Baseball Toaster Cub Town
2005-06-16 07:12
by Derek Smart

In part one of what will be a concerted effort today to pretend that this didn't happen, I thought I'd take a very quick look at something I mentioned in yesterday's recap: average margin of victory.

Just to quickly sum up, I found that during Monday and Tuesday's games that the winning team scored an average of 7.22 runs, while the losing squad put up 1.74 runs, for an average winning margin of 5.48 runs. That seemed pretty darn huge to me, and it got me wondering about what the average margins had been over the last few years. Thankfully, Retrosheet exists, and with a little manipulation of their yearly game log files, the answers came fairly easily.

YearAvg Winning ScoreAvg Losing ScoreAvg Margin

While I expected the average margins to be lower than what we saw in those twenty-three games I looked at, the difference isn't nearly as large as I thought it would be. My surprise comes mostly with the average winning score and how that impacts the victory margin - a whopping (to me, at least) 3.57 over the last five seasons.

I thought we'd be looking at an average margin somewhere in the mid-twos, but obviously, it's much higher. If I get some time I might take a look at how this era compares to seasons long past (unless someone's done it already, in which case, feel free to mention where to find it - I'm looking at this for kicks and because the Cubs got creamed yesterday, not for scholarly purposes, and I'd hate to simply be rehashing already completed work), because my guess is that it's historically high.

2005-06-16 08:17:00
1.   kjk
wouldn't it be more accurate to subtract the losing score from the winning score of each game, then average the differences? i'm NOT a math geek at all, but averaging averages doesn't seem that it would give the best results.
2005-06-16 09:18:24
2.   Derek Smart

Not being worthy of the moniker 'Math Person' myself (I merely dabble occasionally for entertainment, and poorly at that), I thought there might be something to what you said, so I a re-ran the margins by creating a dataset of each actual margin of victory (subtracting, as you suggested, w-score from l-score up front), and averaged those numbers.

They were exactly the same. There's a math principal to be explained in here somewhere, but I'll be damned if I know what it is. ;-)

2005-06-16 10:05:18
3.   Doug
I'd be curious to know what the average margin of victory for the Cubs is as opposed to their average margin of defeat. Sort of a study in whether they "win big / lose small" or "lose big / win small". Not sure if it has any significance, just general curiosity I guess.
2005-06-16 10:10:21
4.   Jason R
There is a math principle here:

(A-B) + (C-D) is the same as (A+C)-(B+D)


(4-2) + (3-1) is the same as (4+3)-(2+1)

each time you get 4. I think that's the commutative rule, but I'm not sure.

2005-06-16 10:50:38
5.   phil
Derek, I would think the average would be a little smaller too, but at the risk of being overly obvious, the minimum is not 0, but 1 and the average includes big time blow outs 14-0 17-2, so I guess it does seem reasonable. Wonder how much those blow outs skew things. Any way you could see what the median differntial is?
2005-06-16 10:55:47
6.   onetimer
Given Phil's point about a minimum being 1 and there being no maximum to the differential, this is precisely the case where median tells more than mean.
2005-06-16 10:57:36
7.   onetimer
Except that the median would be an absolute number (probably three). So I guess not.
2005-06-16 11:00:50
8.   Derek Smart

Yeah, it's three all the way, both with individual seasons and with the whole group lumped together, which is why I didn't bother mentioning it.

2005-06-16 14:29:57
9.   phil
Derek, onetimer, good points both. Still interesting to know that 3 is the median, not sure I'd have guessed that.
2005-06-16 15:31:05
10.   kjk
Wow! Sorry to make you go through all that trouble, Derek!
2005-06-16 16:29:50
11.   Derek Smart
No worries, kjk, I think I made it sound more laborious than it was. Figuring out that the two methods got the same result took, literally, three minutes of doinking around in Access, so it was really no sweat.

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