March 9, 2011

Reliever Strategy

One of the things that galls me when watching a game is to see a reliever who is pitching well lifted so another reliever can fulfill a role. Most teams would like to get to the point where they get six innings out of a back of a rotation starter, then bring in a pitcher for the seventh, another for the eighth, and one for the ninth. The problem, as I see it, is that the more pitchers you bring into a game, the more likely one is to have a bad day. In other words, faced with the three inning situation, I’d rather see a team use a setup man for two innings to get to the closer, two pitchers instead of three.

While that sounds right, I thought I would check the odds. This is a very simple study, looking at length of time on the mound and runs runs allowed. I divided reliever outings since 1993 into short and long categories, short being on the mound for one inning (three outs) or less, long anything greater than an inning. I then categorized the outing as good or bad, good when the pitcher allowed one run or less, bad when the pitcher allowed two runs or more. Here are the probabilities in a table:

Reliever Probabilities
Reliever Outing Short Long
Good 0.87 0.81
Bad 0.13 0.19

Doing the calculations yields that in the three pitcher model, there is a 34% chance that at least one reliever suffers a bad outing. In the two pitcher model, that drops to 30%. The difference isn’t as big as I would have thought.

There is another difference that needs to be taken into consideration, however. When a team suffers at least one bad outing from a reliever, the team’s expected winning percentage is .253. When no reliever gives up two or more runs (and at least one reliever pitched), a team’s winning percentage more than doubles to .597. Let’s say that the bullpen matters in about 1/2 of a team’s games. The expected number of wins in the three reliever scenario would be 38.8. In the two reliever scenario, 40.1 In other words, the two pitcher strategy adds just one win.

Now, sometimes one win is a very big deal. Plenty of teams were forced into a one-game playoff due to the lack of a win. In the grand scheme of things, so many random actions of a team during a season can randomly cause a team to win or lose a game, the bullpen philosophy just doesn’t matter that much. I’ll continue to be irked when a pitcher throwing well is removed from the game, but now at least I know it doesn’t matter that much.

7 thoughts on “Reliever Strategy

  1. Jim Kelly

    This is pretty good stuff. I was wondering whether you intended to pursue this by doing a more in depth study of only games that were close at the time of the first reliever’s appearance.

    Either way, I am going to pass this along to my readers at wagerjournal.com

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  2. David Pinto Post author

    @Jim Kelly: I’m thinking about it. The fact that there wasn’t a big difference in the simple model leads me to believe that it might not be worth pursuing. Another way of looking at this might be to explore the relationship between winning percentage and the number of relief pitchers who entered with a lead.

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  3. Pingback: Should You Bet on Bullpens instead of Starting Pitching? Wager Journal

  4. Will

    I think it might be worthwhile… I bet a lot of those “long” outings are by long relievers with the game already decided. I would think that a lot of those bad outings are going to be from them since they are generally pretty mediocre pitchers. The other issue I can see is that the regular relievers who are likely to go more than 1 inning are probably pretty good, which might skew data

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  5. DrBGiantsfan

    There are quite a few relievers who are simply one inning pitchers. They do great for one inning but if you try to stretch them, they fall apart. No, I don’t have the numbers to prove it, but that’s my observation from watching a whole lot of relievers. You have to balance that against the risk that a new reliever will be having an unexpected off day. When you factor in R-L matchups and the desire of managers to keep as many of their relievers available every day as possible, it’s probably a tossup at best and possibly better to keep their outing short and use multiple relievers.

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  6. David Pinto Post author

    DrBGiantsfan » Good point. I think going two innings would be a matter of training. Also, if you use just two relievers in a game, there are four others available for tomorrow.

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  7. David

    I’d assume the thinking is that by letting a set-up man work a second inning, there’s a considerable posibility he’ll fade in the second inning. (Most of these guys are only one-pitch pitchers. Even losing 1 mph off your fastball at the 20 pitch count could prove harmful.) So you’ll need that second set-up man anyways. Most pitchers would rather come in at the start of the inning than with runners on base.

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