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June 20, 2001

Aim For The Head

Response Rates

by Keith Woolner

This week's question comes from. uh. well, BP's Joe Sheehan, who wrote in last Monday's Daily Prospectus:

There's also something that reader Jim Cox mentioned to me that I have to say is very impressive to observe, if an unknown (or even a tautology) from an analytical standpoint. The Mariners score in a ridiculous percentage of their innings, and Cox points out that they seem to score in a ton of the innings that succeed an opponent's score.

During their 15-game winning streak, they scored in 41.7% of their at-bats (53 of 127); they scored 39.3% of the time when batting after the opposition scored. That sounds like a lot--two times in five, they answered runs with runs of their own--but I don't have comparative data, and am half-hoping Keith Woolner takes the bait for Tuesday's "Aim for the Head" column.

All right, Joe, just this once. This column is supposed to be for reader questions, you know. Next time at least have the decency to send me a question from a fake Hotmail or Yahoo mail account, OK?

There are really two different points in Joe's question: one about how frequently a team scores in any inning, and one about how often a team responds to allowing the opposition to score by scoring themselves in their next at bat (which we'll refer to as "answering" the opposition).

First, let's point out the obvious: teams that score lots of runs will score in a higher percentage of their innings. Similarly, by simple chance, a team that scores in a high percentage of innings would be expected to score in a comparably high percentage of innings that follow allowing runs.

In fact, assuming no dependency or influence between the two teams' chances of scoring, the likelihood of a team answering the opposition is exactly equal to the chance of scoring in any old randomly selected inning. In this way, the Mariners were underperforming a bit when in came to producing answering runs. They scored less often following giving up a run than they did across all innings. Though, as we'll see, both figures are well above any full-season performance of recent years.

How would we want to go about investigating which teams answer the opposition more than expected? We could just count the number of times a team answers the opposition. However, that has one large problem--teams that give up lots of runs will have more opportunities to answer than teams that surrender few runs. What we'll want to look at, then, is how often a team answers the opposition's scoring as a fraction of the number of innings in which they allow runs to score.

Let's illustrate this using a couple of examples:

In 1999, the Phillies scored in 28.9% of their innings. When the opposition scored in the previous half-inning, the Phillies scored 26.4% of the time, a rate 2.3% worse than their overall scoring. They were worse at answering the opposition than you'd expect.

The 2000 Yankees scored in 31.2% of their innings, but answered in 36.5% of their opportunities. They were more likely to answer the opposition by 5.3% over their overall chance of scoring in an inning.

I have data to determine scoring and answering rates for the seasons 1978 through 2000, so we can get a feel for how the 2001 Mariners fit. First, let's look at the teams who scored in the largest fraction of overall innings:


Score%: percentage of innings in which the team scored at least one run

Answer%: percentage of times the team scored when batting immediately after allowing at least one run.

Teams with Score% of 33% or more are listed.

Year Team Score% Answer%

1994 CLE 37.8% 36.1% 2000 CHA 37.0% 34.7% 1996 CLE 33.6% 34.3% 1998 NYA 35.5% 34.2% 1999 CLE 32.9% 33.9% 1997 SEA 33.9% 33.8% 1994 CHA 36.6% 33.7% 2000 SFN 34.4% 33.7% 2000 COL 34.0% 33.5% 1996 SEA 31.6% 33.5% 1996 COL 34.0% 33.5% 2000 HOU 32.2% 33.4% 2000 CLE 35.3% 33.4% 1995 CLE 34.9% 33.3% 1996 TEX 31.4% 33.3% 1997 CLE 32.9% 33.2% 1999 TEX 31.2% 33.1% 1996 BOS 34.5% 33.1% 1997 COL 33.8% 33.0% 1995 CAL 34.3% 33.0% 1995 COL 36.9% 33.0%

It's not surprising that the offensive explosion of the 1990s has produced all the teams who have scored in at least a third of their innings. The top representative for pre-1993 is the 1987 Tigers, who ranked #28 overall with a 32.5% scoring percentage. You have to go down to the 1982 Brewers in 41st place to find any other season represented.

By comparison, the worst teams on the list are the 1981 Blue Jays (20.2%), the 1981 Cubs (21.2%), and the 1985 Giants (22.0%).

Now let's look at the list of teams with an Answer% of 33% or better, remembering that we'd expect a comparable number of teams (and probably a lot of overlap with the teams above) by simple chance:


