I always find it funny when old timers talk about "small ball" and "doing the little things" as an efficient way to win baseball games. I found it even funnier when Ozzie Guillen used to talk about how his hitters needed to stop hitting so many home runs and start doing better situational hitting--as if somehow he was going to find a way to make all of his hitters hit .100 points better when there were runners on base.
The theory behind these concepts is that home runs are relatively rare and singles are much easier to come by and so through a combination of getting a lot of singles and being about to manufacture runs in close games, you will win more games. The subtly ironic thing about this way of thinking is that the exact opposite is true. Hitting a lot of home runs is not only a more efficient way to score runs, it is also more effective in scoring runs in close games.
In order to get a better idea of what is going on in situations like this, I often find it useful to look at extreme cases where the situation is considerably simplified. In this situation, I will present to you 2 very unique teams.
First is The Sharks. The Sharks hitters are all 500 pound men who come to the plate swinging a telephone pole. Unfortunately for them, they all need a respirator after running half way to first base and so anything that's not hit out of the ball park is an automatic out. However, because of the incredible force they're able to impart on the ball, they're successful in hitting many, many homeruns.
The Second team is called The Piranhas. They are a team composed entirely of ninjas who are no taller than 5-6. They have great team speed and never hit into double plays and can always score from second on a single. Unfortunately, due to their diminutive stature, nobody on the team can hit the ball more than 200 feet and so everything they hit is a single. While playing the Sharks, they are unfortunately unable to ever steal a base because the Shark's catcher can throw the ball 200 miles an hour--resulting in an automatic out. Thus, in order for the Piranhas to ever score, they need to get 3 hits in an inning. However, every hit they get in an inning past their second hit in an inning scores a run.
Here's how the teams match up:
| Team | Avg. | Slg. | Runs/9 |
|---|---|---|---|
| Piranhas | .361 | .361 | 4.5 |
| Sharks | .143 | .572 | 4.5 |
As you can see, despite the two teams drastic differences in playing style, both teams average the exact same number of runs per game. Because we know exactly what will happen each time the teams get a hit, it is easy to model exactly how frequently we expect each of the teams to score a given number of runs in an inning. Once we know that, we can figure out exactly how many runs each team will score in a game. Finally, with these two things we can make a table that tells us exactly how many times each team will win.
Note that the following numbers are exact. These are not numbers based on simulation.
You may expect that since the two teams both score 4.5 R/9 that each team would win 50% of the games. This is not the case!!! In fact, the Sharks will win over 54% of the games played between these two teams! This may not seem like a lot, but keep in mind (a) both teams are scoring the same number of runs and (b) over the course of a 162 game season, an extra 4% amounts to over 6 additional wins. How does this happen?
The key in this situation is in the distribution of the runs. Let's look at it
| # Runs | Piranhas | Sharks |
|---|---|---|
| 0 | 7% | 2% |
| 1 | 11% | 6% |
| 2 | 13% | 12% |
| 3 | 13% | 17% |
| 4 | 12% | 18% |
| 5 | 11% | 16% |
| 6 | 9% | 12% |
| 7 | 7% | 8% |
| 8 | 5% | 5% |
| 9 | 4% | 3% |
| 10+ | 7.9% | 2.6% |
Notice that the Piranhas will score 0 or 1 runs in 18% of their games whereas the Sharks will only score 0 or 1 runs in 8% of their games. On the other hand, the Piranhas will score more than 10 runs in almost 8% of their games while the Sharks will do so in only about 2.6% of their games. The Piranhas are much more likely to absolutely bludgeon the Sharks by scoring an obscene number of runs. This is due to the way that the Piranhas score. Because of the way they score runs, they are much more likely to put together one or two huge innings over the course of a game. The result of this is that they typically score a bunch of runs that they won't end up needing. On the other hand, they will also frequently waste hits by getting one or two men on base and not scoring. This leaves the Sharks with an advantage since they will never waste base runners and are less likely to put together innings where they score runs they won't need. In this sense, you might say that the Sharks are better situational hitters because the runs they score will tend to be more meaningful.
