| Boyd's World-> Breadcrumbs Back to Omaha-> Theoretical Winning Percentage, Part II | About the author, Boyd Nation |
Publication Date: August 29, 2000
A Closer Look
This week I want to finish up my look at the results from a new rating system I've developed called Theoretical Winning Percentage. The basic idea behind it is to estimate the percentage of games that a team would win if we could magically let them play an infinite number of games against all the other teams. I want to take a look at how the numbers from it differ from those produced by the ISR method in order to get a feel for what has an effect on each method. Obviously, TWP is new, so it's going to take some time to get a feel for how and how well it works, but maybe there's some insight there.
For most teams in most years, the differences aren't significant. As much as we'd like to pretend otherwise when we hand out trophies, there's just not much difference between adjacent teams in a perfect ordering, so we're not likely to find out which ordering is correct in most cases unless the two happen to fall at a breakpoint where there's a gap between a group of similar teams or something. LSU and Stanford were the second and third best teams in the country last year, most likely, and if they had played 100 games it most likely would have gone 51-49 one way or the other. They didn't play 100, they played 1, and LSU won it, and therefore they get the trophy and all the glory and praise you want to associate with it. That doesn't widen the gap between them any more, though, or even prove which team belongs on which side of the gap.
Therefore, looking at teams which differ by only one spot between the two rating systems is kind of pointless. On the other hand, there are a few teams who move significantly between the two, so let's take a look at them.
2000
Once again, here's the top twenty in the TWP rankings for the 2000 season, including the CWS, with their ISR ranking thrown in for comparison:
Rank ISR TWP W L Team 1 1 0.962 56 10 South Carolina 2 3 0.945 52 17 Louisiana State 3 2 0.937 50 16 Stanford 4 5 0.934 53 19 Florida State 5 8 0.924 50 16 Georgia Tech 6 7 0.922 51 18 Clemson 7 6 0.918 44 15 Arizona State 8 4 0.915 44 20 Southern California 9 12 0.901 46 17 North Carolina 10 14 0.899 44 23 Florida 11 9 0.896 42 16 Baylor 12 10 0.895 48 18 Houston 13 13 0.892 48 17 Nebraska 14 18 0.891 41 20 Mississippi State 15 17 0.890 41 20 Auburn 16 11 0.886 45 21 Texas 17 16 0.885 40 24 Alabama 18 15 0.882 47 20 Louisiana-Lafayette 19 26 0.877 39 19 Miami, Florida 20 23 0.875 41 20 Wake Forest
The two teams that make the biggest moves between the two systems, Miami and Southern California, nicely illustrate one plus that the TWP's seem to have over the ISR's. The ISR's implicitly use an average measure of schedule strength -- it's not computed this way, but if you take an average of all of a team's opponents' ISR's, you basically get what the ISR's use a strength-of-schedule measure. I've talked before about how using a flat average can have some problems with measuring unusual schedules, and Miami and Southern Cal fall into opposite ends of that problem. Miami, essentially, plays a lot of really good teams and a lot of really bad teams, which means that their schedule is harder for a fairly good team to put up a great winning percentage against, which means that they may be underrated a bit by the ISR's.
Southern Cal, on the other hand, plays essentially no cream puffs; their schedule is split almost entirely between really good teams and average teams. While this means that it's a tough schedule, it may also mean that the ISR's overrate it by a bit. To make it concrete, while San Diego, for example, is a good bit better than High Point, Southern Cal is not much more likely to lose to San Diego than Miami is to High Point. I'm still not what the implications of this for measuring West Coast baseball on the whole are; that will bear watching and pondering.
I'd also like to take a look at the bottom of the list, since that shows how the ISR's can break down at the fringes:
Rank ISR TWP W L Team 280 270 0.022 14 40 Howard 281 281 0.001 4 31 Coppin State 282 282 0.000 0 39 Maryland-Eastern Shore
I realize that this end of the picture doesn't get much interest, but it's worth looking at because extreme badness is a bit more common than extreme goodness, and the results can be interesting. This is a motley trio indeed. UMES managed the rare feat of going completely winless against Division I teams. Just as impressively, the only four games that Coppin State won were all against UMES. And, for the piece de resistance, of the fourteen games that Howard won, eleven were against either Coppin State or UMES. That .259 winning percentage managed to push Howard all the way up to #270 in the ISR's, but here they come in more accurately.
