East #3   .68%     West #3   1.34%
East #2   4.95%   West #2   3.64%
East #1   41.9%    West #1   17.2%

The East #1 has the advantage because I assume they’ll be the home team against the West #1 due to their higher point differential. You might also notice that the probabilities don’t add to 100% because this is only one way the playoffs could play out (the most obvious other possibility is facing someone besides the #1 seed in the championship game); there are more possible game orders than I want to calculate, but the team ordering and the relative numbers should be right. Overall, the table makes it obvious that you want to be the #1 team in your conference if you want to have a real chance of winning the championship; this happens by having the highest point differential possible.
So, when should you sign a cap-killing free agent? Only if you think he will move your team to the top of the conference. Anything else will improve your chances of winning the championship, but not to a level that gives you a particularly good chance of actually winning, and will also make your chances of improving your team in the near future pretty bleak.

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6 Responses to When Should You Sign a Free Agent?

  1. reservoirgod says:

    This is very interesting. Have you considered using efficiency differential instead of pt differential? The eff. diff. numbers are available at the knickerblogger stats pg. Eff diff would allow you to use Wins Produced to evaluate free agency w/ your model instead of adj +/-.

    • Alex says:

      The stats page looks like it’s down right now, but I’ll try to take a look in the future. The efficiency question is an interesting one; I think I’ll throw up a quick post about it.

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