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The Universe Works on a Math Equation: Extra Bases Taken Percentage Is Not Only Meaningless, It's Misleading

It came up earlier today that extra bases taken percentage is a bad stat because it relies too much on contextual factors at play.  However, even assuming that it can be estimated correctly by correcting for contextual factors or assuming they even out over large enough samples, there are much bigger flaws in the way the statistic is calculated.

The bigger problem with that kind of analysis is that it doesn't account for how much it hurts your team to make an out on the basepaths.  Take, for example, the extra bases taken percentage of two good baserunners: Maury Wills (53%) and Tim Raines (50%).  The stat makes Wills look like the better baserunner, but that is because it is misleading.

I am not surprised to find that, over their careers, Wills -- known to be an aggressive baserunner -- would take the extra base more frequently than Raines.  Wills attempted to steal in 23.0% (794 of 3459) of opportunities (times when the runner occupied first or second base and the next base was open).  Raines attempted to steal in only 21.7% of opportunities (954 of 4397).  Wills comes out looking like an aggressive baserunner but this obviously tells us nothing besides that.  That Wills successfully stole 16.9% of the time he had an opportunity but Raines successfully stole 18.4% of the time he had an opportunity implies that Raines was a slightly better basestealer but drastically underestimates how much better he was.

The issue here is that unsuccessful attempts send you to the dugout (costing your team both a baserunner and an out) but not attempting to steal at all only costs your team the opportunity of stealing.  For this reason, the rate at which a player successfully steals as a function of opportunity (SB/Opportunity) is much less informative than the rate at which he successfully steals as a function of attempt [ SB/ (SB+CS) ].  Raines was, of course, successful at a much higher rate (85% vs. 74%) and that is why his base-stealing was so much more valuable than Wills.  As we said earlier, if one looks only at bases stolen as a function of opportunity, Wills grades out as merely slightly worse when he was in fact much worse.  This method is insufficient, however, because it rewards players for being extremely conservative.  As an example, it would be better to have a player steal successfully 99 times out of 100 than to have a player steal successfully one time, even though the second players SB/Attempt rate would technically be better.  It is also makes it seem as if a SB helps as much as a CS hurts.

To correct for this, we need to adjust the number of unsuccessful attempts to account for the fact that unsuccessful attempts hurt about twice as much as successful attempts help (or whatever you happen to believe the break-even rate to be).  Our modified SB/attempt rate (assuming the breakeven rate at 67%) would look something like  [ SB - 2(CS) ] /  (SB + CS) or (assuming the break-even rate at 75%) [ SB - 3(CS) ] / (SB + CS).  This should make the break-even rate of our modified rate 0.  We could then multiply our modified SB/attempt rate by the rate at which the runner attempts to steal as a function of opportunity [Att / Opp] to give credit to runners for taking advantage of opportunities as often as they can.  This will tell us the number of bases stolen (taking into account a penalty for being caught stealing) per opportunity.  As an example, we will use this modified method to compare Wills and Raines:

modified SB/attempt rate (67% break-even):

Wills: [ 586 - 2(208) ] / [ 586 + 208] = 0.214 SB/attempt
Raines: [ 808 - 2(146) / [ 808 + 146] = 0.541 SB/attempt

modified SB/attempt rate (75% break-even):

Wills: [ 586 - 3(208) / [ 586 + 208 ] = -.047 SB / attempt
Raines: [ 808 - 3(146) ] / [ 808 + 146] = 0.388 SB/ attempt

Now that we have modified the SB/attempt rate to demonstrate how much being caught stealing harms in relation to how much successfully stealing helps (note how much the gap between Raines and Wills widens when compared to a breakeven rate of 0 rather than 67% or 75%).

modified SB/attempt rate multiplied by attempt/opportunity rate (67% break-even rate):
Wills: (0.214)(0.230) = 0.0492 SB / opportunity
Raines: (0.541)(0.217) = 0.1174 SB / opportunity

modified SB/attempt rate multiplied by attempt/opportunity rate (75% break-even rate):
Wills: (-0.047)(0.230) = -0.0108 SB / opportunity
Raines: (0.388)(0.217) = 0.0842 SB / opportunity

While these numbers may seem insignificant, over the course of a season with 300 opportunities, the difference would amount to the value of 20 steals!

Finally, this brings us back to "extra base taken percentage."  Its worst mistake is that it looks only at the number of extra bases a player takes as a function of his opportunity and neglects unsuccessful attempts.  To look back at Wills and Raines, Wills took the extra base 53% of the time and Raines took the extra base 50% of the time, so Wills must be better, right?  Except that Wills took only 249 extra bases and made 105 outs, while Raines took 103 more bases (352) and made just one more out (106).  Like stolen bases, the better way to look at this would be our modified extra bases taken as a function of attempt (70.3% for Wills and 76.9% for Raines) and then adjust that to reward players for making the most of their opportunities.  It becomes much trickier to try to calculate a break-even point for baserunning, but, on average, it should be slightly lower than the breakeven point for stealing (since you do not steal home, but you can take home as an extra base).  For our sake, let's say that you simply need to be successful 50% of the time to make it worth it to try to take the extra base and our formula is (Extra Bases - Outs on Base) / Attempts.

modified EB/attempt rate:
Wills: (249 - 105) / (249 + 105) = 0.41 extra bases taken / attempt
Raines: (352 - 106) / (352 + 106) = 0.54 extra bases taken / attempt

Now, we can look at extra bases taken / attempt as a function of opportunity as we did with stolen bases.  Unfortunately baseball-reference does not give the number of opportunities, but we can calculate this based on the number of extra bases taken and the extra bases taken percentage: Opp = (Total number of bases taken) / (XBT%).  Wills had 470 opportunities and Raines had 704 opportunities.

modified EB/attempt rate multiplied by attempt/opportunity rate:
Wills: (0.410) [ (249 + 105) / (470) ] = 0.31 EB / opportunity
Raines: (0.54) [ (352 + 106) / (704) ] = 0.35 EB / opportunity

Again, Raines grades out as a much better baserunner.  Over the course of a season (about 55 opportunities for Raines), the difference does not amount to much (just two bases), but over the course of a career with as many as Raines had, it would be around 28 extra bases.

Anyway, the point of this exersize was to demonstrate the flaws in XBT%, even assuming that over the course of an entire career, situational and contextual factors would even out.  I hope I didn't bore you too terribly!