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Saturday, July 29, 2006

Valuing Outs

Scoring my first of four consecutive games tonight at Coors Field as the Rockies take on the Padres. For the Rockies this is an extremely important series and they've responded by winning the first two games; on Thursday night with a 6 run comeback to win 9-8 and last night winning 3-1 on some fine pitching by Byung-Hyun Kim. Coming into tonight they were just 4.5 games in back of the Padres.

Tonight they lost 4-2. A costly error by Garrett Atkins led to 2 runs for the Padres in the top of the 5th that ended up being the difference.

But what interested me thus far was the situation that occurred in the bottom of the third inning. After Jeff Francis grounded out to third, Jamey Carroll slapped a single to right. With Clint Barmes up he stole second base despite a nice throw by Mike Piazza. So at this point Carroll is on second with one out. Early in the at bat Barmes actually acted as if he were going to bunt but continued to foul off pitches to work the count to 2 and 2. At this point he hits a lazy fly ball that Mike Cameron in center drifts under. Carroll tags at second and makes it easily to third. What surprised me was the reaction of the crowd of more than 43,000 to this sequence of events. They erupted in applause almost as if Barmes had driven in the run.

There are two possible explanations for this. The first is that perhaps the expectations for a Barmes at bat are so low that any perceived positive outcome is treated as a victory. I myself am of that persuasion. However, I'm inclined to think that the real reason is a fundamental misunderstanding regarding probability and the importance of outs. With one out and a man on second the run expectancy over the last six years, as shown in the following table, has been .704 runs.

Base/Out 0 1 2
xxx 0.530 0.287 0.112
1xx 0.921 0.552 0.242
x2x 1.160 0.704 0.335
xx3 1.441 0.978 0.371
12x 1.523 0.935 0.445
1x3 1.844 1.214 0.510
x23 2.030 1.430 0.599
123 2.364 1.579 0.789

In other words, all other things being equal a team will score on average about seven tenths of a run in the remainder of the inning when you reach this base/out state. After Barmes flied out to center the run expectancy dropped almost in half to .371. In other words, the Rockies situation had deteriorated markedly and yet the crowd reacted as if something good had happened. Of course what they were reacting to was the fact a runner had advanced 90 feet and was therefore physically closer to home plate.

That perspective is flawed however since in reality Carroll (and subsequent hitters) were more likely to score while he was standing on second a few moments prior. The reason is that the number of outs, the quantity of which is in limited supply and therefore what actually controls the game, is all important in baseball. Fundamentally, sacrificing a base (other than home) for an out always decreases run potential. There are situations where doing so increases the probability of scoring a single run but those are few and far between and generally occur only with the weakest of hitters (pitchers) at the plate. In any case, this early in the game it is always a better bet to try and maximize run potential rather than playing for the single run, a lesson that Rockies manager Clint Hurdle should take to heart.

So this is a case where our eyes deceive us. Carroll standing on third with two outs is not better than him standing on second with one out. The structure of the game makes this the case.

Of course the fans also engaged in a spirited round of "the wave" in the 8th inning during a crucial situation with Padre runners on board.


Anonymous said...

hi dan -- i think you might be being a bit too hard on rockie fan. have we become so statistically-minded that we overlook something so basic? i mean, runner on 3rd and 2 out is better than runner on 2nd and 2 outs, no? we don't need to look at the run expanctancy table to come to this conclusion. seems as though, based on your thinking, anything short of a hit or walk from barmes could be crticized (i mean, the guy either gets on base or makes an out and we know getting on base is preferred). barmes flied out, moving the runner to third, and crowd cheered an out that at least wasn't a wasted out. i'm with you and think that barmes is a pretty terrible player and we expect him to make an out, so maybe we celebrate even the small victories for him. but in baseball, when failure (making an out)is expected 60 to 70% of the time, at least moving the runner over helps your team increase its chances of scoring with 2 outs.

Dan Agonistes said...

Ok, perhaps I am being a bit too hard but what surprised me was not that the fans cheered - after all as you say the game is built on failure, but the enthusiasm with which they did it.

It struck me as out of place for so meager a "contribution" and my mind immediately raced to Joe Morgan's often repeated comment about how many more ways there are to score from 3rd than from 2nd. True of course but the relative frequency of those additional ways makes them inconsequential in most cases.

And as I wrote I did consider the option that fans were simply surprised that Barmes actually didn't popup weakly to shortstop on one of the innumerble pitches on which he is so easily jammed. He's also a bit of a fan favorite. That said though, the reaction just seemed a little over the top for me and perhaps pointed to something else.

BTW, I'm not saying anything short of a hit or walk should be criticized but as a fan I'm not cheering when a play happens on the field that leaves my team in a worse situation than the one they just had.

obsessivegiantscompulsive said...

Perhaps the crowd was being sarcastic? I've seen that before, the batter has not been hitting that well, so when they do something as simple as advancing the runner, which is much better than striking out or popping up weakly, the crowd cheers loudly.

Since you brought up this topic, I have been wanting to ask someone who understands this run expectancy table this question: obviously, the run expectancy is different between, say, Derrek Lee at the plate, versus, say, Neifi Perez, so why do we use the average run expectancy for each batter equally?

I've read some articles but admit that I have not done a lot of deeper thinking on it because I could not get over the fact that the run expectancy for Barry Bonds would be the same as for [pick any lame Giants hitter of the past 5 years]. Can you explain this to me or is there a good site/book you can recommend? Thanks either way and take care.

Anonymous said...

dan -- thanks for the response, and i hear you loud and clear. i guess where i'm going with this is that, by the nature of baseball, ~70% of the time the batter is going to leave the team in a worse situation than the one they had before the batter came to bat. it's part of the game. this holds true for barmes or helton or holliday or anyone. so i guess it's a matter of much worse did the batter leave his team? most hitters waste outs and get nothing for them. at least the rockies got something out of that out. again, ~70% of the time the batter is going to make an out, so it's worth an applause if the runner is moved up. but not too much applause :)

Dan Agonistes said...

On run expectancy, you're absolutely correct. Each hitter would have his own RE matrix and you could make it as granular as you wanted by including pitcher, park, weather, score, etc. etc. The RE matrix I presented is the overall matrix for all hitters and all teams over the past six seasons. The one for Barry Bonds would of course have larger values than the one for Neifi.

They're simply used as a tool for evaluating strategy in the large. Your mileage may vary.

Tangotiger said...

You of course wouldn't take the average RE table, if Bonds is the batter, or on deck. Whoever does it does not understand RE or baseball.

However, it's much easier to present one RE table, than to present 750 RE tables, one for each MLB player. (In fact, you'd have to present 750 x 9, depending on where he happens to be batting that inning.)

Here's a set of RE charts based on the *average* batter in a batting slot.