Year  Team   Score%   Answer%

1994 CLE 37.8% 36.1% 1999 HOU 37.3% 31.1% 2000 CHA 37.0% 34.7% 1995 COL 36.9% 33.0% 1994 CHA 36.6% 33.7% 2000 NYA 36.5% 31.2% 1993 PHI 35.9% 31.9% 1998 NYA 35.5% 34.2% 1994 DET 35.3% 32.1% 2000 CLE 35.3% 33.4% 1998 COL 35.0% 30.7% 1998 TEX 34.9% 31.1% 1995 CLE 34.9% 33.3% 1991 PIT 34.8% 29.2% 2000 TEX 34.8% 31.9% 1999 NYN 34.6% 32.4% 1996 BOS 34.5% 33.1% 1993 TOR 34.5% 32.6% 2000 SFN 34.4% 33.7% 1999 SEA 34.3% 31.0% 1995 CAL 34.3% 33.0% 2000 ANA 34.2% 32.2% 1999 TOR 34.1% 32.3% 1997 ANA 34.1% 31.5% 1999 SFN 34.1% 31.7% 1994 HOU 34.1% 32.1% 2000 COL 34.0% 33.5% 1996 COL 34.0% 33.5% 1978 BOS 34.0% 30.2% 1997 SEA 33.9% 33.8% 1997 COL 33.8% 33.0% 1991 DET 33.8% 29.7% 1994 BAL 33.7% 32.3% 1979 BAL 33.6% 29.6% 1996 CLE 33.6% 34.3% 2000 ATL 33.4% 32.7% 1995 BOS 33.3% 32.9% 1996 SDN 33.3% 28.1% 1991 TOR 33.2% 28.3% 1999 ARI 33.1% 31.9% 1998 TOR 33.1% 32.2% 1998 CHN 33.1% 30.4% 1999 TBA 33.0% 30.2% 1999 BAL 33.0% 31.8% 1979 CAL 33.0% 30.5% 1988 NYN 33.0% 28.5% 1994 KCA 33.0% 29.8%

Whoa! The 47 teams that answered back a third of time is more than double the size of the previous list. Six teams had higher Answer% than the best Score%, and 15 teams were better than the second best Score%. Why would this be?

Remember what I said earlier: assuming no dependency or influence between the two teams' chances of scoring, the likelihood of a team answering the opposition is exactly equal to the chance of scoring in any old randomly selected inning.

Is this really a reasonable assumption to make? I would suggest it's not because both teams are affected by the park environment, and if the game is played in a hitters' park, both teams are more likely to score. Thus, there are more expected opportunities to answer the opposition (since the opposition is scoring more often), as well as a better chance of answering (since you are also scoring more often). The chances of the two teams scoring are both being influenced by a common factor, and thus can't be said to be completely independent from each other.

Which is not to say that a team's basic scoring rate doesn't have primary influence over a team's answering rate. In fact, the two measures correlate with each other very well (R^2 of 0.79), and the graph below demonstrates the strength of the relationship far better than I could in words:

Getting back to the original question for a moment, the lists above clearly show that the Mariners' Score% of 41.7% and Answer% of 39.3% far exceed what any other team has been able to do for a whole season. Of course, teams also don't generally play .800 ball for two months, so we'd expect the Mariners to be remarkable in a lot of ways during such a stretch. But is it a good thing for teams to answer the opposition a large percentage of the time? Yes, if only because it means the team is scoring often in all situations.

So, what teams have "stepped up" the most to respond to the challenge of the opposition scoring? Here, I'll look at teams with the highest differential between their Answer% and their Score%. These are the teams who were the biggest surprises, relative to how often they put runs on the board:


Year  Team   Answer%   Score%   Diff

1999 HOU 37.3% 31.1% 6.2% 1991 PIT 34.8% 29.2% 5.6% 1980 CHN 29.7% 24.3% 5.4% 2000 NYA 36.5% 31.2% 5.3% 1996 SDN 33.3% 28.1% 5.2% 1991 TOR 33.2% 28.3% 4.9% 1978 SDN 29.7% 24.8% 4.9% 1988 NYN 33.0% 28.5% 4.5% 1992 NYA 30.7% 26.2% 4.5% 1993 SDN 30.7% 26.4% 4.3% 1998 COL 35.0% 30.7% 4.3% 1992 MIL 32.3% 28.0% 4.3% 1978 BAL 31.3% 27.0% 4.3% 1994 LAN 31.7% 27.5% 4.2% 1984 LAN 27.6% 23.4% 4.2% 1991 DET 33.8% 29.7% 4.1% 1979 BAL 33.6% 29.6% 4.1% 1988 BAL 26.9% 22.8% 4.1% 1993 PHI 35.9% 31.9% 4.0% 1984 CHA 30.5% 26.6% 4.0%

At first glance, it looks like good teams are able to answer the opposition proportionally more. The '99 Astros and the '91 Pirates both won their division, and the 2000 Yankees were World Champions. But it's not quite that easy. The #3 team on the list is the 1980 Cubs, who lost 98 games and finished last in their division. Buck Showalter's '92 Yankees were 10 games below .500. The fire-sale '93 Padres lost 101 games, yet answered the opposition better than their run scoring would predict.

Nor is there a clear pattern for park effects, though I'm just eyeballing the data here. The '99 Astros--the last year of the Astrodome--tops the list, but Coors Field ('98 Rockies) and Wrigley Field ('80 Cubs) are also represented.

Lastly we might ask whether the tendency for answering runs more often than the overall scoring rate would predict is persistent from year to year. It turns out that it probably isn't. There is a very small correlation between DIFF in one year to the next (R^2 of 0.03), and plotting one year versus the next doesn't show anything like the trend we saw earlier.

Of course, in all of the analysis we've done so far, there's been no consideration for whether being able to answer runs (beyond a team's ordinary scoring rate) has any value. Do winning teams tend to have Actual% > Score%? While I don't have time to address that this week, if there's sufficient interest, it may appear in a future column.

Thanks for writing, Joe. Now get back to work on tomorrow's Daily Prospectus!

Keith Woolner is an author of Baseball Prospectus.

Keith Woolner is an author of Baseball Prospectus. 
Click here to see Keith's other articles. You can contact Keith by clicking here

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