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Power and OBP

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Jeff's note: there is a Hannahan post below that went up 14 minutes before this one. We suck at this.

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A common refrain so far this winter is that the Mariners need to add a power hitter to replace the departing Adrian Beltre and Russell Branyan. The argument goes that we might have a fantastic top of the order in Ichiro-Figgins-Bradley, but there's going to be nobody driving in all of these baserunners. This line of thought is flawed in many ways, some of which have been previously discussed on the site, but I wanted to share the results of a little thought experiment with you all.

Consider the relationship between runs scored in an inning, on base percentage, and slugging. First let's just look at OBP. Assuming an even distribution (this doesn't happen, of course), for a given on base percentage, we get a certain number of baserunners per inning. An OBP of .500? Three baserunners. .900? 27 baserunners. .000? Zero baserunners. I could keep doing this, but I'm sure you get my drift. Now let's look at the runs that would score for each situation. X amount of baserunners means that there is a minimum amount of runs and a maximum amount of possible runs scored in an inning. Obviously, you can strand three players at a time, and the most efficient way to end an inning is to clear the bases with a home run and then make the final out.

Therefore what governs the relationship between baserunners per inning and runs scored per inning is power. It should be fairly clear to everyone that a team that OBPs .900 is going to score a lot of runs whether they walk 90% of the time or hit home runs 90% of the time, but a team that OBPs .100? The only way that team ever scores is with a home run. Power, in other words, maximises one's efficiency in run scoring. On-base percentage increases the number of runs you can possibly score. It therefore follows that the higher the OBP, the less vital it is to squeeze every last run out of the guys you do get on base, since you have an better chance of scoring runs by stringing together a rally.

The conclusion that falls out of the above is that power is probably less important as you start giving up fewer outs. The 2010 Mariners need home runs far less than the 2009 club did.