The problem here is not with the placements, but with the actual numbers. Since all the algorithm has to go on is the thirty-nine games that UMES actually played, the most logical decision for it is to decide that they would never win no matter how many games they played. However, looking at it by hand, we see that that's not actually the case. After all, as bad as this team was, they did win one game against a non-D1 team, and four of their other games were one- or two-run losses. I doubt they could push the losing streak past one hundred if given the chance, much less take it on out to infinity. Likewise, a team that was 60-0 wouldn't be unbeatable. The game just has too much randomness for that to be true.
1999
Starting to look back now, here's the top twenty for 1999:
Rank ISR TWP W L Team 1 1 0.952 57 14 Florida State 2 6 0.947 49 13 Miami, Florida 3 5 0.937 52 16 Alabama 4 2 0.935 50 14 Cal State Fullerton 5 4 0.934 46 15 Baylor 6 3 0.927 50 15 Stanford 7 8 0.921 51 18 Texas A&M 8 7 0.920 57 15 Rice 9 9 0.910 56 14 Wichita State 10 12 0.906 47 16 Wake Forest 11 13 0.899 46 19 Auburn 12 11 0.895 38 16 Texas Tech 13 25 0.891 54 9 Florida Atlantic 14 23 0.886 48 14 Ohio State 15 20 0.884 42 21 Mississippi State 16 14 0.884 40 22 Arkansas 17 22 0.883 44 21 Oklahoma State 18 15 0.883 48 17 Tulane 19 18 0.878 41 24 Louisiana State 20 17 0.877 40 24 Houston
Again, Miami moves up a significant bit. I don't have an explanation for some of the other changes, such as Florida Atlantic or Ohio State, that will take some more observation and thought.
1998
Finally, here's the 1998 list:
Rank ISR TWP W L Team 1 1 0.939 47 16 Southern California 2 4 0.936 47 12 Miami, Florida 3 2 0.928 40 14 Stanford 4 5 0.926 52 18 Florida State 5 9 0.921 46 18 Florida 6 3 0.921 45 19 Louisiana State 7 11 0.918 47 7 Wichita State 8 7 0.917 44 18 Alabama 9 13 0.904 46 18 Auburn 10 6 0.900 41 22 Arizona State 11 14 0.896 41 23 Mississippi State 12 8 0.890 45 17 Cal State Fullerton 13 16 0.888 32 21 Arkansas 14 20 0.884 43 16 Clemson 15 25 0.883 43 18 South Carolina 16 10 0.878 45 17 Rice 17 12 0.876 37 16 Washington 18 17 0.869 42 20 Texas A&M 19 24 0.869 48 15 Tulane 20 15 0.863 42 23 Long Beach State
Smaller differences here, with some added confirmation that 1998 was one of those rare times when the best team in the country wins the CWS. Some nostalgia here, as one wonders how Washington and Arkansas could go from here to the seasons they had in 2000, and a reminder that Tulane has been fairly good for so long that it wouldn't be surprising if they finally had a season when they were really good.
What Next?
Having created this, what should I do with it? Well, as with all things, I won't move quickly; after all, the world doesn't hinge on whether the ISR's or TWP's are more accurate, and there's a certain inertia preventing a switch from one to the other and a certain laziness (as well as a prevention-of-confusion factor) keeping me from maintaining two systems over the course of the season. Unless there's a groundswell of support for one system or the other, I will most likely just run the TWP's for my own amusement and edification over the course of the 2001 season while running the ISR's the same as last year, possibly using the TWP's in season to point out certain teams that may be better than they appear, and then make a long-term decision after that.
As with most things I do, this is a work in progress, so I'd love to hear any ideas for tweaking that might be offered.
| Boyd's World-> Breadcrumbs Back to Omaha-> Theoretical Winning Percentage, Part II | About the author, Boyd Nation |