I know some people may be critical about this example because it seems like an over simplification, but it is meant to give a clearer understanding of a general principle. Teams that score more runs via the home run (and via extra base hits) will tend to be more consistent than those that rely on stringing singles together. When you apply this to the current Twins situation, you can see why it's not surprising that they scored 11 runs in one game while scoring no more than one in 4 of the last 5.
Part II
Twins run distribution, 2007
This is exactly what's happening. Great post, GH.
Comparing this to the Piranhas:
That's really pretty remarkable. There is obviously a bit of noise, but the picture is enough to make me believe that my math is spot on!
It's not really even that much noise by my eye. Shovel some of the 3 column to the 2 and 4, move some of th 7 to the 6 and 8, and you're pretty darned close.
Moss'd rather have the Pirhanas' distribution, frankly.
Or the Piranhas', whichever.
The only good thing that has come from this whole piranha mess is that I can now remember how to spell piranha.
Or, remember it's a Portugese spelling, and "nh" is the Portugese "ñ"
These 2007 Twins put the "ha" in piranha.
This is how I'll always remember it.
I thought about looking up these numbers, but in the end I was just too lazy.
It's good to know that what's happening is exactly as I would have predicted it. The Twins hitting problems go a bit deeper than just this, but I think this problem is at the heart of it. The Twins marginally winning record this season is obviously a result of their fantastic pitching. Some hitters with even a marginal amount of power at the bottom of the order would greatly improve the Twins consistency and could have very likely contributed to 6 (or perhaps many more) wins so far this season.
If I feel up to it, I may try to run some of those numbers before part 2, or maybe even make it into a part 3.
Let me know what you need and I'll get it for you. I have ways to get it very easily with my BP subscription.
what I really like is the comment about efficiency. The Piranhas strand lots of runners and are dependent on what has been called elsewhere "long-sequence" offense. That's poor efficiency.
The third option is the Dusty Baker school -- ideally you don't want anyone on the bases, because that just clogs the basepaths.
That's also the school where you don't use the bullpen, right?
For those visual learners out there, here is the run frequency data in graphical form:
Excellent work, GreekHouse. That's pretty cool how closely that models the Twins' offense.
Do you have data for the Sharks and Piranhas per inning? That seems important for the purpose of the general "small ball" vs. "smash ball" debate. One of the main advantages to small ball is that it's supposed to be better in close games where you might just need one run. The number of shutouts for the piranhas suggests that they probably get shut out per inning a lot, but...while it seems unlikely to me that the per inning distribution is much different than the per game distribution, I'm curious.
Since we're all doing graphics here.
Same trend per inning. Fewer 0 run innings for the sharks, more 1 and 2 run innings, fewer of everything else.
One more thing: the Piranhas probably cost a lost less money than the Sharks. Back in 2004 at BP, Ben Murphy and Jared Weiss looked at free agent salaries and determined that they were correlated more closely to total bases than to VORP. That's not exactly what we're looking at here, but I'd guess that each hitter on the Sharks and Piranhas would have the same VORP since each lineup produces the same number of runs over the course of the season. Since the Sharks have a much higher SLG, though, they should wind up with more total bases, and will be a lot more expensive.
Maybe Ryan is starting to see the light, and got rid of Castillo because he wasn't worth the cash. He's got Morneau and Cuddyer for relatively cheap to provide power -- no sense paying a non-power guy millions of dollars. (You could even justify letting Cirillo go on these grounds, since he wasn't exactly knocking the ball out with any regularity.)
Now if he can just stay with the theme and find one or two young, cheap power hitters for 3B and DH, the Twins could survive having no power out of SS and 2B. (CF is going to be a problem regardless -- it's either going to be lacking power, or very expensive.)
Are we saying that Tony Batista is better than Nick Punto?
