Saturday, March 7, 2009

Do You Need Your Star to Have a Great Year?: Standard Deviations of Batting Runs

As spring training rolls around, you often hear people say that they need their star player to "have a big year." Player performance fluctuates quite a bit and a lot of this is due to chance - so what people probably mean by this is that they need their star to have a lucky year in which they perform even better than their usual ability. The question is whether a star having a "great year" will improve your team better than, say, your average starting shortstop having a "great year".

This post explores whether this is true. To look at this we need to find a metric for how a player's batting performance translates in runs for his team. There are plenty of these out there and Pete Palmer's classic Linear Weights Batting Runs will do nicely. For those not in the know, the formula gives a weighted value to each major batting event (singles, doubles, triples, homers, walks, and outs) and adds up the player's run producing value to the team compared to league average.

Now we'd like to find the standard deviation of the Linear Weights statistic for an average player over the course of a regular 600 plate appearance season. The average player in the 2008 NL had the following line: .260 BAV, 29 2B's, 3 3B's, 16 HR's, 54 BB's. His run producing value compared to league average is, by definition, 0. But how much does this fluctuate? Calculating the simple standard deviation of the Batting Runs statistic, the standard deviation over 600 AB's is 10.75 runs. This means that the average player will produce between 10.75 runs below average to 10.75 runs above average 68% of the time. 95% of the time the player will be between worth -21.5 runs to +21.5 runs compared to league average.

That is for an average player, but what about for a great player? What is his standard deviation of Batting Runs? Take the following Albert Pujols style player: .311 BAV, 36 2B's, 3 3B's, 48 HR's, 90 BB's. His standard deviation is indeed higher at 13.5 runs. So indeed, it appears that the adage is true - your star player's Batting Runs do fluctuate more often and so there IS more of a need for him to "have a big year".

But wait - what about another type of star player? Take this Ichiro type guy: .375 BAV, 30 2B's, 4 3B's, 6 HR's. His standard deviation is only 10.25 - even less than the average player. This player is indeed a great hitter, but one without power.

Perhaps power is the key. Take the following masher who hits homers, but not much else: .236 BAV, 30 2B's, 3 3B's, 48 HR's, 54 BB's. His Batting Runs standard deviation is also high at 13.25.

We see from the examples, that in fact, it's not merely the star hitters that need to have a "big year", but actually power hitters. From the standard deviation we see that power hitters value are somewhat more affected by luck than other hitters.

The effect is not huge - a no-power hitter performing 2 standard deviations above his ability will produce 20 runs above his usual ability, while a power hitter performing 2 SD's above his ability will produce 27 runs above his usual ability. Not a huge difference, but enough to perhaps make up 1 crucial game in the standings.

So indeed, the old bar room adage mostly is right - it usually is more important for a star hitter to have a big year - but it's the power hitters that really need the luck