The 2014 Schedule

January 27, 2014

I begin every season's analysis with a look at the games graph: every team is a vertex and every game is an edge. This season there are 8108[1] regular season games between 302 division 1 teams. The schedule can be characterized by the average number of teams each vertex is connected to by a given number of edges, and the average number of edges that connect them.

For 2014 the average D1 baseball team will face 22 opponents (Southern only 11, UConn 34!) Continuing a trend, the field is slightly more connected than the 2013 field despite having four more teams. (The grapph is connected when there is an A plays B plays ... plays Z path between every pair of teams.) By the end of the regular season only 187 of the 45451 team-pairs require four edges to be connected compared to 274 of 44253 in 2013, and the average path length will be 2.34 compared to 2.36.

Games Through Pairs %Conn %O+OO APL Diam %P_1 %P_2 %P_3 %P_4 %P_5 %P_6 %P_7 %P_8 %P_9+
531 20-Feb 288 9.1 1.2 ∞ 24 0.6 0.6 0.7 0.7 0.7 0.7 0.8 0.8 3.5
1100 27-Feb 618 92.2 5.4 ∞ 11 1.4 4.0 10.5 21.0 27.7 19.4 6.8 1.2 0.2
1721 6-Mar 951 99.3 11.9 ∞ 8 2.1 9.8 31.2 41.0 14.0 1.3 0.0 0.0
2351 13-Mar 1262 100 19.1 3.13 6 2.8 16.3 48.4 30.7 1.8 0.0
2986 20-Mar 1560   26.9 2.85 5 3.4 23.5 58.2 14.9 0.1
3605 27-Mar 1828   33.6 2.70 5 4.0 29.6 58.7 7.7 0.0
4236 3-Apr 2095   39.6 2.60 4 4.6 35.0 56.2 4.2
4870 10-Apr 2338   44.7 2.53   5.1 39.5 52.8 2.5
5553 17-Apr 2608   49.1 2.47   5.7 43.4 49.3 1.5
6102 24-Apr 2750   51.4 2.44   6.1 45.3 47.4 1.2
6688 1-May 2918   53.7 2.41   6.4 47.3 45.3 1.0
7199 8-May 3075   55.9 2.38   6.8 49.1 43.4 0.7
7782 15-May 3308   58.6 2.35   7.3 51.3 40.9 0.5
8083 22-May 3341   58.9 2.34   7.4 51.5 40.7 0.4
8108 Reg Seasn 3346   58.9 2.34   7.4 51.6 40.7 0.4
It only takes four weeks for the field to become connected, and it is nearly so after only three. By the first week of April the graph diameter is at it's minimum value, by tax day the average path length is less than 2.5 and by April 24 more than half of all team-pairs will have either played or will have common opponents.

The links from the dates are graphical illustrations of the number of connections between teams that are four edges long. The teams are in the same order as the standings page. The color of the cell at row i, column j is based upon the number of connections between team i and team j. The interconference game count matrix provides a key, and shows how the connections at path length one between conferences.
The connectivity by team numbers continue to improve. A decade ago a quarter of the teams had less than 37 percent of the field as an opponent or opponent's opponent, in 2014 there are only 10, and nearly 80 percent of the teams have more than half the field in that category. (Interestingly, all four of the new teams do.)

PL≤: #Pairs #Paths Paths/Pair Min Max
1 3346 8108 2.42   9
2 26787 421288 15.73   178
3 45264 23637875 522.22   6877
4 45451 1280530874 28173.88 1175 218497
Rating systems don't just consider the length of the connecting paths, though. Advanced systems take into account the number of paths.[2] There are over a billion unique paths four games long with different teams at the ends.

The weakest connection at path length four is that between Maryland-Eastern Shore and Portland with "only" 1175 paths. The strongest with over 218000 paths is that between Illinois-Chicago and Wisconsin-Milwaukee.

A breakdown by number of paths at each distance by team offers a number of possible metrics that characterize how teams are embedded in the graph. For example, the difference between the mean and minimum values is used to order the histograms of the path count distribution for each team.
Some miscellaneous schedule trivia:

 [1]D1baseball.com as of 24 January. The actual schedules will be slightly different, but these measurements will not change significantly.
 [2]Advanced systems process the directed games graph (A beat B beat ... chains - one-way paths) which will have a much larger "diameter" and consequently many orders of magnitudes more paths.

In memory of
SEBaseball.com

Paul Kislanko