Part 2 will deal with just how useless players like Nick Punto and Jason Tyner actually are. Basically, it's impossible to be a very good major league hitter if you don't have any power at all.
How did you arrive at the BA's for the teams? Did you do it exhaustively until you hit on 4.5 runs/game?
Interestingly, the Guppies have a marginally higher OPS than the Sharks. Although the margin is really razor-thin, one could conclude that it takes a higher OPS to score the same number of runs if you are doing it all by singles. And then the real problem with the Twins' offense comes into view -- their OPS is sub-standard, so there's no way in hell they can score an average number of runs with their complete lack of power in 6/9ths of the order.
An observation about the BA's -- it seems that the Sharks' scoring scales directly with their BA, while the Guppies' scoring would increase non-linearly with an increase in BA. (And conversely, a downtick in BA means a non-linear decrease in number of runs.)
And another problem for the Twins comes into view -- in games when they get few hits (today), they absolutely cannot score. This year, they are 10th in the AL in BA; last year, as Dick points out nightly, they led the league in BA. No surprise that the run scoring is down significantly, and they are back to getting shut out regularly (as in 2004).
An observation about the BA’s — it seems that the Sharks’ scoring scales directly with their BA, while the Guppies’ scoring would increase non-linearly with an increase in BA. (And conversely, a downtick in BA means a non-linear decrease in number of runs.)
Bingo! This is also on the slate for part 2.
And another problem for the Twins comes into view — in games when they get few hits (today), they absolutely cannot score. This year, they are 10th in the AL in BA; last year, as Dick points out nightly, they led the league in BA. No surprise that the run scoring is down significantly, and they are back to getting shut out regularly (as in 2004).
Yep, when you rely on singles to score runs and don't get any, it's essentially a crap shoot. If you manage to clump them all together, you might do ok. Unfortunately, this will normally not be the case and you will not get much of anything.
From today's game story by LENIII:
I mean, hey, they scored 11 last night. Problems over, right? Heh.
I think Ryan's real hope was that he could replicate last year, vis-a-vis installing Casilla and anybody but Punto at 3rd base -essentially the Batista/Castro, Puto/Bartlett flip flop. And that, coaxing anything at all from White would be a pure bonus over what Tyner was giving them. The net result would be to eke out a few more games in the 2nd half with at least 4 runs.
I suspect he was (is) also counting on Mauer to have a monster 2nd half.
Are we going to start calling Nick Punto 'puto' now? It's a very bad word in Spanish, but then again he is a very bad baseball player.
That should read "...they are back to getting shut out regularly (as in 2005)."
How did you arrive at the BA’s for the teams? Did you do it exhaustively until you hit on 4.5 runs/game?
For the sharks it was easy. I just need them to have 4.5 HR for every 27 outs they made. So their average becomes 4.5/(27+4.5) = 1/7.
For the Piranhas, I just had to do trial and error until I got something really close. Eventually I got .361174 to be a close enough mark which scores the piranhas 0.500001 runs/inning.
Interestingly, using the basic formula for RC=OBP × SLG × AB (http://en.wikipedia.org/wiki/Runs_created), this is what comes out:
Sharks 2.57 (4.5 hits, 31.5 AB)
Piranhas 5.50 (15.25 hits, 42.25 AB)
Most likely, that just shows the formula breaks down at the extremes.
Using the 2002 formula helps slightly, 3.44 for Sharks and 5.53 for Piranhas.
My guess is that the RC formula was designed for people with a standard distribution of hits. Obviously there's no way a hitter can get a home run every 7 ABs without occasionally smashing one off the wall for a double or hitting a sharp liner for a single. Likewise, no MLB hitter is going to be able to hit .361 without hitting the ball sharply enough to get a decent number of extra base hits as well.
My guess is that the formula was based on empirical evidence. If you wanted to adjust the formula so that it fit the model more closely, you'd need to come up with a statistic that says "How hard does this player hit the ball on average?". The closest thing we have to that above is SLG.