Expected Win Totals

Well, as you can see, my BayStars have been beaten up by pretty much everybody. They're the only team below .500. And they just won their first one run game this season last week against the Giants, while being blown out quite a bit.

Removing Yokohama from the standings, this is how it would be:

         Games  W  L T   W%  RS  RA
Hanshin    33  19 13 1 .594 174 141
Hiroshima  29  15 14 0 .517 120 147
Chunichi   35  17 18 0 .486 150  90
Yakult     33  15 18 0 .455 190 150
Kyojin     32  14 17 1 .452 163 169

Scores are something I have in my database, so I subtracted the scores against Yokohama for each team as well. But it looks like my hypothisis that Yokohama is the cause of Chunichi's and Hiroshima's annomolies doesn't hold water.

So, let's look at the breakdown of scores for Chunichi, which is the farthest out of wack:

Chunichi as home team:
+------+-------+------+--------+------+------+------+------+
| Vs.  | Games | Wins | Losses | Ties | W%   | RS   | RA   |
+------+-------+------+--------+------+------+------+------+
| HC   |     5 |    1 |      4 |    0 | 0.20 |   14 |   28 |
| HT   |     6 |    4 |      2 |    0 | 0.67 |   36 |   28 |
| YBS  |     6 |    3 |      3 |    0 | 0.50 |   31 |   31 |
| YG   |     3 |    1 |      2 |    0 | 0.33 |    9 |   14 |
| YS   |     6 |    4 |      2 |    0 | 0.67 |   35 |   29 |
+------+-------+------+--------+------+------+------+------+

Chunichi as away team:
+------+-------+------+--------+------+------+------+------+
| Vs.  | Games | Wins | Losses | Ties | W%   | RS   | RA   |
+------+-------+------+--------+------+------+------+------+
| HC   |     3 |    0 |      3 |    0 | 0.00 |    6 |   10 |
| HT   |     3 |    2 |      1 |    0 | 0.67 |    9 |    9 |
| YBS  |     2 |    2 |      0 |    0 | 1.00 |   10 |    6 |
| YG   |     6 |    4 |      2 |    0 | 0.67 |   32 |   43 |
| YS   |     3 |    1 |      2 |    0 | 0.33 |    9 |   29 |
+------+-------+------+--------+------+------+------+------+

Chunichi is 5 and 4 against Yakult while being outscored 44 to 58. Similarly, they've got a winning record of 5 and 4 against the Giants while being outscored 41 to 57. Looking at Chunichi's game results, I see that they lost 0-11 to the Giants on March 29, then won a one run game the next day. That'll cause such a discrepency.

Glancing through Hiroshima's scores, I see an 8-1 loss to Yakult on April 19, a 9-1 loss to them again on May 9, and a 12-2 loss to the Tigers on May 13. Those three losses account for most of the difference, I think.

This kind of playing with numbers is fun. But it's well past my bed time. Hope to see more ideas in the morning.

Good night.

- Glancing through Hiroshima's scores, I see an 8-1 loss to Yakult on April 19, a 9-1 loss to them again on May 9

This helps explain Yakult's discrepency as well. I guess they must have a good record in blowouts but fare poorly in close games. Unreliable bullpen?

Also, Chunichi's runs (less Yokohama games) allowed column should be "190", rather than "90". That makes Chunichi and Yakult out of whack, exactly opposite to each other. Interesting that their records are very similiar.

The formula to get expected winning percentage is the so-called Pythagorean Theorem (because it looks somewhat like the geometry equation of the same name), which is:

runs scored squared divided by the sum of runs scored squared plus runs allowed squared

Expressed algebraically:

WT = RS² / (RS² + RA²)

Doing the math quickly and without using a spreadsheet, I get the following expectations for wins and losses, expressed to the tenth of a game:

Hanshin    27.9-14.1
Hiroshima  15.0-21.0
Kyojin     22.0-18.0
Chunichi   17.8-25.2
Yakult     24.9-17.1
Yokohoma   13.9-27.1

Blowouts, especially in a small portion of a season, can throw off the accuracy of this empirical formula. Also, pure chance has a much greater impact with smaller sample sizes such as this.

Jim Albright

Thanks for the insights, Jim. I kind of had you in mind when I posted the questions. I didn't know that formula.

You're right about the small sample size throwing off the results. I think the fact that each team plays all it's games against only five other teams has an effect as well.

Still, it's interesting. Hanshin, Yokohama, and Kyojin's expected totals are pretty close.

I know or can find almost all of Bill James' formulas, since I own all his books, save one (which reprises the others) which were not self-published. You might guess that I'm rather familiar with James' work if you read my stuff. Jim Allen's work in this regard with Japanese data has also been informative. I'm glad to help use the insights those analyses generate to help look at Japanese ball.

On the specific topic at hand, I would expect over the season that everybody will wind up within say five wins of expectation. In rare cases a few may miss, mostly due to a) luck in one-run games, and 2) blowouts not evening out like they should.

Finally, I know James had a method for predicting World Series winners. I am thinking of visiting that one at the end of the season. However, I suspect that the different style of ball in Japan probably merits a recalculation of the points assigned to various categories. Has anyone happened to play with this formula before or have ideas on how to arrive at the point totals for various aspects (more HR, more shutouts, etc.)?

Jim Albright